Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates

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728       "Quot.sound"
729     ],
730     "in_project_namespace": true,
731     "kind": "theorem",
732     "module": "PaperIRelease.CoordinateTransport",
733     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_11",
734     "runtime_only": false
735   },
736   {
737     "axioms": [
738       "propext",
739       "Classical.choice",
740       "Quot.sound"
741     ],
742     "in_project_namespace": true,
743     "kind": "theorem",
744     "module": "PaperIRelease.TensorPackets",
745     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_2",
746     "runtime_only": false
747   },
748   {
749     "axioms": [
750       "propext",
751       "Classical.choice",
752       "Quot.sound"
753     ],
754     "in_project_namespace": true,
755     "kind": "theorem",
756     "module": "PaperIRelease.CategoryUniversal",
757     "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial_map",
758     "runtime_only": false
759   },
760   {
761     "axioms": [
762       "propext",
763       "Classical.choice",
764       "Quot.sound"
765     ],
766     "in_project_namespace": true,
767     "kind": "theorem",
768     "module": "KomorebiVerification.EllipticAlgorithms",
769     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_eq_orbitHull_of_stop",
770     "runtime_only": false
771   },
772   {
773     "axioms": [
774       "propext",
775       "Classical.choice",
776       "Quot.sound"
777     ],
778     "in_project_namespace": true,
779     "kind": "theorem",
780     "module": "PaperIRelease.AlgebraQuotient",
781     "name": "Komorebi.PaperIRelease.restrict_diagonal_mul",
782     "runtime_only": false
783   },
784   {
785     "axioms": [
786       "propext",
787       "Classical.choice",
788       "Quot.sound"
789     ],
790     "in_project_namespace": true,
791     "kind": "theorem",
792     "module": "KomorebiVerification.PacketNaturalityCompletion",
793     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA._proof_1",
794     "runtime_only": false
795   },
796   {
797     "axioms": [
798       "propext",
799       "Classical.choice",
800       "Quot.sound"
801     ],
802     "in_project_namespace": true,
803     "kind": "definition",
804     "module": "PaperICompletion3.OperatorPrimaryAPI",
805     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.recOn",
806     "runtime_only": false
807   },
808   {
809     "axioms": [
810       "propext",
811       "Quot.sound"
812     ],
813     "in_project_namespace": true,
814     "kind": "theorem",
815     "module": "PaperIRelease.ScalarExtension",
816     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_4",
817     "runtime_only": false
818   },
819   {
820     "axioms": [
821       "propext",
822       "Classical.choice",
823       "Quot.sound"
824     ],
825     "in_project_namespace": true,
826     "kind": "theorem",
827     "module": "KomorebiVerification.EllipticAlgorithms",
828     "name": "Komorebi.EllipticCoordinates.normalFormToQuotient._proof_1",
829     "runtime_only": false
830   },
831   {
832     "axioms": [],
833     "in_project_namespace": true,
834     "kind": "theorem",
835     "module": "PaperIRelease.CategoryExport",
836     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.sizeOf_spec",
837     "runtime_only": false
838   },
839   {
840     "axioms": [
841       "propext",
842       "Classical.choice",
843       "Quot.sound"
844     ],
845     "in_project_namespace": true,
846     "kind": "theorem",
847     "module": "PaperIRelease.GrammarAlgebra",
848     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ext",
849     "runtime_only": false
850   },
851   {
852     "axioms": [
853       "propext",
854       "Classical.choice",
855       "Quot.sound"
856     ],
857     "in_project_namespace": true,
858     "kind": "theorem",
859     "module": "PaperICompletion3.PrimarySeedFormula",
860     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.familyGenerates_linearEquiv_iff",
861     "runtime_only": false
862   },
863   {
864     "axioms": [
865       "propext",
866       "Classical.choice",
867       "Quot.sound"
868     ],
869     "in_project_namespace": true,
870     "kind": "theorem",
871     "module": "KomorebiVerification.TopologicalCompletion",
872     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_hasTopologicalSeedRankOne",
873     "runtime_only": false
874   },
875   {
876     "axioms": [],
877     "in_project_namespace": false,
878     "kind": "theorem",
879     "module": "PaperIRelease.CategoryExport",
880     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_3",
881     "runtime_only": false
882   },
883   {
884     "axioms": [
885       "propext",
886       "Classical.choice",
887       "Quot.sound"
888     ],
889     "in_project_namespace": true,
890     "kind": "theorem",
891     "module": "KomorebiVerification.PacketNaturalityCompletion",
892     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB._proof_2",
893     "runtime_only": false
894   },
895   {
896     "axioms": [
897       "propext",
898       "Quot.sound"
899     ],
900     "in_project_namespace": true,
901     "kind": "theorem",
902     "module": "KomorebiVerification.SeedRankOperations",
903     "name": "Komorebi.SeedRankOperations.productModule._proof_6",
904     "runtime_only": false
905   },
906   {
907     "axioms": [
908       "propext",
909       "Classical.choice",
910       "Quot.sound"
911     ],
912     "in_project_namespace": true,
913     "kind": "definition",
914     "module": "PaperIRelease.CategoryPackets",
915     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.seeds",
916     "runtime_only": false
917   },
918   {
919     "axioms": [
920       "propext",
921       "Classical.choice",
922       "Quot.sound"
923     ],
924     "in_project_namespace": true,
925     "kind": "theorem",
926     "module": "KomorebiVerification.SemisimpleSeedRank",
927     "name": "Komorebi.SemisimpleSeedRank.ceilDiv_isLeast_generatorCount",
928     "runtime_only": false
929   },
930   {
931     "axioms": [
932       "propext",
933       "Classical.choice",
934       "Quot.sound"
935     ],
936     "in_project_namespace": true,
937     "kind": "theorem",
938     "module": "PaperICompletion5.CyclicGeometricCriterion",
939     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_6",
940     "runtime_only": false
941   },
942   {
943     "axioms": [
944       "propext",
945       "Classical.choice",
946       "Quot.sound"
947     ],
948     "in_project_namespace": true,
949     "kind": "theorem",
950     "module": "PaperIRelease.CategoryBoundaries",
951     "name": "Komorebi.PaperIRelease.CategoryBoundaries.onePacket._proof_1",
952     "runtime_only": false
953   },
954   {
955     "axioms": [
956       "propext",
957       "Classical.choice",
958       "Quot.sound"
959     ],
960     "in_project_namespace": true,
961     "kind": "theorem",
962     "module": "PaperIRelease.GeneralConditionedCoordinates",
963     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.norm_coordinateOperator_le",
964     "runtime_only": false
965   },
966   {
967     "axioms": [
968       "propext",
969       "Quot.sound"
970     ],
971     "in_project_namespace": true,
972     "kind": "theorem",
973     "module": "PaperICompletion4.GroupedPrimary",
974     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_9",
975     "runtime_only": false
976   },
977   {
978     "axioms": [
979       "propext",
980       "Quot.sound"
981     ],
982     "in_project_namespace": true,
983     "kind": "theorem",
984     "module": "KomorebiVerification.PacketNaturalityCompletion",
985     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2082.eq_1",
986     "runtime_only": false
987   },
988   {
989     "axioms": [
990       "propext",
991       "Classical.choice",
992       "Quot.sound"
993     ],
994     "in_project_namespace": true,
995     "kind": "theorem",
996     "module": "KomorebiVerification.SingleOperatorGraph",
997     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_7",
998     "runtime_only": false
999   },
1000   {
1001     "axioms": [
1002       "propext",
1003       "Classical.choice",
1004       "Quot.sound"
1005     ],
1006     "in_project_namespace": true,
1007     "kind": "constructor",
1008     "module": "PaperIRelease.CategoryPackets",
1009     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk",
1010     "runtime_only": false
1011   },
1012   {
1013     "axioms": [
1014       "propext",
1015       "Classical.choice",
1016       "Quot.sound"
1017     ],
1018     "in_project_namespace": true,
1019     "kind": "theorem",
1020     "module": "PaperIRelease.CategoryBoundaries",
1021     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets.eq_1",
1022     "runtime_only": false
1023   },
1024   {
1025     "axioms": [
1026       "propext",
1027       "Classical.choice",
1028       "Quot.sound"
1029     ],
1030     "in_project_namespace": true,
1031     "kind": "theorem",
1032     "module": "PaperICompletion8.SemisimpleFormula",
1033     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.semisimple_seedFinrank_of_decompositions",
1034     "runtime_only": false
1035   },
1036   {
1037     "axioms": [
1038       "propext",
1039       "Classical.choice",
1040       "Quot.sound"
1041     ],
1042     "in_project_namespace": true,
1043     "kind": "definition",
1044     "module": "PaperIRelease.CategoryPackets",
1045     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk._flat_ctor",
1046     "runtime_only": false
1047   },
1048   {
1049     "axioms": [
1050       "propext",
1051       "Classical.choice",
1052       "Quot.sound"
1053     ],
1054     "in_project_namespace": true,
1055     "kind": "theorem",
1056     "module": "PaperIRelease.GrammarEquivalence",
1057     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_6",
1058     "runtime_only": false
1059   },
1060   {
1061     "axioms": [
1062       "propext",
1063       "Classical.choice",
1064       "Quot.sound"
1065     ],
1066     "in_project_namespace": true,
1067     "kind": "inductive",
1068     "module": "KomorebiVerification.PacketNaturalityCompletion",
1069     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism",
1070     "runtime_only": false
1071   },
1072   {
1073     "axioms": [
1074       "propext",
1075       "Classical.choice",
1076       "Quot.sound"
1077     ],
1078     "in_project_namespace": true,
1079     "kind": "definition",
1080     "module": "PaperICompletion4.OperatorIntrinsicFormula",
1081     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues",
1082     "runtime_only": false
1083   },
1084   {
1085     "axioms": [
1086       "propext",
1087       "Classical.choice",
1088       "Quot.sound"
1089     ],
1090     "in_project_namespace": true,
1091     "kind": "theorem",
1092     "module": "PaperICompletion8.ProductPresentation",
1093     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_5",
1094     "runtime_only": false
1095   },
1096   {
1097     "axioms": [
1098       "propext",
1099       "Classical.choice",
1100       "Quot.sound"
1101     ],
1102     "in_project_namespace": true,
1103     "kind": "theorem",
1104     "module": "PaperIRelease.GrammarAlgebra",
1105     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_5",
1106     "runtime_only": false
1107   },
1108   {
1109     "axioms": [
1110       "propext",
1111       "Classical.choice",
1112       "Quot.sound"
1113     ],
1114     "in_project_namespace": true,
1115     "kind": "theorem",
1116     "module": "PaperIRelease.PacketTopologyGeneral",
1117     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictedProjector_bounded",
1118     "runtime_only": false
1119   },
1120   {
1121     "axioms": [
1122       "propext",
1123       "Classical.choice",
1124       "Quot.sound"
1125     ],
1126     "in_project_namespace": false,
1127     "kind": "theorem",
1128     "module": "PaperIRelease.TopologyCountablePackets",
1129     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues_nonempty",
1130     "runtime_only": false
1131   },
1132   {
1133     "axioms": [
1134       "propext",
1135       "Quot.sound"
1136     ],
1137     "in_project_namespace": true,
1138     "kind": "theorem",
1139     "module": "PaperIRelease.GrammarModules",
1140     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_4",
1141     "runtime_only": false
1142   },
1143   {
1144     "axioms": [
1145       "propext",
1146       "Classical.choice",
1147       "Quot.sound"
1148     ],
1149     "in_project_namespace": true,
1150     "kind": "inductive",
1151     "module": "PaperIRelease.TopologyCategories",
1152     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject",
1153     "runtime_only": false
1154   },
1155   {
1156     "axioms": [],
1157     "in_project_namespace": true,
1158     "kind": "definition",
1159     "module": "KomorebiVerification.ProjectorCore",
1160     "name": "Komorebi.ClaimKind._sizeOf_1",
1161     "runtime_only": false
1162   },
1163   {
1164     "axioms": [],
1165     "in_project_namespace": true,
1166     "kind": "theorem",
1167     "module": "KomorebiVerification.ProjectorCore",
1168     "name": "Komorebi.FormalizationStatus.queued.sizeOf_spec",
1169     "runtime_only": false
1170   },
1171   {
1172     "axioms": [
1173       "propext",
1174       "Classical.choice",
1175       "Quot.sound"
1176     ],
1177     "in_project_namespace": true,
1178     "kind": "theorem",
1179     "module": "KomorebiVerification.TopologicalCompletion",
1180     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.idempotent",
1181     "runtime_only": false
1182   },
1183   {
1184     "axioms": [
1185       "propext",
1186       "Classical.choice",
1187       "Quot.sound"
1188     ],
1189     "in_project_namespace": true,
1190     "kind": "theorem",
1191     "module": "KomorebiVerification.PacketNaturalityCompletion",
1192     "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_1",
1193     "runtime_only": false
1194   },
1195   {
1196     "axioms": [
1197       "propext",
1198       "Classical.choice",
1199       "Quot.sound"
1200     ],
1201     "in_project_namespace": false,
1202     "kind": "theorem",
1203     "module": "PaperIRelease.TopologyCountablePackets",
1204     "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace.ext",
1205     "runtime_only": false
1206   },
1207   {
1208     "axioms": [
1209       "propext",
1210       "Classical.choice",
1211       "Quot.sound"
1212     ],
1213     "in_project_namespace": true,
1214     "kind": "theorem",
1215     "module": "KomorebiVerification.EllipticAlgorithms",
1216     "name": "Komorebi.EllipticCoordinates.My_apply",
1217     "runtime_only": false
1218   },
1219   {
1220     "axioms": [
1221       "propext",
1222       "Quot.sound"
1223     ],
1224     "in_project_namespace": false,
1225     "kind": "theorem",
1226     "module": "KomorebiVerification.SeedRankOperations",
1227     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_4",
1228     "runtime_only": false
1229   },
1230   {
1231     "axioms": [
1232       "propext",
1233       "Classical.choice",
1234       "Quot.sound"
1235     ],
1236     "in_project_namespace": false,
1237     "kind": "theorem",
1238     "module": "PaperIRelease.TopologyCountablePackets",
1239     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv._proof_2",
1240     "runtime_only": false
1241   },
1242   {
1243     "axioms": [
1244       "propext",
1245       "Classical.choice",
1246       "Quot.sound"
1247     ],
1248     "in_project_namespace": true,
1249     "kind": "theorem",
1250     "module": "KomorebiVerification.EllipticAlgorithms",
1251     "name": "Komorebi.EllipticCoordinates.P0._proof_2",
1252     "runtime_only": false
1253   },
1254   {
1255     "axioms": [
1256       "propext",
1257       "Classical.choice",
1258       "Quot.sound"
1259     ],
1260     "in_project_namespace": false,
1261     "kind": "theorem",
1262     "module": "PaperIRelease.TopologyCountablePackets",
1263     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_5",
1264     "runtime_only": false
1265   },
1266   {
1267     "axioms": [
1268       "propext",
1269       "Classical.choice",
1270       "Quot.sound"
1271     ],
1272     "in_project_namespace": true,
1273     "kind": "theorem",
1274     "module": "PaperICompletion8.SemisimpleFormula",
1275     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.finiteAlgebra_radicalQuotient_decomposition",
1276     "runtime_only": false
1277   },
1278   {
1279     "axioms": [
1280       "propext",
1281       "Quot.sound"
1282     ],
1283     "in_project_namespace": true,
1284     "kind": "theorem",
1285     "module": "KomorebiVerification.PacketNaturalityCompletion",
1286     "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull.eq_1",
1287     "runtime_only": false
1288   },
1289   {
1290     "axioms": [],
1291     "in_project_namespace": true,
1292     "kind": "theorem",
1293     "module": "PaperIRelease.CategoryExport",
1294     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.sizeOf_spec",
1295     "runtime_only": false
1296   },
1297   {
1298     "axioms": [
1299       "propext",
1300       "Classical.choice",
1301       "Quot.sound"
1302     ],
1303     "in_project_namespace": true,
1304     "kind": "theorem",
1305     "module": "PaperIRelease.PacketExactSequence",
1306     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinate_shortExact",
1307     "runtime_only": false
1308   },
1309   {
1310     "axioms": [
1311       "propext",
1312       "Classical.choice",
1313       "Quot.sound"
1314     ],
1315     "in_project_namespace": true,
1316     "kind": "theorem",
1317     "module": "PaperIRelease.PacketDescent",
1318     "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_3",
1319     "runtime_only": false
1320   },
1321   {
1322     "axioms": [
1323       "propext",
1324       "Classical.choice",
1325       "Quot.sound"
1326     ],
1327     "in_project_namespace": true,
1328     "kind": "definition",
1329     "module": "PaperIRelease.TopologyCategories",
1330     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.noConfusion",
1331     "runtime_only": false
1332   },
1333   {
1334     "axioms": [
1335       "propext",
1336       "Classical.choice",
1337       "Quot.sound"
1338     ],
1339     "in_project_namespace": true,
1340     "kind": "theorem",
1341     "module": "KomorebiVerification.ResidueProjectors",
1342     "name": "Komorebi.Residue.residueFibre_refinement",
1343     "runtime_only": false
1344   },
1345   {
1346     "axioms": [
1347       "propext",
1348       "Quot.sound"
1349     ],
1350     "in_project_namespace": true,
1351     "kind": "theorem",
1352     "module": "PaperICompletion.CyclicClassification",
1353     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_1",
1354     "runtime_only": false
1355   },
1356   {
1357     "axioms": [
1358       "propext",
1359       "Quot.sound"
1360     ],
1361     "in_project_namespace": true,
1362     "kind": "theorem",
1363     "module": "KomorebiVerification.SingleOperatorGraph",
1364     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_1",
1365     "runtime_only": false
1366   },
1367   {
1368     "axioms": [
1369       "propext",
1370       "Classical.choice",
1371       "Quot.sound"
1372     ],
1373     "in_project_namespace": true,
1374     "kind": "definition",
1375     "module": "PaperIRelease.CategoryPackets",
1376     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism._sizeOf_inst",
1377     "runtime_only": false
1378   },
1379   {
1380     "axioms": [],
1381     "in_project_namespace": true,
1382     "kind": "definition",
1383     "module": "KomorebiVerification.ProjectorCore",
1384     "name": "Komorebi.ClaimRecord.title",
1385     "runtime_only": false
1386   },
1387   {
1388     "axioms": [
1389       "propext",
1390       "Classical.choice",
1391       "Quot.sound"
1392     ],
1393     "in_project_namespace": true,
1394     "kind": "theorem",
1395     "module": "KomorebiVerification.PathGraphKrylov",
1396     "name": "Komorebi.PathGraphKrylov.walkMatrix_apply_eq_zero_of_lt",
1397     "runtime_only": false
1398   },
1399   {
1400     "axioms": [],
1401     "in_project_namespace": false,
1402     "kind": "definition",
1403     "module": "ReleaseBoundary",
1404     "name": "PaperIBlock08Tests.dims",
1405     "runtime_only": false
1406   },
1407   {
1408     "axioms": [
1409       "propext",
1410       "Classical.choice",
1411       "Quot.sound"
1412     ],
1413     "in_project_namespace": true,
1414     "kind": "theorem",
1415     "module": "KomorebiVerification.SingleOperatorGraph",
1416     "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_map_T",
1417     "runtime_only": false
1418   },
1419   {
1420     "axioms": [
1421       "propext",
1422       "Quot.sound"
1423     ],
1424     "in_project_namespace": true,
1425     "kind": "theorem",
1426     "module": "KomorebiVerification.ResidueProjectors",
1427     "name": "Komorebi.Residue.merge_fineAddress",
1428     "runtime_only": false
1429   },
1430   {
1431     "axioms": [
1432       "propext",
1433       "Classical.choice",
1434       "Quot.sound"
1435     ],
1436     "in_project_namespace": true,
1437     "kind": "theorem",
1438     "module": "PaperICompletion8.DivisionProduct",
1439     "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_seedFinrank_eq_maxCeilDiv",
1440     "runtime_only": false
1441   },
1442   {
1443     "axioms": [
1444       "propext",
1445       "Classical.choice",
1446       "Quot.sound"
1447     ],
1448     "in_project_namespace": false,
1449     "kind": "theorem",
1450     "module": "PaperIRelease.AlgebraPreorder",
1451     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPredecessors.eq_1",
1452     "runtime_only": false
1453   },
1454   {
1455     "axioms": [
1456       "propext",
1457       "Classical.choice",
1458       "Quot.sound"
1459     ],
1460     "in_project_namespace": true,
1461     "kind": "theorem",
1462     "module": "PaperICompletion.SpectralCertificates",
1463     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity_le_max",
1464     "runtime_only": false
1465   },
1466   {
1467     "axioms": [
1468       "propext",
1469       "Classical.choice",
1470       "Quot.sound"
1471     ],
1472     "in_project_namespace": true,
1473     "kind": "definition",
1474     "module": "PaperIRelease.GrammarEquivalence",
1475     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.map",
1476     "runtime_only": false
1477   },
1478   {
1479     "axioms": [
1480       "propext",
1481       "Classical.choice",
1482       "Quot.sound"
1483     ],
1484     "in_project_namespace": true,
1485     "kind": "definition",
1486     "module": "PaperIRelease.TopologyCategories",
1487     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.noConfusion",
1488     "runtime_only": false
1489   },
1490   {
1491     "axioms": [
1492       "propext",
1493       "Quot.sound"
1494     ],
1495     "in_project_namespace": true,
1496     "kind": "theorem",
1497     "module": "PaperICompletion5.LinearPrimaryEigenspace",
1498     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_6",
1499     "runtime_only": false
1500   },
1501   {
1502     "axioms": [
1503       "propext",
1504       "Classical.choice",
1505       "Quot.sound"
1506     ],
1507     "in_project_namespace": true,
1508     "kind": "theorem",
1509     "module": "KomorebiVerification.PacketNaturalityCompletion",
1510     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packetMap_injective",
1511     "runtime_only": false
1512   },
1513   {
1514     "axioms": [
1515       "propext",
1516       "Classical.choice",
1517       "Quot.sound"
1518     ],
1519     "in_project_namespace": true,
1520     "kind": "definition",
1521     "module": "KomorebiVerification.EllipticAlgorithms",
1522     "name": "Komorebi.EllipticCoordinates.QuotientModel",
1523     "runtime_only": false
1524   },
1525   {
1526     "axioms": [
1527       "propext",
1528       "Classical.choice",
1529       "Quot.sound"
1530     ],
1531     "in_project_namespace": true,
1532     "kind": "theorem",
1533     "module": "PaperIRelease.GeneralPacketBounds",
1534     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_bound",
1535     "runtime_only": false
1536   },
1537   {
1538     "axioms": [],
1539     "in_project_namespace": true,
1540     "kind": "definition",
1541     "module": "KomorebiVerification.ProjectorCore",
1542     "name": "Komorebi.FormalizationStatus.ctorIdx",
1543     "runtime_only": false
1544   },
1545   {
1546     "axioms": [
1547       "propext",
1548       "Quot.sound"
1549     ],
1550     "in_project_namespace": true,
1551     "kind": "theorem",
1552     "module": "PaperIRelease.ScalarExtension",
1553     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorOperator_smul_tmul",
1554     "runtime_only": false
1555   },
1556   {
1557     "axioms": [
1558       "propext",
1559       "Classical.choice",
1560       "Quot.sound"
1561     ],
1562     "in_project_namespace": false,
1563     "kind": "theorem",
1564     "module": "PaperIRelease.TopologyTransport",
1565     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_5",
1566     "runtime_only": false
1567   },
1568   {
1569     "axioms": [
1570       "propext",
1571       "Classical.choice",
1572       "Quot.sound"
1573     ],
1574     "in_project_namespace": true,
1575     "kind": "theorem",
1576     "module": "PaperIRelease.CategoryPackets",
1577     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.injEq",
1578     "runtime_only": false
1579   },
1580   {
1581     "axioms": [
1582       "propext",
1583       "Classical.choice",
1584       "Quot.sound"
1585     ],
1586     "in_project_namespace": true,
1587     "kind": "theorem",
1588     "module": "KomorebiVerification.SeedRankOperations",
1589     "name": "Komorebi.SeedRankOperations.finrank_le_seedRank_of_scalar_quotient",
1590     "runtime_only": false
1591   },
1592   {
1593     "axioms": [
1594       "propext",
1595       "Classical.choice",
1596       "Quot.sound"
1597     ],
1598     "in_project_namespace": true,
1599     "kind": "theorem",
1600     "module": "KomorebiVerification.FullMatrixCyclicity",
1601     "name": "Komorebi.FullMatrixCyclicity.isCyclic_of_ne_zero",
1602     "runtime_only": false
1603   },
1604   {
1605     "axioms": [
1606       "propext",
1607       "Classical.choice",
1608       "Quot.sound"
1609     ],
1610     "in_project_namespace": true,
1611     "kind": "theorem",
1612     "module": "PaperIRelease.PacketDescent",
1613     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_8",
1614     "runtime_only": false
1615   },
1616   {
1617     "axioms": [
1618       "propext",
1619       "Classical.choice",
1620       "Quot.sound"
1621     ],
1622     "in_project_namespace": false,
1623     "kind": "definition",
1624     "module": "PaperIRelease.TopologyCountablePackets",
1625     "name": "PaperIRelease.TopologyCountablePackets.Projectors.noConfusion",
1626     "runtime_only": false
1627   },
1628   {
1629     "axioms": [
1630       "propext",
1631       "Classical.choice",
1632       "Quot.sound"
1633     ],
1634     "in_project_namespace": true,
1635     "kind": "theorem",
1636     "module": "PaperIRelease.GrammarEquivalence",
1637     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.congr_simp",
1638     "runtime_only": false
1639   },
1640   {
1641     "axioms": [],
1642     "in_project_namespace": true,
1643     "kind": "definition",
1644     "module": "KomorebiVerification.ProjectorCore",
1645     "name": "Komorebi.Seed.OperatorExpr._sizeOf_1",
1646     "runtime_only": false
1647   },
1648   {
1649     "axioms": [
1650       "propext",
1651       "Quot.sound"
1652     ],
1653     "in_project_namespace": true,
1654     "kind": "definition",
1655     "module": "PaperIRelease.GrammarModules",
1656     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.linearMap",
1657     "runtime_only": false
1658   },
1659   {
1660     "axioms": [
1661       "propext",
1662       "Classical.choice",
1663       "Quot.sound"
1664     ],
1665     "in_project_namespace": true,
1666     "kind": "theorem",
1667     "module": "PaperIRelease.AlgebraDiagonal",
1668     "name": "Komorebi.PaperIRelease.diagonalProjection.eq_1",
1669     "runtime_only": false
1670   },
1671   {
1672     "axioms": [
1673       "propext",
1674       "Quot.sound"
1675     ],
1676     "in_project_namespace": true,
1677     "kind": "definition",
1678     "module": "PaperIRelease.ScalarExtension",
1679     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorOperatorModule",
1680     "runtime_only": false
1681   },
1682   {
1683     "axioms": [
1684       "propext",
1685       "Classical.choice",
1686       "Quot.sound"
1687     ],
1688     "in_project_namespace": true,
1689     "kind": "definition",
1690     "module": "PaperIRelease.GrammarTyped",
1691     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction",
1692     "runtime_only": false
1693   },
1694   {
1695     "axioms": [
1696       "propext",
1697       "Classical.choice",
1698       "Quot.sound"
1699     ],
1700     "in_project_namespace": true,
1701     "kind": "definition",
1702     "module": "PaperIRelease.PacketAggregation",
1703     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis",
1704     "runtime_only": false
1705   },
1706   {
1707     "axioms": [],
1708     "in_project_namespace": true,
1709     "kind": "definition",
1710     "module": "KomorebiVerification.ProjectorCore",
1711     "name": "Komorebi.instInhabitedFormalizationStatus.default",
1712     "runtime_only": false
1713   },
1714   {
1715     "axioms": [
1716       "propext",
1717       "Quot.sound"
1718     ],
1719     "in_project_namespace": true,
1720     "kind": "definition",
1721     "module": "KomorebiVerification.PaperITransport",
1722     "name": "Komorebi.Foundation.conjugateEnd",
1723     "runtime_only": false
1724   },
1725   {
1726     "axioms": [
1727       "propext",
1728       "Classical.choice",
1729       "Quot.sound"
1730     ],
1731     "in_project_namespace": true,
1732     "kind": "theorem",
1733     "module": "KomorebiVerification.PathGraphKrylov",
1734     "name": "Komorebi.PathGraphKrylov.walkMatrix_det",
1735     "runtime_only": false
1736   },
1737   {
1738     "axioms": [
1739       "propext",
1740       "Classical.choice",
1741       "Quot.sound"
1742     ],
1743     "in_project_namespace": true,
1744     "kind": "definition",
1745     "module": "PaperIRelease.GrammarTyped",
1746     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split",
1747     "runtime_only": false
1748   },
1749   {
1750     "axioms": [],
1751     "in_project_namespace": true,
1752     "kind": "theorem",
1753     "module": "KomorebiVerification.ProjectorCore",
1754     "name": "Komorebi.Seed.OperatorRelation.mk.inj",
1755     "runtime_only": false
1756   },
1757   {
1758     "axioms": [],
1759     "in_project_namespace": true,
1760     "kind": "theorem",
1761     "module": "PaperICompletion4.IntrinsicPrimary",
1762     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal._proof_1",
1763     "runtime_only": false
1764   },
1765   {
1766     "axioms": [
1767       "propext",
1768       "Classical.choice",
1769       "Quot.sound"
1770     ],
1771     "in_project_namespace": true,
1772     "kind": "definition",
1773     "module": "KomorebiVerification.ExactCoordinates",
1774     "name": "Komorebi.Foundation.LinearProjectorFamily.PacketSpace",
1775     "runtime_only": false
1776   },
1777   {
1778     "axioms": [
1779       "propext",
1780       "Classical.choice",
1781       "Quot.sound"
1782     ],
1783     "in_project_namespace": true,
1784     "kind": "theorem",
1785     "module": "KomorebiVerification.PacketNaturalityCompletion",
1786     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.injEq",
1787     "runtime_only": false
1788   },
1789   {
1790     "axioms": [
1791       "propext",
1792       "Quot.sound"
1793     ],
1794     "in_project_namespace": true,
1795     "kind": "theorem",
1796     "module": "KomorebiVerification.SingleOperatorGraph",
1797     "name": "Komorebi.SingleOperatorGraph.evalVector._proof_2",
1798     "runtime_only": false
1799   },
1800   {
1801     "axioms": [
1802       "propext",
1803       "Quot.sound"
1804     ],
1805     "in_project_namespace": true,
1806     "kind": "theorem",
1807     "module": "KomorebiVerification.SeedRankOperations",
1808     "name": "Komorebi.SeedRankOperations.tensorRightTower",
1809     "runtime_only": false
1810   },
1811   {
1812     "axioms": [
1813       "propext",
1814       "Classical.choice",
1815       "Quot.sound"
1816     ],
1817     "in_project_namespace": true,
1818     "kind": "theorem",
1819     "module": "PaperIRelease.GrammarIdeal",
1820     "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented_quotient",
1821     "runtime_only": false
1822   },
1823   {
1824     "axioms": [
1825       "propext",
1826       "Classical.choice",
1827       "Quot.sound"
1828     ],
1829     "in_project_namespace": true,
1830     "kind": "definition",
1831     "module": "KomorebiVerification.SemisimpleCompletion",
1832     "name": "Komorebi.SemisimpleCompletion.abstractSplitBlockModuleAction",
1833     "runtime_only": false
1834   },
1835   {
1836     "axioms": [],
1837     "in_project_namespace": true,
1838     "kind": "inductive",
1839     "module": "PaperIRelease.GrammarPaths",
1840     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath",
1841     "runtime_only": false
1842   },
1843   {
1844     "axioms": [
1845       "propext",
1846       "Classical.choice",
1847       "Quot.sound"
1848     ],
1849     "in_project_namespace": true,
1850     "kind": "definition",
1851     "module": "PaperIRelease.AlgebraClassGrouping",
1852     "name": "Komorebi.PaperIRelease.preorderQuotientEquiv",
1853     "runtime_only": false
1854   },
1855   {
1856     "axioms": [],
1857     "in_project_namespace": true,
1858     "kind": "definition",
1859     "module": "KomorebiVerification.ProjectorCore",
1860     "name": "Komorebi.Seed.instReprOperatorExpr.repr",
1861     "runtime_only": false
1862   },
1863   {
1864     "axioms": [
1865       "propext",
1866       "Classical.choice",
1867       "Quot.sound"
1868     ],
1869     "in_project_namespace": true,
1870     "kind": "theorem",
1871     "module": "KomorebiVerification.ProjectorCore",
1872     "name": "Komorebi.Quantum.logPhase_zero",
1873     "runtime_only": false
1874   },
1875   {
1876     "axioms": [
1877       "propext",
1878       "Classical.choice",
1879       "Quot.sound"
1880     ],
1881     "in_project_namespace": true,
1882     "kind": "definition",
1883     "module": "PaperICompletion8.ProductPresentation",
1884     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors",
1885     "runtime_only": false
1886   },
1887   {
1888     "axioms": [
1889       "propext",
1890       "Classical.choice",
1891       "Quot.sound"
1892     ],
1893     "in_project_namespace": false,
1894     "kind": "definition",
1895     "module": "PaperIRelease.TopologyCountablePackets",
1896     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv",
1897     "runtime_only": false
1898   },
1899   {
1900     "axioms": [
1901       "propext",
1902       "Classical.choice",
1903       "Quot.sound"
1904     ],
1905     "in_project_namespace": false,
1906     "kind": "theorem",
1907     "module": "PaperIRelease.TopologySemilinearRank",
1908     "name": "PaperIRelease.TopologySemilinearRank.rank_le_of_continuous_additive_surjective",
1909     "runtime_only": false
1910   },
1911   {
1912     "axioms": [
1913       "propext",
1914       "Quot.sound"
1915     ],
1916     "in_project_namespace": true,
1917     "kind": "theorem",
1918     "module": "PaperIRelease.PacketLocalRank",
1919     "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_1",
1920     "runtime_only": false
1921   },
1922   {
1923     "axioms": [
1924       "propext",
1925       "Classical.choice",
1926       "Quot.sound"
1927     ],
1928     "in_project_namespace": true,
1929     "kind": "theorem",
1930     "module": "PaperIRelease.ScalarExtension",
1931     "name": "Komorebi.PaperIRelease.ScalarExtension.scalar_extension_seedRank_le",
1932     "runtime_only": false
1933   },
1934   {
1935     "axioms": [
1936       "propext",
1937       "Classical.choice",
1938       "Quot.sound"
1939     ],
1940     "in_project_namespace": true,
1941     "kind": "theorem",
1942     "module": "PaperIRelease.PacketTopologyGeneral",
1943     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM_toLinearMap",
1944     "runtime_only": false
1945   },
1946   {
1947     "axioms": [
1948       "propext",
1949       "Quot.sound"
1950     ],
1951     "in_project_namespace": true,
1952     "kind": "theorem",
1953     "module": "PaperIRelease.AlgebraTransfer",
1954     "name": "Komorebi.PaperIRelease.operatorWord.eq_1",
1955     "runtime_only": false
1956   },
1957   {
1958     "axioms": [
1959       "propext",
1960       "Classical.choice",
1961       "Quot.sound"
1962     ],
1963     "in_project_namespace": true,
1964     "kind": "theorem",
1965     "module": "PaperIRelease.GrammarEquivalence",
1966     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_5",
1967     "runtime_only": false
1968   },
1969   {
1970     "axioms": [
1971       "propext",
1972       "Classical.choice",
1973       "Quot.sound"
1974     ],
1975     "in_project_namespace": true,
1976     "kind": "theorem",
1977     "module": "KomorebiVerification.PacketNaturalityCompletion",
1978     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum_zero_same",
1979     "runtime_only": false
1980   },
1981   {
1982     "axioms": [
1983       "propext",
1984       "Classical.choice",
1985       "Quot.sound"
1986     ],
1987     "in_project_namespace": true,
1988     "kind": "theorem",
1989     "module": "PaperIRelease.GeneralConditionedCoordinates",
1990     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditioned_coordinate_bounds",
1991     "runtime_only": false
1992   },
1993   {
1994     "axioms": [
1995       "propext",
1996       "Classical.choice",
1997       "Quot.sound"
1998     ],
1999     "in_project_namespace": true,
2000     "kind": "definition",
2001     "module": "KomorebiVerification.SingleOperatorGraph",
2002     "name": "Komorebi.SingleOperatorGraph.seedPresentation",
2003     "runtime_only": false
2004   },
2005   {
2006     "axioms": [
2007       "propext",
2008       "Classical.choice",
2009       "Quot.sound"
2010     ],
2011     "in_project_namespace": true,
2012     "kind": "theorem",
2013     "module": "KomorebiVerification.ProjectorCore",
2014     "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize_analyze",
2015     "runtime_only": false
2016   },
2017   {
2018     "axioms": [
2019       "propext",
2020       "Classical.choice",
2021       "Quot.sound"
2022     ],
2023     "in_project_namespace": true,
2024     "kind": "theorem",
2025     "module": "PaperIRelease.AlgebraPreorder",
2026     "name": "Komorebi.PaperIRelease.mem_strictSupportIdeal._simp_1",
2027     "runtime_only": false
2028   },
2029   {
2030     "axioms": [
2031       "propext",
2032       "Quot.sound"
2033     ],
2034     "in_project_namespace": true,
2035     "kind": "theorem",
2036     "module": "KomorebiVerification.PathGraphKrylov",
2037     "name": "Komorebi.PathGraphKrylov.krylov_diagonal._proof_1_3",
2038     "runtime_only": false
2039   },
2040   {
2041     "axioms": [
2042       "propext",
2043       "Quot.sound"
2044     ],
2045     "in_project_namespace": true,
2046     "kind": "definition",
2047     "module": "KomorebiVerification.SeedRankBasics",
2048     "name": "Komorebi.SeedRankBasics.Cyclic",
2049     "runtime_only": false
2050   },
2051   {
2052     "axioms": [
2053       "propext",
2054       "Classical.choice",
2055       "Quot.sound"
2056     ],
2057     "in_project_namespace": true,
2058     "kind": "theorem",
2059     "module": "KomorebiVerification.SingleOperatorGraph",
2060     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow.eq_1",
2061     "runtime_only": false
2062   },
2063   {
2064     "axioms": [
2065       "propext",
2066       "Classical.choice",
2067       "Quot.sound"
2068     ],
2069     "in_project_namespace": true,
2070     "kind": "definition",
2071     "module": "PaperICompletion7.Nakayama",
2072     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap",
2073     "runtime_only": false
2074   },
2075   {
2076     "axioms": [],
2077     "in_project_namespace": true,
2078     "kind": "theorem",
2079     "module": "KomorebiVerification.ProjectorCore",
2080     "name": "Komorebi.Packet.fibreProj.eq_1",
2081     "runtime_only": false
2082   },
2083   {
2084     "axioms": [
2085       "propext",
2086       "Classical.choice",
2087       "Quot.sound"
2088     ],
2089     "in_project_namespace": true,
2090     "kind": "definition",
2091     "module": "PaperICompletion3.PrimarySeedFormula",
2092     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds",
2093     "runtime_only": false
2094   },
2095   {
2096     "axioms": [
2097       "propext",
2098       "Quot.sound"
2099     ],
2100     "in_project_namespace": true,
2101     "kind": "definition",
2102     "module": "KomorebiVerification.PathGraphKrylov",
2103     "name": "Komorebi.PathGraphKrylov.krylov",
2104     "runtime_only": false
2105   },
2106   {
2107     "axioms": [
2108       "propext",
2109       "Classical.choice",
2110       "Quot.sound"
2111     ],
2112     "in_project_namespace": true,
2113     "kind": "theorem",
2114     "module": "PaperICompletion8.RegularMultiplicity",
2115     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_2",
2116     "runtime_only": false
2117   },
2118   {
2119     "axioms": [
2120       "propext",
2121       "Classical.choice",
2122       "Quot.sound"
2123     ],
2124     "in_project_namespace": true,
2125     "kind": "definition",
2126     "module": "PaperIRelease.GrammarIdeal",
2127     "name": "Komorebi.PaperIRelease.GrammarAlgebra.IdealQuotient",
2128     "runtime_only": false
2129   },
2130   {
2131     "axioms": [
2132       "propext",
2133       "Classical.choice",
2134       "Quot.sound"
2135     ],
2136     "in_project_namespace": true,
2137     "kind": "theorem",
2138     "module": "PaperIRelease.TopologyCategories",
2139     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.seed_condition",
2140     "runtime_only": false
2141   },
2142   {
2143     "axioms": [
2144       "propext",
2145       "Classical.choice",
2146       "Quot.sound"
2147     ],
2148     "in_project_namespace": true,
2149     "kind": "definition",
2150     "module": "PaperIRelease.TopologyCategories",
2151     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.casesOn",
2152     "runtime_only": false
2153   },
2154   {
2155     "axioms": [
2156       "propext",
2157       "Classical.choice",
2158       "Quot.sound"
2159     ],
2160     "in_project_namespace": true,
2161     "kind": "theorem",
2162     "module": "PaperIRelease.BoundedStar",
2163     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_9",
2164     "runtime_only": false
2165   },
2166   {
2167     "axioms": [
2168       "propext",
2169       "Classical.choice",
2170       "Quot.sound"
2171     ],
2172     "in_project_namespace": true,
2173     "kind": "theorem",
2174     "module": "KomorebiVerification.EllipticAlgorithms",
2175     "name": "Komorebi.EllipticCoordinates.P0_not_full_algebra_linear",
2176     "runtime_only": false
2177   },
2178   {
2179     "axioms": [
2180       "propext",
2181       "Quot.sound"
2182     ],
2183     "in_project_namespace": false,
2184     "kind": "theorem",
2185     "module": "KomorebiVerification.SeedRankOperations",
2186     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_3",
2187     "runtime_only": false
2188   },
2189   {
2190     "axioms": [
2191       "propext",
2192       "Classical.choice",
2193       "Quot.sound"
2194     ],
2195     "in_project_namespace": false,
2196     "kind": "theorem",
2197     "module": "PaperIRelease.TopologyUnconditional",
2198     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_20",
2199     "runtime_only": false
2200   },
2201   {
2202     "axioms": [],
2203     "in_project_namespace": true,
2204     "kind": "definition",
2205     "module": "KomorebiVerification.PathGraphKrylov",
2206     "name": "Komorebi.PathGraphKrylov.krylov.match_1",
2207     "runtime_only": false
2208   },
2209   {
2210     "axioms": [
2211       "propext",
2212       "Classical.choice",
2213       "Quot.sound"
2214     ],
2215     "in_project_namespace": true,
2216     "kind": "theorem",
2217     "module": "KomorebiVerification.ExactCoordinates",
2218     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_1",
2219     "runtime_only": false
2220   },
2221   {
2222     "axioms": [],
2223     "in_project_namespace": true,
2224     "kind": "definition",
2225     "module": "PaperIRelease.GraphSources",
2226     "name": "Komorebi.PaperIRelease.FiniteDigraph.SCC",
2227     "runtime_only": false
2228   },
2229   {
2230     "axioms": [
2231       "propext",
2232       "Classical.choice",
2233       "Quot.sound"
2234     ],
2235     "in_project_namespace": true,
2236     "kind": "definition",
2237     "module": "KomorebiVerification.EllipticAlgorithms",
2238     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._f",
2239     "runtime_only": false
2240   },
2241   {
2242     "axioms": [
2243       "propext",
2244       "Quot.sound"
2245     ],
2246     "in_project_namespace": true,
2247     "kind": "theorem",
2248     "module": "PaperICompletion5.GeometricSeedFormula",
2249     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues._proof_2",
2250     "runtime_only": false
2251   },
2252   {
2253     "axioms": [],
2254     "in_project_namespace": true,
2255     "kind": "theorem",
2256     "module": "KomorebiVerification.ProjectorCore",
2257     "name": "Komorebi.Seed.OperatorExpr.comp.sizeOf_spec",
2258     "runtime_only": false
2259   },
2260   {
2261     "axioms": [
2262       "propext",
2263       "Classical.choice",
2264       "Quot.sound"
2265     ],
2266     "in_project_namespace": true,
2267     "kind": "theorem",
2268     "module": "PaperICompletion7.ModuleTop",
2269     "name": "Komorebi.PaperICompletion7.ModuleTop.idealTop_finite",
2270     "runtime_only": false
2271   },
2272   {
2273     "axioms": [
2274       "propext",
2275       "Classical.choice",
2276       "Quot.sound"
2277     ],
2278     "in_project_namespace": true,
2279     "kind": "definition",
2280     "module": "KomorebiVerification.EllipticAlgorithms",
2281     "name": "Komorebi.EllipticCoordinates.P0",
2282     "runtime_only": false
2283   },
2284   {
2285     "axioms": [
2286       "propext",
2287       "Classical.choice",
2288       "Quot.sound"
2289     ],
2290     "in_project_namespace": false,
2291     "kind": "theorem",
2292     "module": "ReleaseBoundary",
2293     "name": "PaperIBlock08Tests.quaternion_five_copies_rank_three",
2294     "runtime_only": false
2295   },
2296   {
2297     "axioms": [
2298       "propext",
2299       "Classical.choice",
2300       "Quot.sound"
2301     ],
2302     "in_project_namespace": false,
2303     "kind": "theorem",
2304     "module": "PaperIRelease.TopologyCountablePackets",
2305     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_7",
2306     "runtime_only": false
2307   },
2308   {
2309     "axioms": [
2310       "propext",
2311       "Classical.choice",
2312       "Quot.sound"
2313     ],
2314     "in_project_namespace": true,
2315     "kind": "definition",
2316     "module": "KomorebiVerification.SingleOperatorGraph",
2317     "name": "Komorebi.SingleOperatorGraph.FamilyGenerates",
2318     "runtime_only": false
2319   },
2320   {
2321     "axioms": [
2322       "propext",
2323       "Classical.choice",
2324       "Quot.sound"
2325     ],
2326     "in_project_namespace": false,
2327     "kind": "theorem",
2328     "module": "ReleaseBoundary",
2329     "name": "PaperIBlock08Tests.empty_product_rank_zero",
2330     "runtime_only": false
2331   },
2332   {
2333     "axioms": [
2334       "propext",
2335       "Classical.choice",
2336       "Quot.sound"
2337     ],
2338     "in_project_namespace": true,
2339     "kind": "theorem",
2340     "module": "PaperIRelease.AlgebraClassGrouping",
2341     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_11",
2342     "runtime_only": false
2343   },
2344   {
2345     "axioms": [
2346       "propext",
2347       "Classical.choice",
2348       "Quot.sound"
2349     ],
2350     "in_project_namespace": true,
2351     "kind": "definition",
2352     "module": "PaperIRelease.GeneralNormedPackets",
2353     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.proj",
2354     "runtime_only": false
2355   },
2356   {
2357     "axioms": [
2358       "propext",
2359       "Quot.sound"
2360     ],
2361     "in_project_namespace": true,
2362     "kind": "theorem",
2363     "module": "PaperIRelease.GrammarModules",
2364     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_6",
2365     "runtime_only": false
2366   },
2367   {
2368     "axioms": [
2369       "propext",
2370       "Classical.choice",
2371       "Quot.sound"
2372     ],
2373     "in_project_namespace": false,
2374     "kind": "definition",
2375     "module": "PaperIRelease.TopologyCountablePackets",
2376     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk._flat_ctor",
2377     "runtime_only": false
2378   },
2379   {
2380     "axioms": [
2381       "propext"
2382     ],
2383     "in_project_namespace": true,
2384     "kind": "theorem",
2385     "module": "KomorebiVerification.PathGraphKrylov",
2386     "name": "Komorebi.PathGraphKrylov.leftTerm._proof_1",
2387     "runtime_only": false
2388   },
2389   {
2390     "axioms": [
2391       "propext",
2392       "Classical.choice",
2393       "Quot.sound"
2394     ],
2395     "in_project_namespace": true,
2396     "kind": "theorem",
2397     "module": "KomorebiVerification.TopologicalCompletion",
2398     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_4",
2399     "runtime_only": false
2400   },
2401   {
2402     "axioms": [
2403       "propext",
2404       "Classical.choice",
2405       "Quot.sound"
2406     ],
2407     "in_project_namespace": true,
2408     "kind": "theorem",
2409     "module": "KomorebiVerification.PacketNaturalityCompletion",
2410     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_3",
2411     "runtime_only": false
2412   },
2413   {
2414     "axioms": [
2415       "propext",
2416       "Quot.sound"
2417     ],
2418     "in_project_namespace": true,
2419     "kind": "definition",
2420     "module": "KomorebiVerification.KernelAudit",
2421     "name": "Komorebi.Verification.parityAddress",
2422     "runtime_only": false
2423   },
2424   {
2425     "axioms": [
2426       "propext",
2427       "Quot.sound"
2428     ],
2429     "in_project_namespace": true,
2430     "kind": "theorem",
2431     "module": "PaperIRelease.GrammarModules",
2432     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_2",
2433     "runtime_only": false
2434   },
2435   {
2436     "axioms": [
2437       "propext",
2438       "Classical.choice",
2439       "Quot.sound"
2440     ],
2441     "in_project_namespace": true,
2442     "kind": "theorem",
2443     "module": "PaperIRelease.GeneralNormedPackets",
2444     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_analysis",
2445     "runtime_only": false
2446   },
2447   {
2448     "axioms": [
2449       "propext",
2450       "Classical.choice",
2451       "Quot.sound"
2452     ],
2453     "in_project_namespace": false,
2454     "kind": "theorem",
2455     "module": "PaperIRelease.TopologyUnconditional",
2456     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues.eq_1",
2457     "runtime_only": false
2458   },
2459   {
2460     "axioms": [
2461       "propext",
2462       "Classical.choice",
2463       "Quot.sound"
2464     ],
2465     "in_project_namespace": true,
2466     "kind": "definition",
2467     "module": "KomorebiVerification.PaperITransport",
2468     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate",
2469     "runtime_only": false
2470   },
2471   {
2472     "axioms": [
2473       "propext",
2474       "Quot.sound"
2475     ],
2476     "in_project_namespace": true,
2477     "kind": "theorem",
2478     "module": "KomorebiVerification.PacketNaturalityCompletion",
2479     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraGeneratedHull.eq_1",
2480     "runtime_only": false
2481   },
2482   {
2483     "axioms": [
2484       "propext",
2485       "Classical.choice",
2486       "Quot.sound"
2487     ],
2488     "in_project_namespace": true,
2489     "kind": "theorem",
2490     "module": "PaperIRelease.AlgebraClassGrouping",
2491     "name": "Komorebi.Foundation.LinearProjectorFamily.mk.congr_simp",
2492     "runtime_only": false
2493   },
2494   {
2495     "axioms": [
2496       "propext",
2497       "Classical.choice",
2498       "Quot.sound"
2499     ],
2500     "in_project_namespace": true,
2501     "kind": "theorem",
2502     "module": "PaperICompletion4.OperatorIntrinsicFormula",
2503     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_le_seedFinrank",
2504     "runtime_only": false
2505   },
2506   {
2507     "axioms": [
2508       "propext",
2509       "Classical.choice",
2510       "Quot.sound"
2511     ],
2512     "in_project_namespace": true,
2513     "kind": "theorem",
2514     "module": "KomorebiVerification.TopologicalCompletion",
2515     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit",
2516     "runtime_only": false
2517   },
2518   {
2519     "axioms": [
2520       "propext",
2521       "Classical.choice",
2522       "Quot.sound"
2523     ],
2524     "in_project_namespace": true,
2525     "kind": "theorem",
2526     "module": "PaperIRelease.AlgebraTransfer",
2527     "name": "Komorebi.PaperIRelease.packetWordSum.eq_1",
2528     "runtime_only": false
2529   },
2530   {
2531     "axioms": [
2532       "propext",
2533       "Quot.sound"
2534     ],
2535     "in_project_namespace": true,
2536     "kind": "definition",
2537     "module": "PaperIRelease.GrammarModules",
2538     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk._flat_ctor",
2539     "runtime_only": false
2540   },
2541   {
2542     "axioms": [
2543       "propext",
2544       "Classical.choice",
2545       "Quot.sound"
2546     ],
2547     "in_project_namespace": true,
2548     "kind": "definition",
2549     "module": "PaperIRelease.TensorPackets",
2550     "name": "Komorebi.PaperIRelease.tensorPackets",
2551     "runtime_only": false
2552   },
2553   {
2554     "axioms": [
2555       "propext",
2556       "Quot.sound"
2557     ],
2558     "in_project_namespace": true,
2559     "kind": "theorem",
2560     "module": "PaperIRelease.ScalarExtension",
2561     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorLeftTowerInstalled",
2562     "runtime_only": false
2563   },
2564   {
2565     "axioms": [],
2566     "in_project_namespace": true,
2567     "kind": "definition",
2568     "module": "KomorebiVerification.ProjectorCore",
2569     "name": "Komorebi.FiniteDifference.weightedDiff",
2570     "runtime_only": false
2571   },
2572   {
2573     "axioms": [
2574       "propext",
2575       "Classical.choice",
2576       "Quot.sound"
2577     ],
2578     "in_project_namespace": true,
2579     "kind": "definition",
2580     "module": "PaperIRelease.PacketDescent",
2581     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo",
2582     "runtime_only": false
2583   },
2584   {
2585     "axioms": [
2586       "propext",
2587       "Quot.sound"
2588     ],
2589     "in_project_namespace": true,
2590     "kind": "theorem",
2591     "module": "PaperIRelease.ScalarExtension",
2592     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_7",
2593     "runtime_only": false
2594   },
2595   {
2596     "axioms": [
2597       "propext",
2598       "Classical.choice",
2599       "Quot.sound"
2600     ],
2601     "in_project_namespace": true,
2602     "kind": "theorem",
2603     "module": "PaperICompletion3.PrimarySeedFormula",
2604     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv._proof_2",
2605     "runtime_only": false
2606   },
2607   {
2608     "axioms": [
2609       "propext",
2610       "Classical.choice",
2611       "Quot.sound"
2612     ],
2613     "in_project_namespace": false,
2614     "kind": "definition",
2615     "module": "PaperIRelease.AlgebraPreorder",
2616     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPredecessors",
2617     "runtime_only": false
2618   },
2619   {
2620     "axioms": [
2621       "propext",
2622       "Classical.choice",
2623       "Quot.sound"
2624     ],
2625     "in_project_namespace": true,
2626     "kind": "definition",
2627     "module": "PaperIRelease.CategoryPackets",
2628     "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory",
2629     "runtime_only": false
2630   },
2631   {
2632     "axioms": [
2633       "propext",
2634       "Quot.sound"
2635     ],
2636     "in_project_namespace": true,
2637     "kind": "theorem",
2638     "module": "PaperICompletion4.GroupedPrimary",
2639     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_2",
2640     "runtime_only": false
2641   },
2642   {
2643     "axioms": [
2644       "propext",
2645       "Classical.choice",
2646       "Quot.sound"
2647     ],
2648     "in_project_namespace": true,
2649     "kind": "theorem",
2650     "module": "PaperIRelease.GeneralNormedPackets",
2651     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_synthesis",
2652     "runtime_only": false
2653   },
2654   {
2655     "axioms": [
2656       "propext",
2657       "Classical.choice",
2658       "Quot.sound"
2659     ],
2660     "in_project_namespace": true,
2661     "kind": "recursor",
2662     "module": "PaperIRelease.CategoryPackets",
2663     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.rec",
2664     "runtime_only": false
2665   },
2666   {
2667     "axioms": [
2668       "propext",
2669       "Classical.choice",
2670       "Quot.sound"
2671     ],
2672     "in_project_namespace": true,
2673     "kind": "theorem",
2674     "module": "PaperICompletion4.ResidueQuotient",
2675     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_9",
2676     "runtime_only": false
2677   },
2678   {
2679     "axioms": [
2680       "propext",
2681       "Classical.choice",
2682       "Quot.sound"
2683     ],
2684     "in_project_namespace": true,
2685     "kind": "theorem",
2686     "module": "PaperIRelease.GeneralNormedPackets",
2687     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.complete",
2688     "runtime_only": false
2689   },
2690   {
2691     "axioms": [],
2692     "in_project_namespace": true,
2693     "kind": "theorem",
2694     "module": "PaperIRelease.CategoryExport",
2695     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.sizeOf_spec",
2696     "runtime_only": false
2697   },
2698   {
2699     "axioms": [
2700       "propext",
2701       "Classical.choice",
2702       "Quot.sound"
2703     ],
2704     "in_project_namespace": true,
2705     "kind": "definition",
2706     "module": "PaperIRelease.TopologyCategories",
2707     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism._sizeOf_1",
2708     "runtime_only": false
2709   },
2710   {
2711     "axioms": [
2712       "propext",
2713       "Classical.choice",
2714       "Quot.sound"
2715     ],
2716     "in_project_namespace": true,
2717     "kind": "theorem",
2718     "module": "PaperIRelease.PacketTopology",
2719     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM._proof_1",
2720     "runtime_only": false
2721   },
2722   {
2723     "axioms": [
2724       "propext",
2725       "Classical.choice",
2726       "Quot.sound"
2727     ],
2728     "in_project_namespace": true,
2729     "kind": "theorem",
2730     "module": "PaperIRelease.AlgebraDiagonal",
2731     "name": "Komorebi.PaperIRelease.diagonalProjection._proof_3",
2732     "runtime_only": false
2733   },
2734   {
2735     "axioms": [
2736       "propext",
2737       "Classical.choice",
2738       "Quot.sound"
2739     ],
2740     "in_project_namespace": true,
2741     "kind": "theorem",
2742     "module": "PaperICompletion5.CyclicGeometricCriterion",
2743     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_8",
2744     "runtime_only": false
2745   },
2746   {
2747     "axioms": [
2748       "propext",
2749       "Quot.sound"
2750     ],
2751     "in_project_namespace": true,
2752     "kind": "theorem",
2753     "module": "KomorebiVerification.SingleOperatorGraph",
2754     "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_4",
2755     "runtime_only": false
2756   },
2757   {
2758     "axioms": [
2759       "propext",
2760       "Classical.choice",
2761       "Quot.sound"
2762     ],
2763     "in_project_namespace": true,
2764     "kind": "definition",
2765     "module": "PaperIRelease.PacketLocalRank",
2766     "name": "Komorebi.PaperIRelease.localPureSeedRank",
2767     "runtime_only": false
2768   },
2769   {
2770     "axioms": [
2771       "propext",
2772       "Classical.choice",
2773       "Quot.sound"
2774     ],
2775     "in_project_namespace": true,
2776     "kind": "theorem",
2777     "module": "PaperIRelease.CategoryBoundaries",
2778     "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_1",
2779     "runtime_only": false
2780   },
2781   {
2782     "axioms": [
2783       "propext",
2784       "Classical.choice",
2785       "Quot.sound"
2786     ],
2787     "in_project_namespace": false,
2788     "kind": "definition",
2789     "module": "PaperIRelease.TopologyUnconditional",
2790     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule",
2791     "runtime_only": false
2792   },
2793   {
2794     "axioms": [
2795       "propext",
2796       "Classical.choice",
2797       "Quot.sound"
2798     ],
2799     "in_project_namespace": true,
2800     "kind": "theorem",
2801     "module": "KomorebiVerification.PacketNaturalityCompletion",
2802     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_ne_zero",
2803     "runtime_only": false
2804   },
2805   {
2806     "axioms": [
2807       "propext",
2808       "Classical.choice",
2809       "Quot.sound"
2810     ],
2811     "in_project_namespace": true,
2812     "kind": "theorem",
2813     "module": "PaperICompletion5.GeometricSeedFormula",
2814     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.monic_irreducible_eq_X_sub_C",
2815     "runtime_only": false
2816   },
2817   {
2818     "axioms": [
2819       "propext",
2820       "Classical.choice",
2821       "Quot.sound"
2822     ],
2823     "in_project_namespace": true,
2824     "kind": "theorem",
2825     "module": "PaperIRelease.PacketEquivalentNorm",
2826     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_3",
2827     "runtime_only": false
2828   },
2829   {
2830     "axioms": [
2831       "propext",
2832       "Classical.choice",
2833       "Quot.sound"
2834     ],
2835     "in_project_namespace": false,
2836     "kind": "theorem",
2837     "module": "PaperIRelease.TopologyCountablePackets",
2838     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_21",
2839     "runtime_only": false
2840   },
2841   {
2842     "axioms": [],
2843     "in_project_namespace": true,
2844     "kind": "definition",
2845     "module": "KomorebiVerification.PathGraphKrylov",
2846     "name": "Komorebi.PathGraphKrylov.rightTerm",
2847     "runtime_only": false
2848   },
2849   {
2850     "axioms": [],
2851     "in_project_namespace": true,
2852     "kind": "definition",
2853     "module": "KomorebiVerification.ResidueProjectors",
2854     "name": "Komorebi.Residue.residueAddress",
2855     "runtime_only": false
2856   },
2857   {
2858     "axioms": [
2859       "propext",
2860       "Classical.choice",
2861       "Quot.sound"
2862     ],
2863     "in_project_namespace": true,
2864     "kind": "definition",
2865     "module": "KomorebiVerification.EllipticAlgorithms",
2866     "name": "Komorebi.FiniteAlgorithms.orbitClosureChain",
2867     "runtime_only": false
2868   },
2869   {
2870     "axioms": [
2871       "propext"
2872     ],
2873     "in_project_namespace": true,
2874     "kind": "theorem",
2875     "module": "KomorebiVerification.SingleOperatorGraph",
2876     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun._simp_1_3",
2877     "runtime_only": false
2878   },
2879   {
2880     "axioms": [
2881       "propext",
2882       "Classical.choice",
2883       "Quot.sound"
2884     ],
2885     "in_project_namespace": true,
2886     "kind": "theorem",
2887     "module": "PaperIRelease.GrammarAlgebra",
2888     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_idempotent",
2889     "runtime_only": false
2890   },
2891   {
2892     "axioms": [
2893       "propext",
2894       "Quot.sound"
2895     ],
2896     "in_project_namespace": true,
2897     "kind": "theorem",
2898     "module": "KomorebiVerification.SeedRankOperations",
2899     "name": "Komorebi.SeedRankOperations.productModule._proof_5",
2900     "runtime_only": false
2901   },
2902   {
2903     "axioms": [],
2904     "in_project_namespace": true,
2905     "kind": "definition",
2906     "module": "PaperIRelease.CategoryExport",
2907     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorElim",
2908     "runtime_only": false
2909   },
2910   {
2911     "axioms": [
2912       "propext",
2913       "Classical.choice",
2914       "Quot.sound"
2915     ],
2916     "in_project_namespace": true,
2917     "kind": "theorem",
2918     "module": "KomorebiVerification.TopologicalCompletion",
2919     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_1",
2920     "runtime_only": false
2921   },
2922   {
2923     "axioms": [],
2924     "in_project_namespace": true,
2925     "kind": "theorem",
2926     "module": "KomorebiVerification.ProjectorCore",
2927     "name": "Komorebi.Seed.OperatorExpr.atom.sizeOf_spec",
2928     "runtime_only": false
2929   },
2930   {
2931     "axioms": [],
2932     "in_project_namespace": true,
2933     "kind": "definition",
2934     "module": "PaperIRelease.CategoryExport",
2935     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.recOn",
2936     "runtime_only": false
2937   },
2938   {
2939     "axioms": [
2940       "propext",
2941       "Classical.choice",
2942       "Quot.sound"
2943     ],
2944     "in_project_namespace": true,
2945     "kind": "theorem",
2946     "module": "PaperICompletion8.SemisimpleExistence",
2947     "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_compatible_presentation",
2948     "runtime_only": false
2949   },
2950   {
2951     "axioms": [
2952       "propext",
2953       "Classical.choice",
2954       "Quot.sound"
2955     ],
2956     "in_project_namespace": true,
2957     "kind": "definition",
2958     "module": "KomorebiVerification.ProjectorCore",
2959     "name": "Komorebi.Foundation.LinearProjectorFamily.recOn",
2960     "runtime_only": false
2961   },
2962   {
2963     "axioms": [
2964       "propext",
2965       "Classical.choice",
2966       "Quot.sound"
2967     ],
2968     "in_project_namespace": true,
2969     "kind": "theorem",
2970     "module": "PaperIRelease.GeneralNormedPackets",
2971     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet._proof_1",
2972     "runtime_only": false
2973   },
2974   {
2975     "axioms": [
2976       "propext",
2977       "Classical.choice",
2978       "Quot.sound"
2979     ],
2980     "in_project_namespace": true,
2981     "kind": "theorem",
2982     "module": "PaperIRelease.TensorPackets",
2983     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_3",
2984     "runtime_only": false
2985   },
2986   {
2987     "axioms": [
2988       "propext",
2989       "Classical.choice",
2990       "Quot.sound"
2991     ],
2992     "in_project_namespace": true,
2993     "kind": "theorem",
2994     "module": "PaperICompletion3.OperatorPrimaryAPI",
2995     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedRank_eq",
2996     "runtime_only": false
2997   },
2998   {
2999     "axioms": [
3000       "propext",
3001       "Classical.choice",
3002       "Quot.sound"
3003     ],
3004     "in_project_namespace": false,
3005     "kind": "definition",
3006     "module": "PaperIRelease.TopologyCountablePackets",
3007     "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace",
3008     "runtime_only": false
3009   },
3010   {
3011     "axioms": [
3012       "propext",
3013       "Classical.choice",
3014       "Quot.sound"
3015     ],
3016     "in_project_namespace": false,
3017     "kind": "theorem",
3018     "module": "PaperIRelease.TopologyUnconditional",
3019     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_11",
3020     "runtime_only": false
3021   },
3022   {
3023     "axioms": [
3024       "propext",
3025       "Classical.choice",
3026       "Quot.sound"
3027     ],
3028     "in_project_namespace": true,
3029     "kind": "theorem",
3030     "module": "KomorebiVerification.SemisimpleSeedRank",
3031     "name": "Komorebi.SemisimpleSeedRank.exists_leftGenerators_iff",
3032     "runtime_only": false
3033   },
3034   {
3035     "axioms": [
3036       "propext",
3037       "Classical.choice",
3038       "Quot.sound"
3039     ],
3040     "in_project_namespace": true,
3041     "kind": "definition",
3042     "module": "PaperIRelease.PacketCorners",
3043     "name": "Komorebi.PaperIRelease.cornerCompression",
3044     "runtime_only": false
3045   },
3046   {
3047     "axioms": [
3048       "propext",
3049       "Quot.sound"
3050     ],
3051     "in_project_namespace": true,
3052     "kind": "theorem",
3053     "module": "KomorebiVerification.PacketNaturalityCompletion",
3054     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2081.eq_1",
3055     "runtime_only": false
3056   },
3057   {
3058     "axioms": [
3059       "propext",
3060       "Quot.sound"
3061     ],
3062     "in_project_namespace": true,
3063     "kind": "theorem",
3064     "module": "KomorebiVerification.PathGraphKrylov",
3065     "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt",
3066     "runtime_only": false
3067   },
3068   {
3069     "axioms": [
3070       "propext",
3071       "Classical.choice",
3072       "Quot.sound"
3073     ],
3074     "in_project_namespace": true,
3075     "kind": "theorem",
3076     "module": "PaperICompletion7.Nakayama",
3077     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_3",
3078     "runtime_only": false
3079   },
3080   {
3081     "axioms": [
3082       "propext",
3083       "Quot.sound"
3084     ],
3085     "in_project_namespace": true,
3086     "kind": "definition",
3087     "module": "PaperIRelease.GrammarModules",
3088     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.noConfusionType",
3089     "runtime_only": false
3090   },
3091   {
3092     "axioms": [
3093       "propext",
3094       "Classical.choice",
3095       "Quot.sound"
3096     ],
3097     "in_project_namespace": true,
3098     "kind": "theorem",
3099     "module": "KomorebiVerification.SingleOperatorGraph",
3100     "name": "Komorebi.SingleOperatorGraph.seedNumberLE_iff_operatorAlgebra_family._simp_1_2",
3101     "runtime_only": false
3102   },
3103   {
3104     "axioms": [
3105       "propext",
3106       "Quot.sound"
3107     ],
3108     "in_project_namespace": true,
3109     "kind": "definition",
3110     "module": "PaperIRelease.ScalarExtension",
3111     "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease",
3112     "runtime_only": false
3113   },
3114   {
3115     "axioms": [
3116       "propext",
3117       "Classical.choice",
3118       "Quot.sound"
3119     ],
3120     "in_project_namespace": false,
3121     "kind": "theorem",
3122     "module": "PaperIRelease.TopologyUnconditional",
3123     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_le_norm",
3124     "runtime_only": false
3125   },
3126   {
3127     "axioms": [],
3128     "in_project_namespace": true,
3129     "kind": "definition",
3130     "module": "KomorebiVerification.ProjectorCore",
3131     "name": "Komorebi.FormalizationStatus.noConfusion",
3132     "runtime_only": false
3133   },
3134   {
3135     "axioms": [
3136       "propext",
3137       "Classical.choice",
3138       "Quot.sound"
3139     ],
3140     "in_project_namespace": true,
3141     "kind": "definition",
3142     "module": "PaperICompletion4.OperatorIntrinsicFormula",
3143     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity",
3144     "runtime_only": false
3145   },
3146   {
3147     "axioms": [],
3148     "in_project_namespace": true,
3149     "kind": "theorem",
3150     "module": "KomorebiVerification.ProjectorCore",
3151     "name": "Komorebi.Seed.OperatorExpr.comp.inj",
3152     "runtime_only": false
3153   },
3154   {
3155     "axioms": [
3156       "propext",
3157       "Classical.choice",
3158       "Quot.sound"
3159     ],
3160     "in_project_namespace": true,
3161     "kind": "theorem",
3162     "module": "KomorebiVerification.PacketNaturalityCompletion",
3163     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_3",
3164     "runtime_only": false
3165   },
3166   {
3167     "axioms": [
3168       "propext",
3169       "Quot.sound"
3170     ],
3171     "in_project_namespace": true,
3172     "kind": "definition",
3173     "module": "PaperIRelease.GrammarAlgebra",
3174     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar._sizeOf_1",
3175     "runtime_only": false
3176   },
3177   {
3178     "axioms": [
3179       "propext",
3180       "Classical.choice",
3181       "Quot.sound"
3182     ],
3183     "in_project_namespace": false,
3184     "kind": "theorem",
3185     "module": "PaperIRelease.AlgebraPreorder",
3186     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono._simp_1_2",
3187     "runtime_only": false
3188   },
3189   {
3190     "axioms": [
3191       "propext",
3192       "Classical.choice",
3193       "Quot.sound"
3194     ],
3195     "in_project_namespace": true,
3196     "kind": "theorem",
3197     "module": "PaperIRelease.GrammarAlgebra",
3198     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction_action",
3199     "runtime_only": false
3200   },
3201   {
3202     "axioms": [
3203       "propext",
3204       "Classical.choice",
3205       "Quot.sound"
3206     ],
3207     "in_project_namespace": true,
3208     "kind": "theorem",
3209     "module": "PaperIRelease.CategoryPackets",
3210     "name": "Komorebi.PaperIRelease.CategoryPackets.imageHull_le",
3211     "runtime_only": false
3212   },
3213   {
3214     "axioms": [
3215       "propext",
3216       "Classical.choice",
3217       "Quot.sound"
3218     ],
3219     "in_project_namespace": true,
3220     "kind": "theorem",
3221     "module": "KomorebiVerification.SeedRankBasics",
3222     "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv_apply_mk",
3223     "runtime_only": false
3224   },
3225   {
3226     "axioms": [
3227       "propext",
3228       "Classical.choice",
3229       "Quot.sound"
3230     ],
3231     "in_project_namespace": false,
3232     "kind": "definition",
3233     "module": "PaperIRelease.TopologyUnconditional",
3234     "name": "PaperIRelease.TopologyUnconditional.finiteSum",
3235     "runtime_only": false
3236   },
3237   {
3238     "axioms": [
3239       "propext",
3240       "Classical.choice",
3241       "Quot.sound"
3242     ],
3243     "in_project_namespace": true,
3244     "kind": "theorem",
3245     "module": "PaperIRelease.CategoryBoundaries",
3246     "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_2",
3247     "runtime_only": false
3248   },
3249   {
3250     "axioms": [
3251       "propext",
3252       "Classical.choice",
3253       "Quot.sound"
3254     ],
3255     "in_project_namespace": true,
3256     "kind": "theorem",
3257     "module": "PaperIRelease.GrammarTyped",
3258     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_idempotent",
3259     "runtime_only": false
3260   },
3261   {
3262     "axioms": [
3263       "propext",
3264       "Classical.choice",
3265       "Quot.sound"
3266     ],
3267     "in_project_namespace": true,
3268     "kind": "theorem",
3269     "module": "PaperIRelease.GraphSources",
3270     "name": "Komorebi.PaperIRelease.FiniteDigraph.source_iff_no_incoming_edge",
3271     "runtime_only": false
3272   },
3273   {
3274     "axioms": [
3275       "propext",
3276       "Classical.choice",
3277       "Quot.sound"
3278     ],
3279     "in_project_namespace": true,
3280     "kind": "definition",
3281     "module": "PaperICompletion5.GeometricSeedFormula",
3282     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues",
3283     "runtime_only": false
3284   },
3285   {
3286     "axioms": [
3287       "propext",
3288       "Classical.choice",
3289       "Quot.sound"
3290     ],
3291     "in_project_namespace": true,
3292     "kind": "definition",
3293     "module": "PaperICompletion5.CyclicGeometricCriterion",
3294     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv",
3295     "runtime_only": false
3296   },
3297   {
3298     "axioms": [
3299       "propext",
3300       "Quot.sound"
3301     ],
3302     "in_project_namespace": true,
3303     "kind": "definition",
3304     "module": "PaperIRelease.GrammarTyped",
3305     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.noConfusion",
3306     "runtime_only": false
3307   },
3308   {
3309     "axioms": [
3310       "propext",
3311       "Classical.choice",
3312       "Quot.sound"
3313     ],
3314     "in_project_namespace": true,
3315     "kind": "definition",
3316     "module": "PaperICompletion3.OperatorPrimaryAPI",
3317     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount",
3318     "runtime_only": false
3319   },
3320   {
3321     "axioms": [
3322       "propext",
3323       "Quot.sound"
3324     ],
3325     "in_project_namespace": true,
3326     "kind": "theorem",
3327     "module": "KomorebiVerification.PathGraphKrylov",
3328     "name": "Komorebi.PathGraphKrylov.krylov_diagonal._proof_1_2",
3329     "runtime_only": false
3330   },
3331   {
3332     "axioms": [
3333       "propext",
3334       "Classical.choice",
3335       "Quot.sound"
3336     ],
3337     "in_project_namespace": false,
3338     "kind": "theorem",
3339     "module": "ReleaseBoundary",
3340     "name": "PaperIBlock08Tests.quaternion_one_seed_insufficient",
3341     "runtime_only": false
3342   },
3343   {
3344     "axioms": [
3345       "propext",
3346       "Classical.choice",
3347       "Quot.sound"
3348     ],
3349     "in_project_namespace": true,
3350     "kind": "theorem",
3351     "module": "KomorebiVerification.TopologicalCompletion",
3352     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_2",
3353     "runtime_only": false
3354   },
3355   {
3356     "axioms": [
3357       "propext",
3358       "Classical.choice",
3359       "Quot.sound"
3360     ],
3361     "in_project_namespace": true,
3362     "kind": "definition",
3363     "module": "PaperIRelease.PacketAggregation",
3364     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeDirectSumEquiv",
3365     "runtime_only": false
3366   },
3367   {
3368     "axioms": [
3369       "propext",
3370       "Classical.choice",
3371       "Quot.sound"
3372     ],
3373     "in_project_namespace": false,
3374     "kind": "theorem",
3375     "module": "PaperIRelease.TopologyUnconditionalBridge",
3376     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_3",
3377     "runtime_only": false
3378   },
3379   {
3380     "axioms": [],
3381     "in_project_namespace": true,
3382     "kind": "definition",
3383     "module": "PaperIRelease.CategoryExport",
3384     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.elim",
3385     "runtime_only": false
3386   },
3387   {
3388     "axioms": [
3389       "propext",
3390       "Classical.choice",
3391       "Quot.sound"
3392     ],
3393     "in_project_namespace": true,
3394     "kind": "definition",
3395     "module": "KomorebiVerification.PacketNaturalityCompletion",
3396     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraTransferPattern",
3397     "runtime_only": false
3398   },
3399   {
3400     "axioms": [
3401       "propext",
3402       "Classical.choice",
3403       "Quot.sound"
3404     ],
3405     "in_project_namespace": true,
3406     "kind": "theorem",
3407     "module": "PaperIRelease.GrammarTyped",
3408     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_3",
3409     "runtime_only": false
3410   },
3411   {
3412     "axioms": [
3413       "propext",
3414       "Classical.choice",
3415       "Quot.sound"
3416     ],
3417     "in_project_namespace": true,
3418     "kind": "definition",
3419     "module": "PaperIRelease.GeneralNormedPackets",
3420     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.noConfusion",
3421     "runtime_only": false
3422   },
3423   {
3424     "axioms": [
3425       "Quot.sound"
3426     ],
3427     "in_project_namespace": true,
3428     "kind": "theorem",
3429     "module": "KomorebiVerification.ProjectorCore",
3430     "name": "Komorebi.Packet.coordinateProj.congr_simp",
3431     "runtime_only": false
3432   },
3433   {
3434     "axioms": [
3435       "propext",
3436       "Classical.choice",
3437       "Quot.sound"
3438     ],
3439     "in_project_namespace": true,
3440     "kind": "theorem",
3441     "module": "PaperICompletion3.PrimarySeedFormula",
3442     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_operator_primary_seed_formula",
3443     "runtime_only": false
3444   },
3445   {
3446     "axioms": [
3447       "propext",
3448       "Classical.choice",
3449       "Quot.sound"
3450     ],
3451     "in_project_namespace": true,
3452     "kind": "theorem",
3453     "module": "PaperICompletion.CyclicClassification",
3454     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_2",
3455     "runtime_only": false
3456   },
3457   {
3458     "axioms": [],
3459     "in_project_namespace": true,
3460     "kind": "definition",
3461     "module": "KomorebiVerification.ProjectorCore",
3462     "name": "Komorebi.ClaimRecord.sourceStatus._default",
3463     "runtime_only": false
3464   },
3465   {
3466     "axioms": [
3467       "propext",
3468       "Classical.choice",
3469       "Quot.sound"
3470     ],
3471     "in_project_namespace": true,
3472     "kind": "theorem",
3473     "module": "PaperIRelease.PacketBoundaryTests",
3474     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_quotient_projector_norm_zero",
3475     "runtime_only": false
3476   },
3477   {
3478     "axioms": [
3479       "propext",
3480       "Classical.choice",
3481       "Quot.sound"
3482     ],
3483     "in_project_namespace": false,
3484     "kind": "definition",
3485     "module": "PaperIRelease.TopologyCountablePackets",
3486     "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound",
3487     "runtime_only": false
3488   },
3489   {
3490     "axioms": [
3491       "propext",
3492       "Quot.sound"
3493     ],
3494     "in_project_namespace": true,
3495     "kind": "theorem",
3496     "module": "PaperIRelease.AlgebraDiagonal",
3497     "name": "Komorebi.PaperIRelease.diagonalProjection._proof_1",
3498     "runtime_only": false
3499   },
3500   {
3501     "axioms": [
3502       "propext",
3503       "Quot.sound"
3504     ],
3505     "in_project_namespace": true,
3506     "kind": "theorem",
3507     "module": "PaperICompletion6.OneInvariantFactor",
3508     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_2",
3509     "runtime_only": false
3510   },
3511   {
3512     "axioms": [
3513       "propext",
3514       "Quot.sound"
3515     ],
3516     "in_project_namespace": true,
3517     "kind": "theorem",
3518     "module": "PaperIRelease.GrammarModules",
3519     "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_2",
3520     "runtime_only": false
3521   },
3522   {
3523     "axioms": [
3524       "propext",
3525       "Classical.choice",
3526       "Quot.sound"
3527     ],
3528     "in_project_namespace": true,
3529     "kind": "theorem",
3530     "module": "PaperIRelease.PacketTopology",
3531     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient._proof_2",
3532     "runtime_only": false
3533   },
3534   {
3535     "axioms": [
3536       "propext",
3537       "Classical.choice",
3538       "Quot.sound"
3539     ],
3540     "in_project_namespace": true,
3541     "kind": "theorem",
3542     "module": "PaperIRelease.PacketDescent",
3543     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_2",
3544     "runtime_only": false
3545   },
3546   {
3547     "axioms": [],
3548     "in_project_namespace": true,
3549     "kind": "definition",
3550     "module": "PaperIRelease.GrammarPaths",
3551     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.recOn",
3552     "runtime_only": false
3553   },
3554   {
3555     "axioms": [
3556       "propext",
3557       "Classical.choice",
3558       "Quot.sound"
3559     ],
3560     "in_project_namespace": true,
3561     "kind": "definition",
3562     "module": "PaperICompletion8.RegularMultiplicity",
3563     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv",
3564     "runtime_only": false
3565   },
3566   {
3567     "axioms": [
3568       "propext",
3569       "Classical.choice",
3570       "Quot.sound"
3571     ],
3572     "in_project_namespace": true,
3573     "kind": "theorem",
3574     "module": "KomorebiVerification.PacketNaturalityCompletion",
3575     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable",
3576     "runtime_only": false
3577   },
3578   {
3579     "axioms": [
3580       "propext",
3581       "Classical.choice",
3582       "Quot.sound"
3583     ],
3584     "in_project_namespace": true,
3585     "kind": "constructor",
3586     "module": "PaperIRelease.GeneralNormedPackets",
3587     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk",
3588     "runtime_only": false
3589   },
3590   {
3591     "axioms": [],
3592     "in_project_namespace": true,
3593     "kind": "definition",
3594     "module": "KomorebiVerification.ProjectorCore",
3595     "name": "Komorebi.Seed.OperatorRelation.Satisfied",
3596     "runtime_only": false
3597   },
3598   {
3599     "axioms": [
3600       "propext",
3601       "Classical.choice",
3602       "Quot.sound"
3603     ],
3604     "in_project_namespace": false,
3605     "kind": "definition",
3606     "module": "PaperIRelease.TopologyUnconditional",
3607     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.noConfusion",
3608     "runtime_only": false
3609   },
3610   {
3611     "axioms": [
3612       "propext",
3613       "Classical.choice",
3614       "Quot.sound"
3615     ],
3616     "in_project_namespace": true,
3617     "kind": "theorem",
3618     "module": "KomorebiVerification.EllipticAlgorithms",
3619     "name": "Komorebi.EllipticCoordinates.My._proof_1",
3620     "runtime_only": false
3621   },
3622   {
3623     "axioms": [
3624       "propext",
3625       "Quot.sound"
3626     ],
3627     "in_project_namespace": true,
3628     "kind": "definition",
3629     "module": "PaperIRelease.GrammarTyped",
3630     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.addCommGroup",
3631     "runtime_only": false
3632   },
3633   {
3634     "axioms": [
3635       "propext",
3636       "Classical.choice",
3637       "Quot.sound"
3638     ],
3639     "in_project_namespace": true,
3640     "kind": "definition",
3641     "module": "PaperIRelease.PolynomialModule",
3642     "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction",
3643     "runtime_only": false
3644   },
3645   {
3646     "axioms": [
3647       "propext",
3648       "Classical.choice",
3649       "Quot.sound"
3650     ],
3651     "in_project_namespace": true,
3652     "kind": "definition",
3653     "module": "PaperIRelease.CategoryPackets",
3654     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.linearMap",
3655     "runtime_only": false
3656   },
3657   {
3658     "axioms": [],
3659     "in_project_namespace": true,
3660     "kind": "constructor",
3661     "module": "KomorebiVerification.ProjectorCore",
3662     "name": "Komorebi.ClaimKind.exampleClaim",
3663     "runtime_only": false
3664   },
3665   {
3666     "axioms": [],
3667     "in_project_namespace": true,
3668     "kind": "definition",
3669     "module": "PaperIRelease.CategoryExport",
3670     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.noConfusion",
3671     "runtime_only": false
3672   },
3673   {
3674     "axioms": [
3675       "propext",
3676       "Classical.choice",
3677       "Quot.sound"
3678     ],
3679     "in_project_namespace": true,
3680     "kind": "theorem",
3681     "module": "PaperIRelease.GrammarIdeal",
3682     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealToPresented_quotient",
3683     "runtime_only": false
3684   },
3685   {
3686     "axioms": [
3687       "propext",
3688       "Quot.sound"
3689     ],
3690     "in_project_namespace": true,
3691     "kind": "theorem",
3692     "module": "PaperIRelease.GrammarModules",
3693     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_1",
3694     "runtime_only": false
3695   },
3696   {
3697     "axioms": [
3698       "propext",
3699       "Classical.choice",
3700       "Quot.sound"
3701     ],
3702     "in_project_namespace": true,
3703     "kind": "definition",
3704     "module": "PaperIRelease.GrammarTyped",
3705     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator",
3706     "runtime_only": false
3707   },
3708   {
3709     "axioms": [
3710       "propext",
3711       "Classical.choice",
3712       "Quot.sound"
3713     ],
3714     "in_project_namespace": true,
3715     "kind": "definition",
3716     "module": "PaperIRelease.PacketAggregation",
3717     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily",
3718     "runtime_only": false
3719   },
3720   {
3721     "axioms": [
3722       "propext",
3723       "Classical.choice",
3724       "Quot.sound"
3725     ],
3726     "in_project_namespace": true,
3727     "kind": "theorem",
3728     "module": "PaperICompletion7.Nakayama",
3729     "name": "Komorebi.PaperICompletion7.Nakayama.map_eq_top_iff",
3730     "runtime_only": false
3731   },
3732   {
3733     "axioms": [],
3734     "in_project_namespace": true,
3735     "kind": "constructor",
3736     "module": "KomorebiVerification.ProjectorCore",
3737     "name": "Komorebi.FormalizationStatus.conjectural",
3738     "runtime_only": false
3739   },
3740   {
3741     "axioms": [
3742       "propext",
3743       "Classical.choice",
3744       "Quot.sound"
3745     ],
3746     "in_project_namespace": true,
3747     "kind": "theorem",
3748     "module": "PaperIRelease.TopologyCategories",
3749     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.sizeOf_spec",
3750     "runtime_only": false
3751   },
3752   {
3753     "axioms": [
3754       "propext",
3755       "Classical.choice",
3756       "Quot.sound"
3757     ],
3758     "in_project_namespace": false,
3759     "kind": "theorem",
3760     "module": "PaperIRelease.TopologySemilinearRank",
3761     "name": "PaperIRelease.TopologySemilinearRank.rank_le_of_continuous_semilinear_surjective",
3762     "runtime_only": false
3763   },
3764   {
3765     "axioms": [
3766       "propext",
3767       "Classical.choice",
3768       "Quot.sound"
3769     ],
3770     "in_project_namespace": true,
3771     "kind": "definition",
3772     "module": "PaperIRelease.GeneralNormedPackets",
3773     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily._sizeOf_inst",
3774     "runtime_only": false
3775   },
3776   {
3777     "axioms": [
3778       "propext",
3779       "Classical.choice",
3780       "Quot.sound"
3781     ],
3782     "in_project_namespace": true,
3783     "kind": "theorem",
3784     "module": "PaperICompletion6.PrimaryCyclicCriterion",
3785     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.submodule_cyclic_of_hasCyclicVector",
3786     "runtime_only": false
3787   },
3788   {
3789     "axioms": [
3790       "propext",
3791       "Quot.sound"
3792     ],
3793     "in_project_namespace": true,
3794     "kind": "theorem",
3795     "module": "KomorebiVerification.PathGraphKrylov",
3796     "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_2",
3797     "runtime_only": false
3798   },
3799   {
3800     "axioms": [
3801       "propext",
3802       "Classical.choice",
3803       "Quot.sound"
3804     ],
3805     "in_project_namespace": true,
3806     "kind": "theorem",
3807     "module": "PaperIRelease.PacketTopologyGeneral",
3808     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusion_bounded",
3809     "runtime_only": false
3810   },
3811   {
3812     "axioms": [
3813       "propext",
3814       "Classical.choice",
3815       "Quot.sound"
3816     ],
3817     "in_project_namespace": false,
3818     "kind": "theorem",
3819     "module": "PaperIRelease.TopologyDenseCompletion",
3820     "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion._proof_1",
3821     "runtime_only": false
3822   },
3823   {
3824     "axioms": [
3825       "propext",
3826       "Quot.sound"
3827     ],
3828     "in_project_namespace": true,
3829     "kind": "theorem",
3830     "module": "KomorebiVerification.SingleOperatorGraph",
3831     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_11",
3832     "runtime_only": false
3833   },
3834   {
3835     "axioms": [
3836       "propext",
3837       "Classical.choice",
3838       "Quot.sound"
3839     ],
3840     "in_project_namespace": true,
3841     "kind": "definition",
3842     "module": "PaperIRelease.PacketExactSequence",
3843     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates",
3844     "runtime_only": false
3845   },
3846   {
3847     "axioms": [
3848       "propext",
3849       "Quot.sound"
3850     ],
3851     "in_project_namespace": true,
3852     "kind": "definition",
3853     "module": "PaperIRelease.GrammarTyped",
3854     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.recOn",
3855     "runtime_only": false
3856   },
3857   {
3858     "axioms": [
3859       "propext",
3860       "Classical.choice",
3861       "Quot.sound"
3862     ],
3863     "in_project_namespace": true,
3864     "kind": "theorem",
3865     "module": "PaperIRelease.GeneralConditionedCoordinates",
3866     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.one_le_conditionNumber",
3867     "runtime_only": false
3868   },
3869   {
3870     "axioms": [
3871       "propext",
3872       "Classical.choice",
3873       "Quot.sound"
3874     ],
3875     "in_project_namespace": true,
3876     "kind": "theorem",
3877     "module": "PaperIRelease.PacketDescent",
3878     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_4",
3879     "runtime_only": false
3880   },
3881   {
3882     "axioms": [
3883       "propext",
3884       "Classical.choice",
3885       "Quot.sound"
3886     ],
3887     "in_project_namespace": true,
3888     "kind": "theorem",
3889     "module": "KomorebiVerification.PacketNaturalityCompletion",
3890     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_def",
3891     "runtime_only": false
3892   },
3893   {
3894     "axioms": [
3895       "propext",
3896       "Classical.choice",
3897       "Quot.sound"
3898     ],
3899     "in_project_namespace": true,
3900     "kind": "theorem",
3901     "module": "PaperICompletion4.OperatorIntrinsicFormula",
3902     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_7",
3903     "runtime_only": false
3904   },
3905   {
3906     "axioms": [
3907       "propext",
3908       "Classical.choice",
3909       "Quot.sound"
3910     ],
3911     "in_project_namespace": true,
3912     "kind": "theorem",
3913     "module": "KomorebiVerification.TopologicalCompletion",
3914     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.hasTopologicalSeedRankOne",
3915     "runtime_only": false
3916   },
3917   {
3918     "axioms": [
3919       "propext",
3920       "Classical.choice",
3921       "Quot.sound"
3922     ],
3923     "in_project_namespace": true,
3924     "kind": "theorem",
3925     "module": "PaperICompletion7.ModuleTop",
3926     "name": "Komorebi.PaperICompletion7.ModuleTop.seedRank_eq_radicalTop",
3927     "runtime_only": false
3928   },
3929   {
3930     "axioms": [
3931       "propext",
3932       "Classical.choice",
3933       "Quot.sound"
3934     ],
3935     "in_project_namespace": true,
3936     "kind": "theorem",
3937     "module": "KomorebiVerification.PathGraphKrylov",
3938     "name": "Komorebi.PathGraphKrylov.krylov_span_eq_top",
3939     "runtime_only": false
3940   },
3941   {
3942     "axioms": [
3943       "propext",
3944       "Classical.choice",
3945       "Quot.sound"
3946     ],
3947     "in_project_namespace": true,
3948     "kind": "definition",
3949     "module": "PaperIRelease.AlgebraTransfer",
3950     "name": "Komorebi.PaperIRelease.packetWordSum._sunfold",
3951     "runtime_only": false
3952   },
3953   {
3954     "axioms": [],
3955     "in_project_namespace": true,
3956     "kind": "theorem",
3957     "module": "PaperICompletion8.RegularMultiplicity",
3958     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_4",
3959     "runtime_only": false
3960   },
3961   {
3962     "axioms": [
3963       "propext"
3964     ],
3965     "in_project_namespace": true,
3966     "kind": "definition",
3967     "module": "PaperIRelease.CategoryExport",
3968     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._f",
3969     "runtime_only": false
3970   },
3971   {
3972     "axioms": [
3973       "propext"
3974     ],
3975     "in_project_namespace": true,
3976     "kind": "theorem",
3977     "module": "KomorebiVerification.TopologicalCompletion",
3978     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula._simp_1_3",
3979     "runtime_only": false
3980   },
3981   {
3982     "axioms": [
3983       "propext",
3984       "Classical.choice",
3985       "Quot.sound"
3986     ],
3987     "in_project_namespace": false,
3988     "kind": "theorem",
3989     "module": "ReleaseBoundary",
3990     "name": "PaperIBlock08Tests.quaternion_direct_sum_rank_two",
3991     "runtime_only": false
3992   },
3993   {
3994     "axioms": [
3995       "propext",
3996       "Classical.choice",
3997       "Quot.sound"
3998     ],
3999     "in_project_namespace": true,
4000     "kind": "theorem",
4001     "module": "KomorebiVerification.SemisimpleCompletion",
4002     "name": "Komorebi.SemisimpleCompletion.splitProduct_seedFinrank_eq_maxCeilDiv",
4003     "runtime_only": false
4004   },
4005   {
4006     "axioms": [
4007       "propext",
4008       "Classical.choice",
4009       "Quot.sound"
4010     ],
4011     "in_project_namespace": true,
4012     "kind": "theorem",
4013     "module": "KomorebiVerification.PacketNaturalityCompletion",
4014     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockAlgEquiv_apply",
4015     "runtime_only": false
4016   },
4017   {
4018     "axioms": [
4019       "propext",
4020       "Classical.choice",
4021       "Quot.sound"
4022     ],
4023     "in_project_namespace": false,
4024     "kind": "theorem",
4025     "module": "PaperIRelease.TopologyCountablePackets",
4026     "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_neg",
4027     "runtime_only": false
4028   },
4029   {
4030     "axioms": [
4031       "propext",
4032       "Classical.choice",
4033       "Quot.sound"
4034     ],
4035     "in_project_namespace": true,
4036     "kind": "theorem",
4037     "module": "KomorebiVerification.PacketNaturalityCompletion",
4038     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB_eV\u2083",
4039     "runtime_only": false
4040   },
4041   {
4042     "axioms": [],
4043     "in_project_namespace": true,
4044     "kind": "inductive",
4045     "module": "PaperIRelease.CategoryExport",
4046     "name": "Komorebi.PaperIRelease.CategoryExport.Expression",
4047     "runtime_only": false
4048   },
4049   {
4050     "axioms": [
4051       "propext",
4052       "Quot.sound"
4053     ],
4054     "in_project_namespace": true,
4055     "kind": "theorem",
4056     "module": "PaperICompletion4.OperatorIntrinsicFormula",
4057     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_1",
4058     "runtime_only": false
4059   },
4060   {
4061     "axioms": [
4062       "propext",
4063       "Classical.choice",
4064       "Quot.sound"
4065     ],
4066     "in_project_namespace": true,
4067     "kind": "theorem",
4068     "module": "PaperIRelease.GrammarEquivalence",
4069     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_action",
4070     "runtime_only": false
4071   },
4072   {
4073     "axioms": [
4074       "propext",
4075       "Classical.choice",
4076       "Quot.sound"
4077     ],
4078     "in_project_namespace": false,
4079     "kind": "theorem",
4080     "module": "PaperIRelease.TopologyCountablePackets",
4081     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv.eq_1",
4082     "runtime_only": false
4083   },
4084   {
4085     "axioms": [
4086       "propext",
4087       "Classical.choice",
4088       "Quot.sound"
4089     ],
4090     "in_project_namespace": true,
4091     "kind": "definition",
4092     "module": "PaperIRelease.GrammarEquivalence",
4093     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor",
4094     "runtime_only": false
4095   },
4096   {
4097     "axioms": [
4098       "propext",
4099       "Classical.choice",
4100       "Quot.sound"
4101     ],
4102     "in_project_namespace": true,
4103     "kind": "definition",
4104     "module": "PaperIRelease.CategoryPackets",
4105     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.noConfusion",
4106     "runtime_only": false
4107   },
4108   {
4109     "axioms": [
4110       "propext",
4111       "Classical.choice",
4112       "Quot.sound"
4113     ],
4114     "in_project_namespace": true,
4115     "kind": "theorem",
4116     "module": "PaperIRelease.AlgebraClassGrouping",
4117     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_12",
4118     "runtime_only": false
4119   },
4120   {
4121     "axioms": [
4122       "propext",
4123       "Classical.choice",
4124       "Quot.sound"
4125     ],
4126     "in_project_namespace": true,
4127     "kind": "theorem",
4128     "module": "PaperIRelease.PacketBoundaryTests",
4129     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.empty_family_packet_exact",
4130     "runtime_only": false
4131   },
4132   {
4133     "axioms": [
4134       "propext",
4135       "Classical.choice",
4136       "Quot.sound"
4137     ],
4138     "in_project_namespace": false,
4139     "kind": "theorem",
4140     "module": "PaperIRelease.TopologyCountablePackets",
4141     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv_symm_apply",
4142     "runtime_only": false
4143   },
4144   {
4145     "axioms": [
4146       "propext",
4147       "Classical.choice",
4148       "Quot.sound"
4149     ],
4150     "in_project_namespace": true,
4151     "kind": "theorem",
4152     "module": "KomorebiVerification.SingleOperatorGraph",
4153     "name": "Komorebi.SingleOperatorGraph.evalVector_apply",
4154     "runtime_only": false
4155   },
4156   {
4157     "axioms": [
4158       "propext",
4159       "Classical.choice",
4160       "Quot.sound"
4161     ],
4162     "in_project_namespace": true,
4163     "kind": "theorem",
4164     "module": "PaperIRelease.GraphSources",
4165     "name": "Komorebi.PaperIRelease.FiniteDigraph.sourcesFintype._proof_1",
4166     "runtime_only": false
4167   },
4168   {
4169     "axioms": [
4170       "propext",
4171       "Quot.sound"
4172     ],
4173     "in_project_namespace": true,
4174     "kind": "theorem",
4175     "module": "PaperIRelease.ScalarExtension",
4176     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_2",
4177     "runtime_only": false
4178   },
4179   {
4180     "axioms": [
4181       "propext",
4182       "Classical.choice",
4183       "Quot.sound"
4184     ],
4185     "in_project_namespace": true,
4186     "kind": "theorem",
4187     "module": "PaperICompletion5.GeometricSeedFormula",
4188     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedFinrank_eq_spectralSeedMaximum",
4189     "runtime_only": false
4190   },
4191   {
4192     "axioms": [
4193       "propext",
4194       "Quot.sound"
4195     ],
4196     "in_project_namespace": true,
4197     "kind": "theorem",
4198     "module": "KomorebiVerification.SeedRankOperations",
4199     "name": "Komorebi.SeedRankOperations.prodSndSemilinear._proof_2",
4200     "runtime_only": false
4201   },
4202   {
4203     "axioms": [
4204       "propext",
4205       "Classical.choice",
4206       "Quot.sound"
4207     ],
4208     "in_project_namespace": true,
4209     "kind": "theorem",
4210     "module": "PaperIRelease.PacketTopology",
4211     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientLiftCLM._proof_1",
4212     "runtime_only": false
4213   },
4214   {
4215     "axioms": [
4216       "propext",
4217       "Classical.choice",
4218       "Quot.sound"
4219     ],
4220     "in_project_namespace": true,
4221     "kind": "theorem",
4222     "module": "KomorebiVerification.EllipticAlgorithms",
4223     "name": "Komorebi.FiniteAlgorithms.mem_graphSpectrum_iff",
4224     "runtime_only": false
4225   },
4226   {
4227     "axioms": [
4228       "propext",
4229       "Classical.choice",
4230       "Quot.sound"
4231     ],
4232     "in_project_namespace": true,
4233     "kind": "definition",
4234     "module": "KomorebiVerification.EllipticAlgorithms",
4235     "name": "Komorebi.EllipticCoordinates.packetProjectors",
4236     "runtime_only": false
4237   },
4238   {
4239     "axioms": [
4240       "propext",
4241       "Classical.choice",
4242       "Quot.sound"
4243     ],
4244     "in_project_namespace": true,
4245     "kind": "theorem",
4246     "module": "PaperIRelease.GrammarIdeal",
4247     "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeToIdeal_respects",
4248     "runtime_only": false
4249   },
4250   {
4251     "axioms": [],
4252     "in_project_namespace": true,
4253     "kind": "definition",
4254     "module": "KomorebiVerification.ProjectorCore",
4255     "name": "Komorebi.Seed.OperatorExpr.ctorIdx",
4256     "runtime_only": false
4257   },
4258   {
4259     "axioms": [
4260       "propext",
4261       "Classical.choice",
4262       "Quot.sound"
4263     ],
4264     "in_project_namespace": true,
4265     "kind": "theorem",
4266     "module": "PaperIRelease.GraphPropagation",
4267     "name": "Komorebi.PaperIRelease.range_le_of_surjective_block",
4268     "runtime_only": false
4269   },
4270   {
4271     "axioms": [
4272       "propext",
4273       "Classical.choice",
4274       "Quot.sound"
4275     ],
4276     "in_project_namespace": true,
4277     "kind": "theorem",
4278     "module": "PaperICompletion.CyclicClassification",
4279     "name": "Komorebi.PaperICompletion.CyclicClassification.cyclic_of_minpoly_degree_eq_finrank",
4280     "runtime_only": false
4281   },
4282   {
4283     "axioms": [
4284       "propext",
4285       "Classical.choice",
4286       "Quot.sound"
4287     ],
4288     "in_project_namespace": true,
4289     "kind": "definition",
4290     "module": "KomorebiVerification.ProjectorCore",
4291     "name": "Komorebi.Foundation.LinearProjectorFamily.proj",
4292     "runtime_only": false
4293   },
4294   {
4295     "axioms": [
4296       "propext",
4297       "Classical.choice",
4298       "Quot.sound"
4299     ],
4300     "in_project_namespace": true,
4301     "kind": "definition",
4302     "module": "PaperIRelease.PacketDescent",
4303     "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype",
4304     "runtime_only": false
4305   },
4306   {
4307     "axioms": [
4308       "propext",
4309       "Classical.choice",
4310       "Quot.sound"
4311     ],
4312     "in_project_namespace": false,
4313     "kind": "definition",
4314     "module": "PaperIRelease.TopologyPresentations",
4315     "name": "PaperIRelease.TopologyDenseCompletion.completedRestrictedQuotient",
4316     "runtime_only": false
4317   },
4318   {
4319     "axioms": [
4320       "propext",
4321       "Classical.choice",
4322       "Quot.sound"
4323     ],
4324     "in_project_namespace": true,
4325     "kind": "definition",
4326     "module": "PaperIRelease.AlgebraSupport",
4327     "name": "Komorebi.PaperIRelease.supportSubalgebra",
4328     "runtime_only": false
4329   },
4330   {
4331     "axioms": [
4332       "propext",
4333       "Quot.sound"
4334     ],
4335     "in_project_namespace": true,
4336     "kind": "theorem",
4337     "module": "PaperIRelease.PacketUniversal",
4338     "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut._proof_1",
4339     "runtime_only": false
4340   },
4341   {
4342     "axioms": [
4343       "propext",
4344       "Classical.choice",
4345       "Quot.sound"
4346     ],
4347     "in_project_namespace": true,
4348     "kind": "theorem",
4349     "module": "KomorebiVerification.SeedRankBasics",
4350     "name": "Komorebi.SeedRankBasics.cyclic_iff_exists_surjective_oneSeedMap._simp_1_2",
4351     "runtime_only": false
4352   },
4353   {
4354     "axioms": [
4355       "propext",
4356       "Classical.choice",
4357       "Quot.sound"
4358     ],
4359     "in_project_namespace": true,
4360     "kind": "definition",
4361     "module": "PaperIRelease.CategoryPackets",
4362     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism._sizeOf_1",
4363     "runtime_only": false
4364   },
4365   {
4366     "axioms": [
4367       "propext",
4368       "Quot.sound"
4369     ],
4370     "in_project_namespace": true,
4371     "kind": "theorem",
4372     "module": "PaperIRelease.ScalarExtension",
4373     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightTowerInstalled",
4374     "runtime_only": false
4375   },
4376   {
4377     "axioms": [
4378       "propext",
4379       "Classical.choice",
4380       "Quot.sound"
4381     ],
4382     "in_project_namespace": true,
4383     "kind": "theorem",
4384     "module": "KomorebiVerification.PacketNaturalityCompletion",
4385     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.typed_reachability_certificate",
4386     "runtime_only": false
4387   },
4388   {
4389     "axioms": [
4390       "propext",
4391       "Classical.choice",
4392       "Quot.sound"
4393     ],
4394     "in_project_namespace": true,
4395     "kind": "definition",
4396     "module": "PaperIRelease.GeneralNormedPackets",
4397     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv",
4398     "runtime_only": false
4399   },
4400   {
4401     "axioms": [
4402       "propext",
4403       "Classical.choice",
4404       "Quot.sound"
4405     ],
4406     "in_project_namespace": true,
4407     "kind": "theorem",
4408     "module": "PaperIRelease.AlgebraClassGrouping",
4409     "name": "Komorebi.PaperIRelease.preorderDiagonalHom_surjective",
4410     "runtime_only": false
4411   },
4412   {
4413     "axioms": [
4414       "propext",
4415       "Classical.choice",
4416       "Quot.sound"
4417     ],
4418     "in_project_namespace": true,
4419     "kind": "definition",
4420     "module": "KomorebiVerification.PacketNaturalityCompletion",
4421     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraZeroPattern",
4422     "runtime_only": false
4423   },
4424   {
4425     "axioms": [
4426       "propext",
4427       "Classical.choice",
4428       "Quot.sound"
4429     ],
4430     "in_project_namespace": true,
4431     "kind": "definition",
4432     "module": "KomorebiVerification.TopologicalCompletion",
4433     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concrete",
4434     "runtime_only": false
4435   },
4436   {
4437     "axioms": [
4438       "propext",
4439       "Quot.sound"
4440     ],
4441     "in_project_namespace": true,
4442     "kind": "definition",
4443     "module": "PaperIRelease.GrammarTyped",
4444     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.space",
4445     "runtime_only": false
4446   },
4447   {
4448     "axioms": [
4449       "propext",
4450       "Classical.choice",
4451       "Quot.sound"
4452     ],
4453     "in_project_namespace": false,
4454     "kind": "theorem",
4455     "module": "PaperIRelease.TopologyDenseCompletion",
4456     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv_unique",
4457     "runtime_only": false
4458   },
4459   {
4460     "axioms": [
4461       "propext",
4462       "Classical.choice",
4463       "Quot.sound"
4464     ],
4465     "in_project_namespace": false,
4466     "kind": "theorem",
4467     "module": "PaperIRelease.TopologyUnconditional",
4468     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm_neg",
4469     "runtime_only": false
4470   },
4471   {
4472     "axioms": [
4473       "propext",
4474       "Classical.choice",
4475       "Quot.sound"
4476     ],
4477     "in_project_namespace": true,
4478     "kind": "definition",
4479     "module": "PaperIRelease.PacketTopology",
4480     "name": "Komorebi.Foundation.LinearProjectorFamily.packetIntersection",
4481     "runtime_only": false
4482   },
4483   {
4484     "axioms": [
4485       "propext",
4486       "Quot.sound"
4487     ],
4488     "in_project_namespace": true,
4489     "kind": "theorem",
4490     "module": "PaperIRelease.GraphPropagation",
4491     "name": "Komorebi.PaperIRelease.algebraGeneratedHull_invariant",
4492     "runtime_only": false
4493   },
4494   {
4495     "axioms": [
4496       "propext",
4497       "Classical.choice",
4498       "Quot.sound"
4499     ],
4500     "in_project_namespace": false,
4501     "kind": "inductive",
4502     "module": "PaperIRelease.TopologyUnconditional",
4503     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets",
4504     "runtime_only": false
4505   },
4506   {
4507     "axioms": [
4508       "propext",
4509       "Classical.choice",
4510       "Quot.sound"
4511     ],
4512     "in_project_namespace": true,
4513     "kind": "definition",
4514     "module": "PaperIRelease.BoundedStar",
4515     "name": "Komorebi.PaperIRelease.BoundedSupport.Block",
4516     "runtime_only": false
4517   },
4518   {
4519     "axioms": [
4520       "propext",
4521       "Classical.choice",
4522       "Quot.sound"
4523     ],
4524     "in_project_namespace": true,
4525     "kind": "theorem",
4526     "module": "KomorebiVerification.EllipticAlgorithms",
4527     "name": "Komorebi.FiniteAlgorithms.exactGraphSeedRank_isLeast",
4528     "runtime_only": false
4529   },
4530   {
4531     "axioms": [
4532       "propext",
4533       "Classical.choice",
4534       "Quot.sound"
4535     ],
4536     "in_project_namespace": false,
4537     "kind": "theorem",
4538     "module": "PaperIRelease.TopologyUnconditional",
4539     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_19",
4540     "runtime_only": false
4541   },
4542   {
4543     "axioms": [],
4544     "in_project_namespace": true,
4545     "kind": "theorem",
4546     "module": "KomorebiVerification.ProjectorCore",
4547     "name": "Komorebi.FiniteDifference.weightedDiff.eq_1",
4548     "runtime_only": false
4549   },
4550   {
4551     "axioms": [
4552       "propext",
4553       "Classical.choice",
4554       "Quot.sound"
4555     ],
4556     "in_project_namespace": true,
4557     "kind": "theorem",
4558     "module": "KomorebiVerification.SeedRankOperations",
4559     "name": "Komorebi.SeedRankOperations.exists_minimal_fin_family",
4560     "runtime_only": false
4561   },
4562   {
4563     "axioms": [
4564       "propext",
4565       "Classical.choice",
4566       "Quot.sound"
4567     ],
4568     "in_project_namespace": true,
4569     "kind": "theorem",
4570     "module": "PaperIRelease.AlgebraDiagonal",
4571     "name": "Komorebi.PaperIRelease.commutes_iff_diagonalProjection",
4572     "runtime_only": false
4573   },
4574   {
4575     "axioms": [
4576       "propext"
4577     ],
4578     "in_project_namespace": true,
4579     "kind": "theorem",
4580     "module": "KomorebiVerification.SingleOperatorGraph",
4581     "name": "Komorebi.SingleOperatorGraph.complexCycleRoot._proof_2",
4582     "runtime_only": false
4583   },
4584   {
4585     "axioms": [
4586       "propext",
4587       "Classical.choice",
4588       "Quot.sound"
4589     ],
4590     "in_project_namespace": true,
4591     "kind": "definition",
4592     "module": "KomorebiVerification.PacketNaturalityCompletion",
4593     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.linearMap",
4594     "runtime_only": false
4595   },
4596   {
4597     "axioms": [
4598       "propext",
4599       "Classical.choice",
4600       "Quot.sound"
4601     ],
4602     "in_project_namespace": true,
4603     "kind": "definition",
4604     "module": "KomorebiVerification.TopologicalCompletion",
4605     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv",
4606     "runtime_only": false
4607   },
4608   {
4609     "axioms": [
4610       "propext",
4611       "Classical.choice",
4612       "Quot.sound"
4613     ],
4614     "in_project_namespace": true,
4615     "kind": "theorem",
4616     "module": "KomorebiVerification.TopologicalCompletion",
4617     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2_apply",
4618     "runtime_only": false
4619   },
4620   {
4621     "axioms": [
4622       "propext",
4623       "Classical.choice",
4624       "Quot.sound"
4625     ],
4626     "in_project_namespace": true,
4627     "kind": "theorem",
4628     "module": "PaperICompletion4.OperatorIntrinsicFormula",
4629     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_scalarImage_membership",
4630     "runtime_only": false
4631   },
4632   {
4633     "axioms": [
4634       "propext",
4635       "Classical.choice",
4636       "Quot.sound"
4637     ],
4638     "in_project_namespace": true,
4639     "kind": "theorem",
4640     "module": "KomorebiVerification.SeedRankBasics",
4641     "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquivRange_apply_mk",
4642     "runtime_only": false
4643   },
4644   {
4645     "axioms": [
4646       "propext",
4647       "Classical.choice",
4648       "Quot.sound"
4649     ],
4650     "in_project_namespace": true,
4651     "kind": "theorem",
4652     "module": "PaperIRelease.CategoryUniversal",
4653     "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal_underlying",
4654     "runtime_only": false
4655   },
4656   {
4657     "axioms": [
4658       "propext",
4659       "Classical.choice",
4660       "Quot.sound"
4661     ],
4662     "in_project_namespace": true,
4663     "kind": "theorem",
4664     "module": "KomorebiVerification.PacketNaturalityCompletion",
4665     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_5",
4666     "runtime_only": false
4667   },
4668   {
4669     "axioms": [
4670       "propext",
4671       "Classical.choice",
4672       "Quot.sound"
4673     ],
4674     "in_project_namespace": false,
4675     "kind": "theorem",
4676     "module": "PaperIRelease.TopologyCountablePackets",
4677     "name": "PaperIRelease.TopologyCountablePackets.Projectors.bound",
4678     "runtime_only": false
4679   },
4680   {
4681     "axioms": [
4682       "propext",
4683       "Classical.choice",
4684       "Quot.sound"
4685     ],
4686     "in_project_namespace": true,
4687     "kind": "theorem",
4688     "module": "PaperIRelease.GeneralNormedPackets",
4689     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.injEq",
4690     "runtime_only": false
4691   },
4692   {
4693     "axioms": [],
4694     "in_project_namespace": true,
4695     "kind": "definition",
4696     "module": "KomorebiVerification.ProjectorCore",
4697     "name": "Komorebi.Polyphase.coeffSection",
4698     "runtime_only": false
4699   },
4700   {
4701     "axioms": [
4702       "propext",
4703       "Quot.sound"
4704     ],
4705     "in_project_namespace": true,
4706     "kind": "theorem",
4707     "module": "PaperIRelease.GrammarModules",
4708     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_4",
4709     "runtime_only": false
4710   },
4711   {
4712     "axioms": [
4713       "propext",
4714       "Quot.sound"
4715     ],
4716     "in_project_namespace": true,
4717     "kind": "theorem",
4718     "module": "PaperICompletion5.LinearPrimaryEigenspace",
4719     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_4",
4720     "runtime_only": false
4721   },
4722   {
4723     "axioms": [
4724       "propext",
4725       "Classical.choice",
4726       "Quot.sound"
4727     ],
4728     "in_project_namespace": true,
4729     "kind": "definition",
4730     "module": "PaperIRelease.TopologyCategories",
4731     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject._sizeOf_inst",
4732     "runtime_only": false
4733   },
4734   {
4735     "axioms": [
4736       "propext",
4737       "Quot.sound"
4738     ],
4739     "in_project_namespace": false,
4740     "kind": "theorem",
4741     "module": "PaperIRelease.TopologyTransport",
4742     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_1",
4743     "runtime_only": false
4744   },
4745   {
4746     "axioms": [
4747       "propext",
4748       "Classical.choice",
4749       "Quot.sound"
4750     ],
4751     "in_project_namespace": true,
4752     "kind": "theorem",
4753     "module": "PaperIRelease.AlgebraSupport",
4754     "name": "Komorebi.PaperIRelease.supportSubmodule._proof_4",
4755     "runtime_only": false
4756   },
4757   {
4758     "axioms": [
4759       "propext",
4760       "Quot.sound"
4761     ],
4762     "in_project_namespace": false,
4763     "kind": "theorem",
4764     "module": "PaperIRelease.TopologySemilinearRank",
4765     "name": "PaperIRelease.TopologySemilinearRank.actingOperators.congr_simp",
4766     "runtime_only": false
4767   },
4768   {
4769     "axioms": [],
4770     "in_project_namespace": true,
4771     "kind": "definition",
4772     "module": "PaperIRelease.GrammarPaths",
4773     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn",
4774     "runtime_only": false
4775   },
4776   {
4777     "axioms": [
4778       "propext",
4779       "Quot.sound"
4780     ],
4781     "in_project_namespace": true,
4782     "kind": "theorem",
4783     "module": "KomorebiVerification.PacketNaturalityCompletion",
4784     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds.eq_1",
4785     "runtime_only": false
4786   },
4787   {
4788     "axioms": [
4789       "propext"
4790     ],
4791     "in_project_namespace": true,
4792     "kind": "theorem",
4793     "module": "KomorebiVerification.PacketNaturalityCompletion",
4794     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_1",
4795     "runtime_only": false
4796   },
4797   {
4798     "axioms": [
4799       "propext",
4800       "Classical.choice",
4801       "Quot.sound"
4802     ],
4803     "in_project_namespace": true,
4804     "kind": "theorem",
4805     "module": "PaperIRelease.ExactSequences",
4806     "name": "Komorebi.PaperIRelease.submodule_quotient_seedRank_bounds",
4807     "runtime_only": false
4808   },
4809   {
4810     "axioms": [
4811       "propext",
4812       "Quot.sound"
4813     ],
4814     "in_project_namespace": true,
4815     "kind": "theorem",
4816     "module": "KomorebiVerification.SingleOperatorGraph",
4817     "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_3",
4818     "runtime_only": false
4819   },
4820   {
4821     "axioms": [
4822       "propext",
4823       "Classical.choice",
4824       "Quot.sound"
4825     ],
4826     "in_project_namespace": true,
4827     "kind": "theorem",
4828     "module": "PaperIRelease.PacketAggregation",
4829     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection.eq_1",
4830     "runtime_only": false
4831   },
4832   {
4833     "axioms": [
4834       "propext",
4835       "Classical.choice",
4836       "Quot.sound"
4837     ],
4838     "in_project_namespace": true,
4839     "kind": "inductive",
4840     "module": "PaperIRelease.GrammarAlgebra",
4841     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization",
4842     "runtime_only": false
4843   },
4844   {
4845     "axioms": [
4846       "propext",
4847       "Classical.choice",
4848       "Quot.sound"
4849     ],
4850     "in_project_namespace": true,
4851     "kind": "theorem",
4852     "module": "PaperIRelease.BoundedStar",
4853     "name": "Komorebi.PaperIRelease.BoundedSupport.supported_iff_underlying",
4854     "runtime_only": false
4855   },
4856   {
4857     "axioms": [
4858       "propext",
4859       "Classical.choice",
4860       "Quot.sound"
4861     ],
4862     "in_project_namespace": true,
4863     "kind": "theorem",
4864     "module": "PaperICompletion6.ScalarExtension",
4865     "name": "Komorebi.PaperICompletion6.ScalarExtension.hasCyclicVector_baseChange_iff",
4866     "runtime_only": false
4867   },
4868   {
4869     "axioms": [
4870       "propext",
4871       "Classical.choice",
4872       "Quot.sound"
4873     ],
4874     "in_project_namespace": true,
4875     "kind": "definition",
4876     "module": "KomorebiVerification.PacketNaturalityCompletion",
4877     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv",
4878     "runtime_only": false
4879   },
4880   {
4881     "axioms": [
4882       "propext",
4883       "Classical.choice",
4884       "Quot.sound"
4885     ],
4886     "in_project_namespace": true,
4887     "kind": "theorem",
4888     "module": "KomorebiVerification.TopologicalCompletion",
4889     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.annihilate",
4890     "runtime_only": false
4891   },
4892   {
4893     "axioms": [
4894       "propext",
4895       "Classical.choice",
4896       "Quot.sound"
4897     ],
4898     "in_project_namespace": true,
4899     "kind": "theorem",
4900     "module": "PaperIRelease.GrammarPaths",
4901     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_2",
4902     "runtime_only": false
4903   },
4904   {
4905     "axioms": [
4906       "propext",
4907       "Classical.choice",
4908       "Quot.sound"
4909     ],
4910     "in_project_namespace": true,
4911     "kind": "theorem",
4912     "module": "KomorebiVerification.PacketNaturalityCompletion",
4913     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA._proof_2",
4914     "runtime_only": false
4915   },
4916   {
4917     "axioms": [],
4918     "in_project_namespace": false,
4919     "kind": "definition",
4920     "module": "PaperIRelease.GrammarPaths",
4921     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.splitter",
4922     "runtime_only": false
4923   },
4924   {
4925     "axioms": [
4926       "propext",
4927       "Classical.choice",
4928       "Quot.sound"
4929     ],
4930     "in_project_namespace": true,
4931     "kind": "recursor",
4932     "module": "KomorebiVerification.PacketNaturalityCompletion",
4933     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.rec",
4934     "runtime_only": false
4935   },
4936   {
4937     "axioms": [
4938       "propext",
4939       "Classical.choice",
4940       "Quot.sound"
4941     ],
4942     "in_project_namespace": true,
4943     "kind": "theorem",
4944     "module": "KomorebiVerification.EllipticAlgorithms",
4945     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_2",
4946     "runtime_only": false
4947   },
4948   {
4949     "axioms": [
4950       "propext",
4951       "Classical.choice",
4952       "Quot.sound"
4953     ],
4954     "in_project_namespace": true,
4955     "kind": "theorem",
4956     "module": "PaperICompletion4.IntrinsicPrimary",
4957     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_3",
4958     "runtime_only": false
4959   },
4960   {
4961     "axioms": [
4962       "propext",
4963       "Classical.choice",
4964       "Quot.sound"
4965     ],
4966     "in_project_namespace": true,
4967     "kind": "theorem",
4968     "module": "PaperICompletion3.PrimarySeedFormula",
4969     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.operatorModule_isTorsion",
4970     "runtime_only": false
4971   },
4972   {
4973     "axioms": [
4974       "propext",
4975       "Classical.choice",
4976       "Quot.sound"
4977     ],
4978     "in_project_namespace": true,
4979     "kind": "definition",
4980     "module": "PaperIRelease.GrammarTyped",
4981     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.ctorIdx",
4982     "runtime_only": false
4983   },
4984   {
4985     "axioms": [
4986       "propext",
4987       "Classical.choice",
4988       "Quot.sound"
4989     ],
4990     "in_project_namespace": true,
4991     "kind": "theorem",
4992     "module": "KomorebiVerification.PacketNaturalityCompletion",
4993     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA._proof_2",
4994     "runtime_only": false
4995   },
4996   {
4997     "axioms": [
4998       "propext",
4999       "Quot.sound"
5000     ],
5001     "in_project_namespace": true,
5002     "kind": "definition",
5003     "module": "PaperIRelease.GrammarModules",
5004     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.module",
5005     "runtime_only": false
5006   },
5007   {
5008     "axioms": [
5009       "propext",
5010       "Classical.choice",
5011       "Quot.sound"
5012     ],
5013     "in_project_namespace": true,
5014     "kind": "definition",
5015     "module": "KomorebiVerification.TopologicalCompletion",
5016     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.GeneratesWithNSeeds",
5017     "runtime_only": false
5018   },
5019   {
5020     "axioms": [
5021       "propext",
5022       "Classical.choice",
5023       "Quot.sound"
5024     ],
5025     "in_project_namespace": true,
5026     "kind": "theorem",
5027     "module": "PaperIRelease.PacketEquivalentNorm",
5028     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.finite_packet_equivalent_norm",
5029     "runtime_only": false
5030   },
5031   {
5032     "axioms": [
5033       "propext",
5034       "Classical.choice",
5035       "Quot.sound"
5036     ],
5037     "in_project_namespace": true,
5038     "kind": "theorem",
5039     "module": "PaperIRelease.GraphReachability",
5040     "name": "Komorebi.PaperIRelease.generatedAlgebra_preserves_reachable",
5041     "runtime_only": false
5042   },
5043   {
5044     "axioms": [
5045       "propext",
5046       "Classical.choice",
5047       "Quot.sound"
5048     ],
5049     "in_project_namespace": true,
5050     "kind": "definition",
5051     "module": "PaperICompletion6.OneInvariantFactor",
5052     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv",
5053     "runtime_only": false
5054   },
5055   {
5056     "axioms": [
5057       "propext",
5058       "Classical.choice",
5059       "Quot.sound"
5060     ],
5061     "in_project_namespace": true,
5062     "kind": "theorem",
5063     "module": "PaperIRelease.PacketTopology",
5064     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjector_norm_le",
5065     "runtime_only": false
5066   },
5067   {
5068     "axioms": [
5069       "propext",
5070       "Classical.choice",
5071       "Quot.sound"
5072     ],
5073     "in_project_namespace": true,
5074     "kind": "theorem",
5075     "module": "PaperICompletion4.OperatorIntrinsicFormula",
5076     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_1",
5077     "runtime_only": false
5078   },
5079   {
5080     "axioms": [
5081       "propext",
5082       "Classical.choice",
5083       "Quot.sound"
5084     ],
5085     "in_project_namespace": false,
5086     "kind": "recursor",
5087     "module": "PaperIRelease.TopologyCountablePackets",
5088     "name": "PaperIRelease.TopologyCountablePackets.Projectors.rec",
5089     "runtime_only": false
5090   },
5091   {
5092     "axioms": [
5093       "propext",
5094       "Classical.choice",
5095       "Quot.sound"
5096     ],
5097     "in_project_namespace": true,
5098     "kind": "definition",
5099     "module": "PaperIRelease.GrammarAlgebra",
5100     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.recOn",
5101     "runtime_only": false
5102   },
5103   {
5104     "axioms": [
5105       "propext",
5106       "Classical.choice",
5107       "Quot.sound"
5108     ],
5109     "in_project_namespace": false,
5110     "kind": "theorem",
5111     "module": "PaperIRelease.TopologyCountablePackets",
5112     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.injEq",
5113     "runtime_only": false
5114   },
5115   {
5116     "axioms": [
5117       "propext",
5118       "Classical.choice",
5119       "Quot.sound"
5120     ],
5121     "in_project_namespace": true,
5122     "kind": "definition",
5123     "module": "PaperIRelease.PacketLocalRank",
5124     "name": "Komorebi.PaperIRelease.localCornerAlgebra",
5125     "runtime_only": false
5126   },
5127   {
5128     "axioms": [
5129       "propext",
5130       "Classical.choice",
5131       "Quot.sound"
5132     ],
5133     "in_project_namespace": true,
5134     "kind": "theorem",
5135     "module": "PaperIRelease.GraphSourceCount",
5136     "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_4",
5137     "runtime_only": false
5138   },
5139   {
5140     "axioms": [
5141       "propext",
5142       "Classical.choice",
5143       "Quot.sound"
5144     ],
5145     "in_project_namespace": true,
5146     "kind": "definition",
5147     "module": "PaperIRelease.GraphSourceProjection",
5148     "name": "Komorebi.PaperIRelease.componentProjection",
5149     "runtime_only": false
5150   },
5151   {
5152     "axioms": [],
5153     "in_project_namespace": true,
5154     "kind": "theorem",
5155     "module": "KomorebiVerification.ProjectorCore",
5156     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_1",
5157     "runtime_only": false
5158   },
5159   {
5160     "axioms": [
5161       "propext",
5162       "Classical.choice",
5163       "Quot.sound"
5164     ],
5165     "in_project_namespace": true,
5166     "kind": "theorem",
5167     "module": "PaperICompletion8.DivisionRows",
5168     "name": "Komorebi.PaperICompletion8.DivisionRows.leftGenerates_iff_rowsSpan",
5169     "runtime_only": false
5170   },
5171   {
5172     "axioms": [
5173       "propext",
5174       "Classical.choice",
5175       "Quot.sound"
5176     ],
5177     "in_project_namespace": true,
5178     "kind": "theorem",
5179     "module": "PaperICompletion4.OperatorIntrinsicFormula",
5180     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_3",
5181     "runtime_only": false
5182   },
5183   {
5184     "axioms": [
5185       "propext",
5186       "Classical.choice",
5187       "Quot.sound"
5188     ],
5189     "in_project_namespace": true,
5190     "kind": "theorem",
5191     "module": "PaperIRelease.PacketTopologyGeneral",
5192     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotient_bound_operatorNorm",
5193     "runtime_only": false
5194   },
5195   {
5196     "axioms": [
5197       "propext",
5198       "Classical.choice",
5199       "Quot.sound"
5200     ],
5201     "in_project_namespace": false,
5202     "kind": "theorem",
5203     "module": "PaperIRelease.TopologyDenseCompletion",
5204     "name": "PaperIRelease.TopologyDenseCompletion.presentation_action_uniformContinuous",
5205     "runtime_only": false
5206   },
5207   {
5208     "axioms": [
5209       "propext",
5210       "Classical.choice",
5211       "Quot.sound"
5212     ],
5213     "in_project_namespace": false,
5214     "kind": "theorem",
5215     "module": "PaperIRelease.TopologyCountablePackets",
5216     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_3",
5217     "runtime_only": false
5218   },
5219   {
5220     "axioms": [
5221       "propext",
5222       "Classical.choice",
5223       "Quot.sound"
5224     ],
5225     "in_project_namespace": true,
5226     "kind": "theorem",
5227     "module": "KomorebiVerification.PacketNaturalityCompletion",
5228     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_4",
5229     "runtime_only": false
5230   },
5231   {
5232     "axioms": [
5233       "propext",
5234       "Classical.choice",
5235       "Quot.sound"
5236     ],
5237     "in_project_namespace": false,
5238     "kind": "theorem",
5239     "module": "ReleaseBoundary",
5240     "name": "PaperIBlock08Tests.mixed_natural_is_simple",
5241     "runtime_only": false
5242   },
5243   {
5244     "axioms": [],
5245     "in_project_namespace": true,
5246     "kind": "theorem",
5247     "module": "KomorebiVerification.ProjectorCore",
5248     "name": "Komorebi.Algebra.matrixSupported_zero",
5249     "runtime_only": false
5250   },
5251   {
5252     "axioms": [
5253       "propext",
5254       "Classical.choice",
5255       "Quot.sound"
5256     ],
5257     "in_project_namespace": true,
5258     "kind": "theorem",
5259     "module": "PaperIRelease.AlgebraClassGrouping",
5260     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_13",
5261     "runtime_only": false
5262   },
5263   {
5264     "axioms": [],
5265     "in_project_namespace": true,
5266     "kind": "definition",
5267     "module": "KomorebiVerification.ProjectorCore",
5268     "name": "Komorebi.FiniteDifference.iteratedDiff._sunfold",
5269     "runtime_only": false
5270   },
5271   {
5272     "axioms": [],
5273     "in_project_namespace": true,
5274     "kind": "definition",
5275     "module": "KomorebiVerification.ProjectorCore",
5276     "name": "Komorebi.ClaimKind.conjecture.elim",
5277     "runtime_only": false
5278   },
5279   {
5280     "axioms": [
5281       "propext",
5282       "Classical.choice",
5283       "Quot.sound"
5284     ],
5285     "in_project_namespace": true,
5286     "kind": "theorem",
5287     "module": "PaperIRelease.TopologyCategories",
5288     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.comp._proof_1",
5289     "runtime_only": false
5290   },
5291   {
5292     "axioms": [
5293       "propext",
5294       "Classical.choice",
5295       "Quot.sound"
5296     ],
5297     "in_project_namespace": true,
5298     "kind": "theorem",
5299     "module": "KomorebiVerification.PacketNaturalityCompletion",
5300     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_inclusion_ne",
5301     "runtime_only": false
5302   },
5303   {
5304     "axioms": [
5305       "propext",
5306       "Classical.choice",
5307       "Quot.sound"
5308     ],
5309     "in_project_namespace": true,
5310     "kind": "theorem",
5311     "module": "PaperICompletion8.DivisionProduct",
5312     "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_familyGenerates_iff",
5313     "runtime_only": false
5314   },
5315   {
5316     "axioms": [
5317       "propext",
5318       "Quot.sound"
5319     ],
5320     "in_project_namespace": false,
5321     "kind": "theorem",
5322     "module": "PaperIRelease.TopologySemilinearRank",
5323     "name": "PaperIRelease.TopologySemilinearRank.Generates.eq_1",
5324     "runtime_only": false
5325   },
5326   {
5327     "axioms": [
5328       "propext",
5329       "Classical.choice",
5330       "Quot.sound"
5331     ],
5332     "in_project_namespace": true,
5333     "kind": "theorem",
5334     "module": "KomorebiVerification.SingleOperatorGraph",
5335     "name": "Komorebi.SingleOperatorGraph.graph_seedNumber_eq_max_eigenspace_multiplicity",
5336     "runtime_only": false
5337   },
5338   {
5339     "axioms": [
5340       "propext",
5341       "Quot.sound"
5342     ],
5343     "in_project_namespace": true,
5344     "kind": "theorem",
5345     "module": "PaperIRelease.AlgebraSupport",
5346     "name": "Komorebi.PaperIRelease.supportSubmodule._proof_2",
5347     "runtime_only": false
5348   },
5349   {
5350     "axioms": [
5351       "propext",
5352       "Classical.choice",
5353       "Quot.sound"
5354     ],
5355     "in_project_namespace": true,
5356     "kind": "theorem",
5357     "module": "PaperIRelease.BoundedStar",
5358     "name": "Komorebi.PaperIRelease.BoundedSupport.equality_pattern_boundary",
5359     "runtime_only": false
5360   },
5361   {
5362     "axioms": [
5363       "propext",
5364       "Classical.choice",
5365       "Quot.sound"
5366     ],
5367     "in_project_namespace": true,
5368     "kind": "definition",
5369     "module": "KomorebiVerification.ProjectorCore",
5370     "name": "Komorebi.Foundation.LinearProjectorFamily.ctorIdx",
5371     "runtime_only": false
5372   },
5373   {
5374     "axioms": [
5375       "propext",
5376       "Classical.choice",
5377       "Quot.sound"
5378     ],
5379     "in_project_namespace": true,
5380     "kind": "theorem",
5381     "module": "PaperIRelease.GrammarPaths",
5382     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_1",
5383     "runtime_only": false
5384   },
5385   {
5386     "axioms": [
5387       "propext",
5388       "Classical.choice",
5389       "Quot.sound"
5390     ],
5391     "in_project_namespace": true,
5392     "kind": "definition",
5393     "module": "PaperIRelease.CategoryPackets",
5394     "name": "Komorebi.PaperIRelease.CategoryPackets.ImageHull",
5395     "runtime_only": false
5396   },
5397   {
5398     "axioms": [
5399       "propext",
5400       "Quot.sound"
5401     ],
5402     "in_project_namespace": true,
5403     "kind": "definition",
5404     "module": "PaperIRelease.AlgebraTransfer",
5405     "name": "Komorebi.PaperIRelease.operatorWord",
5406     "runtime_only": false
5407   },
5408   {
5409     "axioms": [
5410       "propext",
5411       "Classical.choice",
5412       "Quot.sound"
5413     ],
5414     "in_project_namespace": true,
5415     "kind": "theorem",
5416     "module": "PaperIRelease.GrammarTyped",
5417     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.injEq",
5418     "runtime_only": false
5419   },
5420   {
5421     "axioms": [
5422       "propext",
5423       "Classical.choice",
5424       "Quot.sound"
5425     ],
5426     "in_project_namespace": true,
5427     "kind": "definition",
5428     "module": "PaperIRelease.CategoryPackets",
5429     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.noConfusionType",
5430     "runtime_only": false
5431   },
5432   {
5433     "axioms": [],
5434     "in_project_namespace": true,
5435     "kind": "theorem",
5436     "module": "KomorebiVerification.ProjectorCore",
5437     "name": "Komorebi.instDecidableEqClaimKind._proof_2",
5438     "runtime_only": false
5439   },
5440   {
5441     "axioms": [
5442       "propext",
5443       "Classical.choice",
5444       "Quot.sound"
5445     ],
5446     "in_project_namespace": true,
5447     "kind": "theorem",
5448     "module": "PaperIRelease.PacketPureRank",
5449     "name": "Komorebi.PaperIRelease.exists_pure_generating_set_card_eq",
5450     "runtime_only": false
5451   },
5452   {
5453     "axioms": [
5454       "propext",
5455       "Classical.choice",
5456       "Quot.sound"
5457     ],
5458     "in_project_namespace": true,
5459     "kind": "theorem",
5460     "module": "KomorebiVerification.TopologicalCompletion",
5461     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_3",
5462     "runtime_only": false
5463   },
5464   {
5465     "axioms": [
5466       "propext",
5467       "Classical.choice",
5468       "Quot.sound"
5469     ],
5470     "in_project_namespace": true,
5471     "kind": "theorem",
5472     "module": "PaperIRelease.PacketEquivalentNorm",
5473     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_1",
5474     "runtime_only": false
5475   },
5476   {
5477     "axioms": [
5478       "propext",
5479       "Classical.choice",
5480       "Quot.sound"
5481     ],
5482     "in_project_namespace": true,
5483     "kind": "definition",
5484     "module": "KomorebiVerification.SingleOperatorGraph",
5485     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow",
5486     "runtime_only": false
5487   },
5488   {
5489     "axioms": [
5490       "propext",
5491       "Classical.choice",
5492       "Quot.sound"
5493     ],
5494     "in_project_namespace": true,
5495     "kind": "theorem",
5496     "module": "PaperICompletion6.OneInvariantFactor",
5497     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_1",
5498     "runtime_only": false
5499   },
5500   {
5501     "axioms": [
5502       "propext",
5503       "Classical.choice",
5504       "Quot.sound"
5505     ],
5506     "in_project_namespace": true,
5507     "kind": "theorem",
5508     "module": "PaperICompletion6.PrimaryCyclicCriterion",
5509     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_nonzero_primary_cyclic._proof_1_1",
5510     "runtime_only": false
5511   },
5512   {
5513     "axioms": [
5514       "propext",
5515       "Quot.sound"
5516     ],
5517     "in_project_namespace": true,
5518     "kind": "theorem",
5519     "module": "PaperIRelease.ScalarExtension",
5520     "name": "Komorebi.PaperIRelease.ScalarExtension.instSMulCommClassTensorProduct_paperIRelease",
5521     "runtime_only": false
5522   },
5523   {
5524     "axioms": [],
5525     "in_project_namespace": true,
5526     "kind": "constructor",
5527     "module": "KomorebiVerification.ProjectorCore",
5528     "name": "Komorebi.ClaimKind.conjecture",
5529     "runtime_only": false
5530   },
5531   {
5532     "axioms": [
5533       "propext"
5534     ],
5535     "in_project_namespace": true,
5536     "kind": "theorem",
5537     "module": "KomorebiVerification.TopologicalCompletion",
5538     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta._proof_1",
5539     "runtime_only": false
5540   },
5541   {
5542     "axioms": [
5543       "propext",
5544       "Quot.sound"
5545     ],
5546     "in_project_namespace": true,
5547     "kind": "theorem",
5548     "module": "PaperICompletion4.GroupedPrimary",
5549     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_4",
5550     "runtime_only": false
5551   },
5552   {
5553     "axioms": [
5554       "propext",
5555       "Classical.choice",
5556       "Quot.sound"
5557     ],
5558     "in_project_namespace": true,
5559     "kind": "theorem",
5560     "module": "KomorebiVerification.EllipticAlgorithms",
5561     "name": "Komorebi.EllipticCoordinates.Mx._proof_1",
5562     "runtime_only": false
5563   },
5564   {
5565     "axioms": [
5566       "propext",
5567       "Classical.choice",
5568       "Quot.sound"
5569     ],
5570     "in_project_namespace": true,
5571     "kind": "theorem",
5572     "module": "PaperIRelease.PacketBoundaryTests",
5573     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.infinite_free_quotient_bounds",
5574     "runtime_only": false
5575   },
5576   {
5577     "axioms": [
5578       "propext",
5579       "Quot.sound"
5580     ],
5581     "in_project_namespace": true,
5582     "kind": "definition",
5583     "module": "PaperIRelease.GrammarAlgebra",
5584     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk._flat_ctor",
5585     "runtime_only": false
5586   },
5587   {
5588     "axioms": [
5589       "propext",
5590       "Quot.sound"
5591     ],
5592     "in_project_namespace": true,
5593     "kind": "theorem",
5594     "module": "PaperIRelease.GraphSources",
5595     "name": "Komorebi.PaperIRelease.FiniteDigraph.intermediate_same_component",
5596     "runtime_only": false
5597   },
5598   {
5599     "axioms": [
5600       "propext",
5601       "Classical.choice",
5602       "Quot.sound"
5603     ],
5604     "in_project_namespace": true,
5605     "kind": "theorem",
5606     "module": "KomorebiVerification.TopologicalCompletion",
5607     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_minimalCardinality_one",
5608     "runtime_only": false
5609   },
5610   {
5611     "axioms": [
5612       "propext",
5613       "Classical.choice",
5614       "Quot.sound"
5615     ],
5616     "in_project_namespace": true,
5617     "kind": "theorem",
5618     "module": "PaperIRelease.PacketSourceRank",
5619     "name": "Komorebi.PaperIRelease.source_component_pureSeedRank",
5620     "runtime_only": false
5621   },
5622   {
5623     "axioms": [
5624       "propext",
5625       "Quot.sound"
5626     ],
5627     "in_project_namespace": true,
5628     "kind": "theorem",
5629     "module": "KomorebiVerification.PathGraphKrylov",
5630     "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_1",
5631     "runtime_only": false
5632   },
5633   {
5634     "axioms": [
5635       "propext",
5636       "Classical.choice",
5637       "Quot.sound"
5638     ],
5639     "in_project_namespace": true,
5640     "kind": "theorem",
5641     "module": "PaperIRelease.PacketTopologyGeneral",
5642     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotient_bounded",
5643     "runtime_only": false
5644   },
5645   {
5646     "axioms": [
5647       "propext",
5648       "Classical.choice",
5649       "Quot.sound"
5650     ],
5651     "in_project_namespace": false,
5652     "kind": "theorem",
5653     "module": "PaperIRelease.TopologyUnconditionalBridge",
5654     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_6",
5655     "runtime_only": false
5656   },
5657   {
5658     "axioms": [
5659       "propext",
5660       "Classical.choice",
5661       "Quot.sound"
5662     ],
5663     "in_project_namespace": false,
5664     "kind": "definition",
5665     "module": "PaperIRelease.TopologyCountablePackets",
5666     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._aux_1",
5667     "runtime_only": false
5668   },
5669   {
5670     "axioms": [
5671       "propext",
5672       "Classical.choice",
5673       "Quot.sound"
5674     ],
5675     "in_project_namespace": true,
5676     "kind": "theorem",
5677     "module": "PaperIRelease.GeneralFiniteCompletion",
5678     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_1",
5679     "runtime_only": false
5680   },
5681   {
5682     "axioms": [
5683       "propext",
5684       "Classical.choice",
5685       "Quot.sound"
5686     ],
5687     "in_project_namespace": true,
5688     "kind": "definition",
5689     "module": "PaperICompletion8.RegularMultiplicity",
5690     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.blockModuleAction",
5691     "runtime_only": false
5692   },
5693   {
5694     "axioms": [
5695       "propext",
5696       "Quot.sound"
5697     ],
5698     "in_project_namespace": true,
5699     "kind": "theorem",
5700     "module": "PaperIRelease.GrammarModules",
5701     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.coefficient_action",
5702     "runtime_only": false
5703   },
5704   {
5705     "axioms": [
5706       "propext",
5707       "Classical.choice",
5708       "Quot.sound"
5709     ],
5710     "in_project_namespace": true,
5711     "kind": "theorem",
5712     "module": "PaperICompletion7.Nakayama",
5713     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_ker",
5714     "runtime_only": false
5715   },
5716   {
5717     "axioms": [
5718       "propext",
5719       "Classical.choice",
5720       "Quot.sound"
5721     ],
5722     "in_project_namespace": true,
5723     "kind": "definition",
5724     "module": "KomorebiVerification.EllipticAlgorithms",
5725     "name": "Komorebi.FiniteAlgorithms.orbitClosureStep",
5726     "runtime_only": false
5727   },
5728   {
5729     "axioms": [
5730       "propext",
5731       "Quot.sound"
5732     ],
5733     "in_project_namespace": true,
5734     "kind": "definition",
5735     "module": "KomorebiVerification.PacketNaturalityCompletion",
5736     "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull",
5737     "runtime_only": false
5738   },
5739   {
5740     "axioms": [
5741       "propext",
5742       "Classical.choice",
5743       "Quot.sound"
5744     ],
5745     "in_project_namespace": true,
5746     "kind": "theorem",
5747     "module": "KomorebiVerification.SingleOperatorGraph",
5748     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow._proof_1",
5749     "runtime_only": false
5750   },
5751   {
5752     "axioms": [
5753       "propext",
5754       "Quot.sound"
5755     ],
5756     "in_project_namespace": false,
5757     "kind": "theorem",
5758     "module": "KomorebiVerification.SeedRankOperations",
5759     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_7",
5760     "runtime_only": false
5761   },
5762   {
5763     "axioms": [],
5764     "in_project_namespace": true,
5765     "kind": "theorem",
5766     "module": "PaperIRelease.CategoryExport",
5767     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.sizeOf_spec",
5768     "runtime_only": false
5769   },
5770   {
5771     "axioms": [
5772       "propext",
5773       "Quot.sound"
5774     ],
5775     "in_project_namespace": true,
5776     "kind": "theorem",
5777     "module": "PaperIRelease.GraphSourceBoundary",
5778     "name": "Komorebi.PaperIRelease.FiniteDigraph.twoCycle_single_component_boundary",
5779     "runtime_only": false
5780   },
5781   {
5782     "axioms": [
5783       "propext",
5784       "Classical.choice",
5785       "Quot.sound"
5786     ],
5787     "in_project_namespace": true,
5788     "kind": "definition",
5789     "module": "KomorebiVerification.PacketNaturalityCompletion",
5790     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraAlgebra",
5791     "runtime_only": false
5792   },
5793   {
5794     "axioms": [
5795       "propext",
5796       "Classical.choice",
5797       "Quot.sound"
5798     ],
5799     "in_project_namespace": true,
5800     "kind": "theorem",
5801     "module": "PaperICompletion8.RegularMultiplicity",
5802     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_1",
5803     "runtime_only": false
5804   },
5805   {
5806     "axioms": [],
5807     "in_project_namespace": true,
5808     "kind": "definition",
5809     "module": "KomorebiVerification.ProjectorCore",
5810     "name": "Komorebi.FormalizationStatus.partialFormalization.elim",
5811     "runtime_only": false
5812   },
5813   {
5814     "axioms": [
5815       "propext",
5816       "Classical.choice",
5817       "Quot.sound"
5818     ],
5819     "in_project_namespace": true,
5820     "kind": "definition",
5821     "module": "PaperIRelease.TopologyCategories",
5822     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.noConfusionType",
5823     "runtime_only": false
5824   },
5825   {
5826     "axioms": [
5827       "propext",
5828       "Classical.choice",
5829       "Quot.sound"
5830     ],
5831     "in_project_namespace": false,
5832     "kind": "theorem",
5833     "module": "PaperIRelease.TopologyPresentations",
5834     "name": "PaperIRelease.TopologyDenseCompletion.restricted_dense",
5835     "runtime_only": false
5836   },
5837   {
5838     "axioms": [
5839       "propext",
5840       "Classical.choice",
5841       "Quot.sound"
5842     ],
5843     "in_project_namespace": true,
5844     "kind": "theorem",
5845     "module": "PaperIRelease.TensorPackets",
5846     "name": "Komorebi.PaperIRelease.dualPackets._proof_4",
5847     "runtime_only": false
5848   },
5849   {
5850     "axioms": [
5851       "propext",
5852       "Classical.choice",
5853       "Quot.sound"
5854     ],
5855     "in_project_namespace": true,
5856     "kind": "theorem",
5857     "module": "KomorebiVerification.SeedRankOperations",
5858     "name": "Komorebi.SeedRankOperations.seedRank_prod_le_add",
5859     "runtime_only": false
5860   },
5861   {
5862     "axioms": [
5863       "Classical.choice"
5864     ],
5865     "in_project_namespace": true,
5866     "kind": "theorem",
5867     "module": "PaperIRelease.GraphSources",
5868     "name": "Komorebi.PaperIRelease.FiniteDigraph.component_surjective",
5869     "runtime_only": false
5870   },
5871   {
5872     "axioms": [],
5873     "in_project_namespace": true,
5874     "kind": "definition",
5875     "module": "KomorebiVerification.ProjectorCore",
5876     "name": "Komorebi.ClaimKind.exampleClaim.elim",
5877     "runtime_only": false
5878   },
5879   {
5880     "axioms": [
5881       "propext",
5882       "Quot.sound"
5883     ],
5884     "in_project_namespace": true,
5885     "kind": "theorem",
5886     "module": "PaperIRelease.GrammarModules",
5887     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.commute",
5888     "runtime_only": false
5889   },
5890   {
5891     "axioms": [
5892       "propext",
5893       "Classical.choice",
5894       "Quot.sound"
5895     ],
5896     "in_project_namespace": true,
5897     "kind": "definition",
5898     "module": "PaperIRelease.TensorPackets",
5899     "name": "Komorebi.PaperIRelease.dualPackets",
5900     "runtime_only": false
5901   },
5902   {
5903     "axioms": [
5904       "propext",
5905       "Classical.choice",
5906       "Quot.sound"
5907     ],
5908     "in_project_namespace": true,
5909     "kind": "theorem",
5910     "module": "PaperIRelease.PacketCorners",
5911     "name": "Komorebi.PaperIRelease.cornerCompression._proof_3",
5912     "runtime_only": false
5913   },
5914   {
5915     "axioms": [
5916       "propext",
5917       "Classical.choice",
5918       "Quot.sound"
5919     ],
5920     "in_project_namespace": false,
5921     "kind": "definition",
5922     "module": "PaperIRelease.TopologyUnconditional",
5923     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup",
5924     "runtime_only": false
5925   },
5926   {
5927     "axioms": [
5928       "propext",
5929       "Classical.choice",
5930       "Quot.sound"
5931     ],
5932     "in_project_namespace": true,
5933     "kind": "definition",
5934     "module": "PaperIRelease.GraphSourceCount",
5935     "name": "Komorebi.PaperIRelease.PacketPropagating",
5936     "runtime_only": false
5937   },
5938   {
5939     "axioms": [
5940       "propext"
5941     ],
5942     "in_project_namespace": true,
5943     "kind": "theorem",
5944     "module": "PaperIRelease.CategoryExport",
5945     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_2",
5946     "runtime_only": false
5947   },
5948   {
5949     "axioms": [
5950       "propext",
5951       "Classical.choice",
5952       "Quot.sound"
5953     ],
5954     "in_project_namespace": true,
5955     "kind": "definition",
5956     "module": "PaperICompletion8.RegularMultiplicity",
5957     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleBlockAction",
5958     "runtime_only": false
5959   },
5960   {
5961     "axioms": [
5962       "propext",
5963       "Classical.choice",
5964       "Quot.sound"
5965     ],
5966     "in_project_namespace": true,
5967     "kind": "theorem",
5968     "module": "PaperIRelease.PacketTopologyGeneral",
5969     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM._proof_2",
5970     "runtime_only": false
5971   },
5972   {
5973     "axioms": [
5974       "propext",
5975       "Quot.sound"
5976     ],
5977     "in_project_namespace": true,
5978     "kind": "definition",
5979     "module": "PaperIRelease.GrammarModules",
5980     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.noConfusion",
5981     "runtime_only": false
5982   },
5983   {
5984     "axioms": [
5985       "propext",
5986       "Classical.choice",
5987       "Quot.sound"
5988     ],
5989     "in_project_namespace": true,
5990     "kind": "theorem",
5991     "module": "PaperICompletion6.SixWayCyclicCriterion",
5992     "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_iff_invariantFactor_count_one",
5993     "runtime_only": false
5994   },
5995   {
5996     "axioms": [
5997       "propext",
5998       "Classical.choice",
5999       "Quot.sound"
6000     ],
6001     "in_project_namespace": true,
6002     "kind": "theorem",
6003     "module": "PaperIRelease.AlgebraQuotient",
6004     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_9",
6005     "runtime_only": false
6006   },
6007   {
6008     "axioms": [
6009       "propext",
6010       "Classical.choice",
6011       "Quot.sound"
6012     ],
6013     "in_project_namespace": true,
6014     "kind": "definition",
6015     "module": "KomorebiVerification.TopologicalCompletion",
6016     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis",
6017     "runtime_only": false
6018   },
6019   {
6020     "axioms": [
6021       "propext",
6022       "Classical.choice",
6023       "Quot.sound"
6024     ],
6025     "in_project_namespace": true,
6026     "kind": "theorem",
6027     "module": "PaperIRelease.GrammarAlgebra",
6028     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_1",
6029     "runtime_only": false
6030   },
6031   {
6032     "axioms": [
6033       "propext",
6034       "Quot.sound"
6035     ],
6036     "in_project_namespace": true,
6037     "kind": "theorem",
6038     "module": "KomorebiVerification.SeedRankBasics",
6039     "name": "Komorebi.SeedRankBasics.FamilyGenerates.eq_1",
6040     "runtime_only": false
6041   },
6042   {
6043     "axioms": [
6044       "propext",
6045       "Classical.choice",
6046       "Quot.sound"
6047     ],
6048     "in_project_namespace": true,
6049     "kind": "theorem",
6050     "module": "PaperIRelease.AlgebraPreorder",
6051     "name": "Komorebi.PaperIRelease.mem_strictSupportIdeal",
6052     "runtime_only": false
6053   },
6054   {
6055     "axioms": [
6056       "propext",
6057       "Quot.sound"
6058     ],
6059     "in_project_namespace": true,
6060     "kind": "definition",
6061     "module": "KomorebiVerification.PacketNaturalityCompletion",
6062     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule",
6063     "runtime_only": false
6064   },
6065   {
6066     "axioms": [
6067       "propext",
6068       "Classical.choice",
6069       "Quot.sound"
6070     ],
6071     "in_project_namespace": true,
6072     "kind": "theorem",
6073     "module": "PaperICompletion8.DivisionProduct",
6074     "name": "Komorebi.PaperICompletion8.DivisionProduct.exists_divisionProduct_generators_iff_coordinate_bounds",
6075     "runtime_only": false
6076   },
6077   {
6078     "axioms": [
6079       "propext",
6080       "Classical.choice",
6081       "Quot.sound"
6082     ],
6083     "in_project_namespace": true,
6084     "kind": "theorem",
6085     "module": "KomorebiVerification.SingleOperatorGraph",
6086     "name": "Komorebi.SingleOperatorGraph.familyGenerates_singleton_of_pow_span_eq_top",
6087     "runtime_only": false
6088   },
6089   {
6090     "axioms": [],
6091     "in_project_namespace": true,
6092     "kind": "definition",
6093     "module": "KomorebiVerification.ProjectorCore",
6094     "name": "Komorebi.Seed.instReprOperatorExpr.repr._unsafe_rec",
6095     "runtime_only": true
6096   },
6097   {
6098     "axioms": [
6099       "propext",
6100       "Quot.sound"
6101     ],
6102     "in_project_namespace": true,
6103     "kind": "definition",
6104     "module": "PaperIRelease.GrammarModules",
6105     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso",
6106     "runtime_only": false
6107   },
6108   {
6109     "axioms": [
6110       "propext",
6111       "Classical.choice",
6112       "Quot.sound"
6113     ],
6114     "in_project_namespace": true,
6115     "kind": "definition",
6116     "module": "PaperIRelease.PacketTopology",
6117     "name": "Komorebi.Foundation.LinearProjectorFamily.boundedProjector",
6118     "runtime_only": false
6119   },
6120   {
6121     "axioms": [
6122       "propext",
6123       "Classical.choice",
6124       "Quot.sound"
6125     ],
6126     "in_project_namespace": true,
6127     "kind": "theorem",
6128     "module": "PaperIRelease.GeneralFiniteCompletion",
6129     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extension_unique",
6130     "runtime_only": false
6131   },
6132   {
6133     "axioms": [
6134       "propext",
6135       "Classical.choice",
6136       "Quot.sound"
6137     ],
6138     "in_project_namespace": true,
6139     "kind": "inductive",
6140     "module": "PaperIRelease.GrammarAlgebra",
6141     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation",
6142     "runtime_only": false
6143   },
6144   {
6145     "axioms": [],
6146     "in_project_namespace": true,
6147     "kind": "definition",
6148     "module": "KomorebiVerification.ProjectorCore",
6149     "name": "Komorebi.ClaimRecord.isOpenOrBoundary",
6150     "runtime_only": false
6151   },
6152   {
6153     "axioms": [
6154       "propext",
6155       "Classical.choice",
6156       "Quot.sound"
6157     ],
6158     "in_project_namespace": true,
6159     "kind": "definition",
6160     "module": "PaperICompletion3.PrimarySeedFormula",
6161     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor",
6162     "runtime_only": false
6163   },
6164   {
6165     "axioms": [
6166       "propext",
6167       "Classical.choice",
6168       "Quot.sound"
6169     ],
6170     "in_project_namespace": true,
6171     "kind": "theorem",
6172     "module": "KomorebiVerification.SingleOperatorGraph",
6173     "name": "Komorebi.SingleOperatorGraph.eval_intertwining_of_map_T_eq_smul",
6174     "runtime_only": false
6175   },
6176   {
6177     "axioms": [
6178       "propext",
6179       "Classical.choice",
6180       "Quot.sound"
6181     ],
6182     "in_project_namespace": true,
6183     "kind": "theorem",
6184     "module": "PaperIRelease.AlgebraTransfer",
6185     "name": "Komorebi.PaperIRelease.target_coordinate_active_sum._simp_1_2",
6186     "runtime_only": false
6187   },
6188   {
6189     "axioms": [
6190       "propext",
6191       "Classical.choice",
6192       "Quot.sound"
6193     ],
6194     "in_project_namespace": true,
6195     "kind": "theorem",
6196     "module": "KomorebiVerification.EllipticAlgorithms",
6197     "name": "Komorebi.FiniteAlgorithms.invariant_of_orbitClosureStep_eq",
6198     "runtime_only": false
6199   },
6200   {
6201     "axioms": [
6202       "propext",
6203       "Classical.choice",
6204       "Quot.sound"
6205     ],
6206     "in_project_namespace": true,
6207     "kind": "recursor",
6208     "module": "PaperIRelease.TopologyCategories",
6209     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.rec",
6210     "runtime_only": false
6211   },
6212   {
6213     "axioms": [
6214       "propext",
6215       "Classical.choice",
6216       "Quot.sound"
6217     ],
6218     "in_project_namespace": true,
6219     "kind": "theorem",
6220     "module": "KomorebiVerification.ExactCoordinates",
6221     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_2",
6222     "runtime_only": false
6223   },
6224   {
6225     "axioms": [
6226       "propext",
6227       "Classical.choice",
6228       "Quot.sound"
6229     ],
6230     "in_project_namespace": true,
6231     "kind": "definition",
6232     "module": "PaperIRelease.AlgebraTransfer",
6233     "name": "Komorebi.PaperIRelease.PacketPure",
6234     "runtime_only": false
6235   },
6236   {
6237     "axioms": [
6238       "propext",
6239       "Classical.choice",
6240       "Quot.sound"
6241     ],
6242     "in_project_namespace": true,
6243     "kind": "theorem",
6244     "module": "PaperICompletion.CyclicClassification",
6245     "name": "Komorebi.PaperICompletion.CyclicClassification.exists_full_annihilator_vector",
6246     "runtime_only": false
6247   },
6248   {
6249     "axioms": [
6250       "propext",
6251       "Classical.choice",
6252       "Quot.sound"
6253     ],
6254     "in_project_namespace": false,
6255     "kind": "theorem",
6256     "module": "PaperIRelease.TopologyCountablePackets",
6257     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetCompleteSpace",
6258     "runtime_only": false
6259   },
6260   {
6261     "axioms": [
6262       "propext",
6263       "Classical.choice",
6264       "Quot.sound"
6265     ],
6266     "in_project_namespace": false,
6267     "kind": "definition",
6268     "module": "PaperIRelease.TopologyCountablePackets",
6269     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_1",
6270     "runtime_only": false
6271   },
6272   {
6273     "axioms": [
6274       "propext",
6275       "Classical.choice",
6276       "Quot.sound"
6277     ],
6278     "in_project_namespace": true,
6279     "kind": "theorem",
6280     "module": "PaperIRelease.GrammarEquivalence",
6281     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total_apply",
6282     "runtime_only": false
6283   },
6284   {
6285     "axioms": [
6286       "propext",
6287       "Classical.choice",
6288       "Quot.sound"
6289     ],
6290     "in_project_namespace": true,
6291     "kind": "theorem",
6292     "module": "KomorebiVerification.TopologicalCompletion",
6293     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_add",
6294     "runtime_only": false
6295   },
6296   {
6297     "axioms": [
6298       "propext",
6299       "Quot.sound"
6300     ],
6301     "in_project_namespace": true,
6302     "kind": "theorem",
6303     "module": "PaperIRelease.PacketAggregation",
6304     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_1",
6305     "runtime_only": false
6306   },
6307   {
6308     "axioms": [],
6309     "in_project_namespace": false,
6310     "kind": "theorem",
6311     "module": "PaperIRelease.TopologySemilinearRank",
6312     "name": "PaperIRelease.TopologySemilinearRank.actingOperator._proof_1",
6313     "runtime_only": false
6314   },
6315   {
6316     "axioms": [
6317       "propext",
6318       "Classical.choice",
6319       "Quot.sound"
6320     ],
6321     "in_project_namespace": true,
6322     "kind": "theorem",
6323     "module": "PaperICompletion4.IntrinsicPrimary",
6324     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal_mk",
6325     "runtime_only": false
6326   },
6327   {
6328     "axioms": [
6329       "propext",
6330       "Classical.choice",
6331       "Quot.sound"
6332     ],
6333     "in_project_namespace": true,
6334     "kind": "theorem",
6335     "module": "PaperIRelease.GrammarAlgebra",
6336     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_3",
6337     "runtime_only": false
6338   },
6339   {
6340     "axioms": [
6341       "Quot.sound"
6342     ],
6343     "in_project_namespace": true,
6344     "kind": "theorem",
6345     "module": "KomorebiVerification.PathGraphKrylov",
6346     "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_2",
6347     "runtime_only": false
6348   },
6349   {
6350     "axioms": [
6351       "propext",
6352       "Quot.sound"
6353     ],
6354     "in_project_namespace": true,
6355     "kind": "theorem",
6356     "module": "PaperIRelease.PacketCorners",
6357     "name": "Komorebi.PaperIRelease.cornerCompression._proof_1",
6358     "runtime_only": false
6359   },
6360   {
6361     "axioms": [
6362       "propext",
6363       "Quot.sound"
6364     ],
6365     "in_project_namespace": false,
6366     "kind": "theorem",
6367     "module": "ReleaseBoundary",
6368     "name": "PaperIBlock08Tests.quaternion_one_seed_insufficient._proof_1_1",
6369     "runtime_only": false
6370   },
6371   {
6372     "axioms": [
6373       "propext",
6374       "Quot.sound"
6375     ],
6376     "in_project_namespace": true,
6377     "kind": "theorem",
6378     "module": "PaperICompletion.CyclicClassification",
6379     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_4",
6380     "runtime_only": false
6381   },
6382   {
6383     "axioms": [
6384       "propext",
6385       "Classical.choice",
6386       "Quot.sound"
6387     ],
6388     "in_project_namespace": true,
6389     "kind": "theorem",
6390     "module": "PaperICompletion.SpectralCertificates",
6391     "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_operatorAlgebra_seedRanks",
6392     "runtime_only": false
6393   },
6394   {
6395     "axioms": [
6396       "propext",
6397       "Quot.sound"
6398     ],
6399     "in_project_namespace": true,
6400     "kind": "definition",
6401     "module": "PaperIRelease.AlgebraTransfer",
6402     "name": "Komorebi.PaperIRelease.operatorWord._sunfold",
6403     "runtime_only": false
6404   },
6405   {
6406     "axioms": [
6407       "propext",
6408       "Classical.choice",
6409       "Quot.sound"
6410     ],
6411     "in_project_namespace": true,
6412     "kind": "theorem",
6413     "module": "PaperICompletion3.OperatorPrimaryAPI",
6414     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.maxCount_eq",
6415     "runtime_only": false
6416   },
6417   {
6418     "axioms": [
6419       "propext",
6420       "Classical.choice",
6421       "Quot.sound"
6422     ],
6423     "in_project_namespace": false,
6424     "kind": "theorem",
6425     "module": "PaperIRelease.TopologyUnconditional",
6426     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_6",
6427     "runtime_only": false
6428   },
6429   {
6430     "axioms": [
6431       "propext",
6432       "Quot.sound"
6433     ],
6434     "in_project_namespace": true,
6435     "kind": "theorem",
6436     "module": "PaperIRelease.ScalarExtension",
6437     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorActionsCommuteInstalled",
6438     "runtime_only": false
6439   },
6440   {
6441     "axioms": [
6442       "propext",
6443       "Classical.choice",
6444       "Quot.sound"
6445     ],
6446     "in_project_namespace": true,
6447     "kind": "theorem",
6448     "module": "KomorebiVerification.ProjectorCore",
6449     "name": "Komorebi.Operator.lowRankApply_zero_vector",
6450     "runtime_only": false
6451   },
6452   {
6453     "axioms": [
6454       "propext"
6455     ],
6456     "in_project_namespace": true,
6457     "kind": "definition",
6458     "module": "KomorebiVerification.ProjectorCore",
6459     "name": "Komorebi.instReprClaimRecord",
6460     "runtime_only": false
6461   },
6462   {
6463     "axioms": [
6464       "propext",
6465       "Classical.choice",
6466       "Quot.sound"
6467     ],
6468     "in_project_namespace": true,
6469     "kind": "definition",
6470     "module": "KomorebiVerification.TopologicalCompletion",
6471     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense",
6472     "runtime_only": false
6473   },
6474   {
6475     "axioms": [
6476       "propext",
6477       "Classical.choice",
6478       "Quot.sound"
6479     ],
6480     "in_project_namespace": true,
6481     "kind": "theorem",
6482     "module": "PaperIRelease.PacketTopologyGeneral",
6483     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM._proof_1",
6484     "runtime_only": false
6485   },
6486   {
6487     "axioms": [
6488       "propext",
6489       "Classical.choice",
6490       "Quot.sound"
6491     ],
6492     "in_project_namespace": false,
6493     "kind": "theorem",
6494     "module": "PaperIRelease.TopologyCountablePackets",
6495     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_2",
6496     "runtime_only": false
6497   },
6498   {
6499     "axioms": [
6500       "propext",
6501       "Classical.choice",
6502       "Quot.sound"
6503     ],
6504     "in_project_namespace": false,
6505     "kind": "theorem",
6506     "module": "ReleaseBoundary",
6507     "name": "PaperIBlock08Tests.quaternion_two_seeds_exist",
6508     "runtime_only": false
6509   },
6510   {
6511     "axioms": [
6512       "propext",
6513       "Classical.choice",
6514       "Quot.sound"
6515     ],
6516     "in_project_namespace": true,
6517     "kind": "definition",
6518     "module": "PaperIRelease.GrammarTyped",
6519     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrowOperator",
6520     "runtime_only": false
6521   },
6522   {
6523     "axioms": [
6524       "propext",
6525       "Classical.choice",
6526       "Quot.sound"
6527     ],
6528     "in_project_namespace": true,
6529     "kind": "theorem",
6530     "module": "PaperIRelease.PacketBoundaryTests",
6531     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_quotient_has_no_nonzero_packets",
6532     "runtime_only": false
6533   },
6534   {
6535     "axioms": [
6536       "propext",
6537       "Classical.choice",
6538       "Quot.sound"
6539     ],
6540     "in_project_namespace": true,
6541     "kind": "theorem",
6542     "module": "PaperIRelease.GeneralConditionedCoordinates",
6543     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditionNumber.eq_1",
6544     "runtime_only": false
6545   },
6546   {
6547     "axioms": [
6548       "propext",
6549       "Classical.choice",
6550       "Quot.sound"
6551     ],
6552     "in_project_namespace": true,
6553     "kind": "definition",
6554     "module": "PaperICompletion5.GeometricSeedFormula",
6555     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum",
6556     "runtime_only": false
6557   },
6558   {
6559     "axioms": [
6560       "propext",
6561       "Classical.choice",
6562       "Quot.sound"
6563     ],
6564     "in_project_namespace": true,
6565     "kind": "theorem",
6566     "module": "PaperIRelease.TopologyCategories",
6567     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.inj",
6568     "runtime_only": false
6569   },
6570   {
6571     "axioms": [
6572       "propext",
6573       "Classical.choice",
6574       "Quot.sound"
6575     ],
6576     "in_project_namespace": true,
6577     "kind": "theorem",
6578     "module": "PaperIRelease.TopologyCategories",
6579     "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull._proof_2",
6580     "runtime_only": false
6581   },
6582   {
6583     "axioms": [
6584       "propext",
6585       "Classical.choice",
6586       "Quot.sound"
6587     ],
6588     "in_project_namespace": true,
6589     "kind": "definition",
6590     "module": "PaperIRelease.GrammarPaths",
6591     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary",
6592     "runtime_only": false
6593   },
6594   {
6595     "axioms": [],
6596     "in_project_namespace": true,
6597     "kind": "definition",
6598     "module": "KomorebiVerification.ProjectorCore",
6599     "name": "Komorebi.FiniteDifference.forwardDiff",
6600     "runtime_only": false
6601   },
6602   {
6603     "axioms": [
6604       "propext",
6605       "Classical.choice",
6606       "Quot.sound"
6607     ],
6608     "in_project_namespace": true,
6609     "kind": "theorem",
6610     "module": "KomorebiVerification.PacketNaturalityCompletion",
6611     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_2",
6612     "runtime_only": false
6613   },
6614   {
6615     "axioms": [],
6616     "in_project_namespace": true,
6617     "kind": "definition",
6618     "module": "KomorebiVerification.ResidueProjectors",
6619     "name": "Komorebi.Residue.mergeAddress",
6620     "runtime_only": false
6621   },
6622   {
6623     "axioms": [
6624       "propext",
6625       "Classical.choice",
6626       "Quot.sound"
6627     ],
6628     "in_project_namespace": true,
6629     "kind": "theorem",
6630     "module": "KomorebiVerification.SeedRankOperations",
6631     "name": "Komorebi.SeedRankOperations.seedRank_tensorProduct_le_mul",
6632     "runtime_only": false
6633   },
6634   {
6635     "axioms": [
6636       "propext",
6637       "Classical.choice",
6638       "Quot.sound"
6639     ],
6640     "in_project_namespace": false,
6641     "kind": "theorem",
6642     "module": "PaperIRelease.TopologyUnconditionalBridge",
6643     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_3",
6644     "runtime_only": false
6645   },
6646   {
6647     "axioms": [
6648       "propext",
6649       "Classical.choice",
6650       "Quot.sound"
6651     ],
6652     "in_project_namespace": true,
6653     "kind": "theorem",
6654     "module": "PaperIRelease.TopologyCategories",
6655     "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_2",
6656     "runtime_only": false
6657   },
6658   {
6659     "axioms": [
6660       "propext",
6661       "Classical.choice",
6662       "Quot.sound"
6663     ],
6664     "in_project_namespace": true,
6665     "kind": "theorem",
6666     "module": "PaperIRelease.TopologyCategories",
6667     "name": "Komorebi.PaperIRelease.TopologyCategories.seeded_surjection_generates",
6668     "runtime_only": false
6669   },
6670   {
6671     "axioms": [
6672       "propext",
6673       "Classical.choice",
6674       "Quot.sound"
6675     ],
6676     "in_project_namespace": true,
6677     "kind": "theorem",
6678     "module": "PaperIRelease.AlgebraClassGrouping",
6679     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_5",
6680     "runtime_only": false
6681   },
6682   {
6683     "axioms": [
6684       "propext",
6685       "Classical.choice",
6686       "Quot.sound"
6687     ],
6688     "in_project_namespace": true,
6689     "kind": "theorem",
6690     "module": "PaperIRelease.AlgebraClassGrouping",
6691     "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_5",
6692     "runtime_only": false
6693   },
6694   {
6695     "axioms": [
6696       "propext",
6697       "Classical.choice",
6698       "Quot.sound"
6699     ],
6700     "in_project_namespace": true,
6701     "kind": "definition",
6702     "module": "PaperIRelease.PacketTopology",
6703     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientLiftCLM",
6704     "runtime_only": false
6705   },
6706   {
6707     "axioms": [],
6708     "in_project_namespace": true,
6709     "kind": "definition",
6710     "module": "PaperIRelease.CategoryExport",
6711     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.noConfusion",
6712     "runtime_only": false
6713   },
6714   {
6715     "axioms": [
6716       "propext",
6717       "Classical.choice",
6718       "Quot.sound"
6719     ],
6720     "in_project_namespace": true,
6721     "kind": "inductive",
6722     "module": "PaperIRelease.TopologyCategories",
6723     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism",
6724     "runtime_only": false
6725   },
6726   {
6727     "axioms": [
6728       "propext",
6729       "Classical.choice",
6730       "Quot.sound"
6731     ],
6732     "in_project_namespace": true,
6733     "kind": "constructor",
6734     "module": "KomorebiVerification.ProjectorCore",
6735     "name": "Komorebi.Foundation.LinearProjectorFamily.mk",
6736     "runtime_only": false
6737   },
6738   {
6739     "axioms": [
6740       "propext",
6741       "Classical.choice",
6742       "Quot.sound"
6743     ],
6744     "in_project_namespace": true,
6745     "kind": "theorem",
6746     "module": "PaperICompletion.ConditionedCoordinates",
6747     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator_inverse",
6748     "runtime_only": false
6749   },
6750   {
6751     "axioms": [
6752       "propext",
6753       "Classical.choice",
6754       "Quot.sound"
6755     ],
6756     "in_project_namespace": true,
6757     "kind": "theorem",
6758     "module": "PaperIRelease.PacketCorners",
6759     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_4",
6760     "runtime_only": false
6761   },
6762   {
6763     "axioms": [
6764       "propext",
6765       "Quot.sound"
6766     ],
6767     "in_project_namespace": false,
6768     "kind": "definition",
6769     "module": "PaperIRelease.AlgebraTransfer",
6770     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.splitter",
6771     "runtime_only": false
6772   },
6773   {
6774     "axioms": [
6775       "propext",
6776       "Classical.choice",
6777       "Quot.sound"
6778     ],
6779     "in_project_namespace": false,
6780     "kind": "theorem",
6781     "module": "PaperIRelease.TopologyCountablePackets",
6782     "name": "PaperIRelease.TopologyCountablePackets.Projectors.annihilate",
6783     "runtime_only": false
6784   },
6785   {
6786     "axioms": [
6787       "propext",
6788       "Classical.choice",
6789       "Quot.sound"
6790     ],
6791     "in_project_namespace": true,
6792     "kind": "theorem",
6793     "module": "PaperIRelease.GrammarTyped",
6794     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.sizeOf_spec",
6795     "runtime_only": false
6796   },
6797   {
6798     "axioms": [
6799       "propext",
6800       "Classical.choice",
6801       "Quot.sound"
6802     ],
6803     "in_project_namespace": true,
6804     "kind": "theorem",
6805     "module": "PaperICompletion8.RegularMultiplicity",
6806     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.other_factor_smul_zero",
6807     "runtime_only": false
6808   },
6809   {
6810     "axioms": [
6811       "propext",
6812       "Classical.choice",
6813       "Quot.sound"
6814     ],
6815     "in_project_namespace": true,
6816     "kind": "theorem",
6817     "module": "KomorebiVerification.SeedRankBasics",
6818     "name": "Komorebi.SeedRankBasics.cyclic_iff_exists_surjective_oneSeedMap",
6819     "runtime_only": false
6820   },
6821   {
6822     "axioms": [
6823       "propext",
6824       "Classical.choice",
6825       "Quot.sound"
6826     ],
6827     "in_project_namespace": true,
6828     "kind": "theorem",
6829     "module": "KomorebiVerification.SeedRankBasics",
6830     "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquivRange_apply_mk",
6831     "runtime_only": false
6832   },
6833   {
6834     "axioms": [
6835       "propext",
6836       "Quot.sound"
6837     ],
6838     "in_project_namespace": true,
6839     "kind": "definition",
6840     "module": "PaperIRelease.GrammarModules",
6841     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.noConfusionType",
6842     "runtime_only": false
6843   },
6844   {
6845     "axioms": [
6846       "propext"
6847     ],
6848     "in_project_namespace": true,
6849     "kind": "theorem",
6850     "module": "PaperIRelease.CategoryExport",
6851     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_def",
6852     "runtime_only": false
6853   },
6854   {
6855     "axioms": [
6856       "propext",
6857       "Classical.choice",
6858       "Quot.sound"
6859     ],
6860     "in_project_namespace": false,
6861     "kind": "theorem",
6862     "module": "PaperIRelease.TopologySeedRank",
6863     "name": "PaperIRelease.TopologyTransport.generates_mono_algebra",
6864     "runtime_only": false
6865   },
6866   {
6867     "axioms": [
6868       "propext"
6869     ],
6870     "in_project_namespace": true,
6871     "kind": "theorem",
6872     "module": "PaperIRelease.CategoryExport",
6873     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_4",
6874     "runtime_only": false
6875   },
6876   {
6877     "axioms": [
6878       "propext",
6879       "Classical.choice",
6880       "Quot.sound"
6881     ],
6882     "in_project_namespace": true,
6883     "kind": "theorem",
6884     "module": "PaperIRelease.PacketUniversal",
6885     "name": "Komorebi.PaperIRelease.PacketUniversal.unique_packet_lift",
6886     "runtime_only": false
6887   },
6888   {
6889     "axioms": [
6890       "propext",
6891       "Classical.choice",
6892       "Quot.sound"
6893     ],
6894     "in_project_namespace": true,
6895     "kind": "theorem",
6896     "module": "PaperIRelease.GraphReachability",
6897     "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra._proof_1",
6898     "runtime_only": false
6899   },
6900   {
6901     "axioms": [
6902       "propext",
6903       "Classical.choice",
6904       "Quot.sound"
6905     ],
6906     "in_project_namespace": false,
6907     "kind": "theorem",
6908     "module": "PaperIRelease.TopologyCountablePackets",
6909     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_6",
6910     "runtime_only": false
6911   },
6912   {
6913     "axioms": [],
6914     "in_project_namespace": true,
6915     "kind": "definition",
6916     "module": "KomorebiVerification.ProjectorCore",
6917     "name": "Komorebi.instDecidableEqFormalizationStatus",
6918     "runtime_only": false
6919   },
6920   {
6921     "axioms": [
6922       "propext",
6923       "Quot.sound"
6924     ],
6925     "in_project_namespace": true,
6926     "kind": "theorem",
6927     "module": "KomorebiVerification.PacketNaturalityCompletion",
6928     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet._proof_1",
6929     "runtime_only": false
6930   },
6931   {
6932     "axioms": [
6933       "propext",
6934       "Classical.choice",
6935       "Quot.sound"
6936     ],
6937     "in_project_namespace": false,
6938     "kind": "theorem",
6939     "module": "PaperIRelease.TopologyTransport",
6940     "name": "PaperIRelease.TopologyTransport.map_aggregated_packetRange_eq",
6941     "runtime_only": false
6942   },
6943   {
6944     "axioms": [],
6945     "in_project_namespace": true,
6946     "kind": "definition",
6947     "module": "KomorebiVerification.ProjectorCore",
6948     "name": "Komorebi.ClaimRecord.notes",
6949     "runtime_only": false
6950   },
6951   {
6952     "axioms": [
6953       "propext",
6954       "Classical.choice",
6955       "Quot.sound"
6956     ],
6957     "in_project_namespace": true,
6958     "kind": "theorem",
6959     "module": "PaperICompletion3.OperatorPrimaryAPI",
6960     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_of_cyclic._simp_1_1",
6961     "runtime_only": false
6962   },
6963   {
6964     "axioms": [
6965       "propext",
6966       "Classical.choice",
6967       "Quot.sound"
6968     ],
6969     "in_project_namespace": true,
6970     "kind": "definition",
6971     "module": "PaperIRelease.PacketTopology",
6972     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL",
6973     "runtime_only": false
6974   },
6975   {
6976     "axioms": [],
6977     "in_project_namespace": true,
6978     "kind": "theorem",
6979     "module": "KomorebiVerification.ProjectorCore",
6980     "name": "Komorebi.ClaimKind.classicalInput.sizeOf_spec",
6981     "runtime_only": false
6982   },
6983   {
6984     "axioms": [
6985       "propext",
6986       "Classical.choice",
6987       "Quot.sound"
6988     ],
6989     "in_project_namespace": true,
6990     "kind": "theorem",
6991     "module": "KomorebiVerification.EllipticAlgorithms",
6992     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_monotone",
6993     "runtime_only": false
6994   },
6995   {
6996     "axioms": [
6997       "propext",
6998       "Classical.choice",
6999       "Quot.sound"
7000     ],
7001     "in_project_namespace": true,
7002     "kind": "definition",
7003     "module": "PaperICompletion4.OperatorIntrinsicFormula",
7004     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv",
7005     "runtime_only": false
7006   },
7007   {
7008     "axioms": [],
7009     "in_project_namespace": true,
7010     "kind": "definition",
7011     "module": "KomorebiVerification.PacketNaturalityCompletion",
7012     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.X",
7013     "runtime_only": false
7014   },
7015   {
7016     "axioms": [
7017       "propext",
7018       "Classical.choice",
7019       "Quot.sound"
7020     ],
7021     "in_project_namespace": false,
7022     "kind": "theorem",
7023     "module": "PaperIRelease.TopologyDenseCompletion",
7024     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_6",
7025     "runtime_only": false
7026   },
7027   {
7028     "axioms": [],
7029     "in_project_namespace": true,
7030     "kind": "definition",
7031     "module": "KomorebiVerification.ProjectorCore",
7032     "name": "Komorebi.instReprClaimKind.repr.match_1",
7033     "runtime_only": false
7034   },
7035   {
7036     "axioms": [
7037       "propext",
7038       "Quot.sound"
7039     ],
7040     "in_project_namespace": true,
7041     "kind": "definition",
7042     "module": "PaperIRelease.GrammarTyped",
7043     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.ctorIdx",
7044     "runtime_only": false
7045   },
7046   {
7047     "axioms": [
7048       "propext",
7049       "Classical.choice",
7050       "Quot.sound"
7051     ],
7052     "in_project_namespace": true,
7053     "kind": "definition",
7054     "module": "PaperIRelease.PacketEquivalentNorm",
7055     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm",
7056     "runtime_only": false
7057   },
7058   {
7059     "axioms": [
7060       "propext"
7061     ],
7062     "in_project_namespace": true,
7063     "kind": "theorem",
7064     "module": "KomorebiVerification.SingleOperatorGraph",
7065     "name": "Komorebi.SingleOperatorGraph.complexCycleRoot._proof_1",
7066     "runtime_only": false
7067   },
7068   {
7069     "axioms": [
7070       "propext"
7071     ],
7072     "in_project_namespace": true,
7073     "kind": "theorem",
7074     "module": "PaperIRelease.CategoryExport",
7075     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_def",
7076     "runtime_only": false
7077   },
7078   {
7079     "axioms": [
7080       "propext",
7081       "Classical.choice",
7082       "Quot.sound"
7083     ],
7084     "in_project_namespace": true,
7085     "kind": "definition",
7086     "module": "PaperICompletion3.OperatorPrimaryAPI",
7087     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.exponent",
7088     "runtime_only": false
7089   },
7090   {
7091     "axioms": [
7092       "propext",
7093       "Classical.choice",
7094       "Quot.sound"
7095     ],
7096     "in_project_namespace": true,
7097     "kind": "theorem",
7098     "module": "PaperIRelease.PacketTopology",
7099     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM._proof_1",
7100     "runtime_only": false
7101   },
7102   {
7103     "axioms": [
7104       "propext",
7105       "Classical.choice",
7106       "Quot.sound"
7107     ],
7108     "in_project_namespace": true,
7109     "kind": "theorem",
7110     "module": "KomorebiVerification.EllipticAlgorithms",
7111     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_1",
7112     "runtime_only": false
7113   },
7114   {
7115     "axioms": [
7116       "propext",
7117       "Classical.choice",
7118       "Quot.sound"
7119     ],
7120     "in_project_namespace": true,
7121     "kind": "definition",
7122     "module": "PaperICompletion4.ResidueQuotient",
7123     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr",
7124     "runtime_only": false
7125   },
7126   {
7127     "axioms": [
7128       "propext",
7129       "Classical.choice",
7130       "Quot.sound"
7131     ],
7132     "in_project_namespace": false,
7133     "kind": "theorem",
7134     "module": "PaperIRelease.TopologyCountablePackets",
7135     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_1",
7136     "runtime_only": false
7137   },
7138   {
7139     "axioms": [
7140       "propext",
7141       "Classical.choice",
7142       "Quot.sound"
7143     ],
7144     "in_project_namespace": true,
7145     "kind": "theorem",
7146     "module": "PaperIRelease.GrammarAlgebra",
7147     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_complete",
7148     "runtime_only": false
7149   },
7150   {
7151     "axioms": [
7152       "propext",
7153       "Classical.choice",
7154       "Quot.sound"
7155     ],
7156     "in_project_namespace": true,
7157     "kind": "definition",
7158     "module": "KomorebiVerification.PacketNaturalityCompletion",
7159     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlocks",
7160     "runtime_only": false
7161   },
7162   {
7163     "axioms": [
7164       "propext",
7165       "Classical.choice",
7166       "Quot.sound"
7167     ],
7168     "in_project_namespace": true,
7169     "kind": "definition",
7170     "module": "KomorebiVerification.PacketNaturalityCompletion",
7171     "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule",
7172     "runtime_only": false
7173   },
7174   {
7175     "axioms": [
7176       "propext",
7177       "Classical.choice",
7178       "Quot.sound"
7179     ],
7180     "in_project_namespace": true,
7181     "kind": "theorem",
7182     "module": "KomorebiVerification.SingleOperatorGraph",
7183     "name": "Komorebi.SingleOperatorGraph.paddedBlockSums_generate",
7184     "runtime_only": false
7185   },
7186   {
7187     "axioms": [],
7188     "in_project_namespace": true,
7189     "kind": "definition",
7190     "module": "PaperIRelease.AlgebraPreorder",
7191     "name": "Komorebi.PaperIRelease.StrictPath.match_1",
7192     "runtime_only": false
7193   },
7194   {
7195     "axioms": [
7196       "propext",
7197       "Classical.choice",
7198       "Quot.sound"
7199     ],
7200     "in_project_namespace": false,
7201     "kind": "definition",
7202     "module": "PaperIRelease.TopologyCountablePackets",
7203     "name": "PaperIRelease.TopologyCountablePackets.Projectors.casesOn",
7204     "runtime_only": false
7205   },
7206   {
7207     "axioms": [
7208       "propext",
7209       "Classical.choice",
7210       "Quot.sound"
7211     ],
7212     "in_project_namespace": true,
7213     "kind": "theorem",
7214     "module": "KomorebiVerification.SingleOperatorGraph",
7215     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_one",
7216     "runtime_only": false
7217   },
7218   {
7219     "axioms": [
7220       "propext",
7221       "Classical.choice",
7222       "Quot.sound"
7223     ],
7224     "in_project_namespace": true,
7225     "kind": "theorem",
7226     "module": "PaperICompletion3.PrimarySeedFormula",
7227     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primePower_quotient_subsingleton_of_exponent_zero",
7228     "runtime_only": false
7229   },
7230   {
7231     "axioms": [
7232       "propext",
7233       "Classical.choice",
7234       "Quot.sound"
7235     ],
7236     "in_project_namespace": true,
7237     "kind": "definition",
7238     "module": "KomorebiVerification.EllipticAlgorithms",
7239     "name": "Komorebi.EllipticCoordinates.Mx",
7240     "runtime_only": false
7241   },
7242   {
7243     "axioms": [],
7244     "in_project_namespace": true,
7245     "kind": "constructor",
7246     "module": "KomorebiVerification.ProjectorCore",
7247     "name": "Komorebi.ClaimKind.numericalCertificate",
7248     "runtime_only": false
7249   },
7250   {
7251     "axioms": [
7252       "propext",
7253       "Quot.sound"
7254     ],
7255     "in_project_namespace": true,
7256     "kind": "theorem",
7257     "module": "PaperIRelease.AlgebraQuotient",
7258     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_6",
7259     "runtime_only": false
7260   },
7261   {
7262     "axioms": [],
7263     "in_project_namespace": true,
7264     "kind": "definition",
7265     "module": "KomorebiVerification.ProjectorCore",
7266     "name": "Komorebi.ClaimKind.noConfusionType",
7267     "runtime_only": false
7268   },
7269   {
7270     "axioms": [
7271       "propext",
7272       "Quot.sound"
7273     ],
7274     "in_project_namespace": true,
7275     "kind": "theorem",
7276     "module": "PaperIRelease.GrammarModules",
7277     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_9",
7278     "runtime_only": false
7279   },
7280   {
7281     "axioms": [
7282       "propext",
7283       "Classical.choice",
7284       "Quot.sound"
7285     ],
7286     "in_project_namespace": true,
7287     "kind": "definition",
7288     "module": "PaperIRelease.GrammarIdeal",
7289     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv",
7290     "runtime_only": false
7291   },
7292   {
7293     "axioms": [
7294       "propext",
7295       "Classical.choice",
7296       "Quot.sound"
7297     ],
7298     "in_project_namespace": true,
7299     "kind": "theorem",
7300     "module": "KomorebiVerification.PacketNaturalityCompletion",
7301     "name": "Komorebi.PacketNaturalityCompletion.Reachability.operator_preserves_reachable_support",
7302     "runtime_only": false
7303   },
7304   {
7305     "axioms": [],
7306     "in_project_namespace": true,
7307     "kind": "definition",
7308     "module": "KomorebiVerification.PacketNaturalityCompletion",
7309     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1",
7310     "runtime_only": false
7311   },
7312   {
7313     "axioms": [
7314       "propext",
7315       "Classical.choice",
7316       "Quot.sound"
7317     ],
7318     "in_project_namespace": true,
7319     "kind": "theorem",
7320     "module": "PaperIRelease.CategoryPackets",
7321     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.sizeOf_spec",
7322     "runtime_only": false
7323   },
7324   {
7325     "axioms": [
7326       "propext",
7327       "Classical.choice",
7328       "Quot.sound"
7329     ],
7330     "in_project_namespace": true,
7331     "kind": "theorem",
7332     "module": "PaperIRelease.AlgebraPreorder",
7333     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_7",
7334     "runtime_only": false
7335   },
7336   {
7337     "axioms": [
7338       "propext",
7339       "Quot.sound"
7340     ],
7341     "in_project_namespace": true,
7342     "kind": "theorem",
7343     "module": "PaperIRelease.AlgebraSupport",
7344     "name": "Komorebi.PaperIRelease.supportSubmodule._proof_1",
7345     "runtime_only": false
7346   },
7347   {
7348     "axioms": [
7349       "propext",
7350       "Classical.choice",
7351       "Quot.sound"
7352     ],
7353     "in_project_namespace": true,
7354     "kind": "theorem",
7355     "module": "KomorebiVerification.EllipticAlgorithms",
7356     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_apply",
7357     "runtime_only": false
7358   },
7359   {
7360     "axioms": [
7361       "propext",
7362       "Classical.choice",
7363       "Quot.sound"
7364     ],
7365     "in_project_namespace": false,
7366     "kind": "theorem",
7367     "module": "PaperIRelease.TopologyUnconditionalBridge",
7368     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_11",
7369     "runtime_only": false
7370   },
7371   {
7372     "axioms": [
7373       "propext",
7374       "Classical.choice",
7375       "Quot.sound"
7376     ],
7377     "in_project_namespace": true,
7378     "kind": "definition",
7379     "module": "PaperIRelease.TopologyCategories",
7380     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.toContinuousPacketMorphism",
7381     "runtime_only": false
7382   },
7383   {
7384     "axioms": [
7385       "propext",
7386       "Classical.choice",
7387       "Quot.sound"
7388     ],
7389     "in_project_namespace": true,
7390     "kind": "definition",
7391     "module": "PaperIRelease.CategoryPackets",
7392     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.noConfusion",
7393     "runtime_only": false
7394   },
7395   {
7396     "axioms": [
7397       "propext",
7398       "Classical.choice",
7399       "Quot.sound"
7400     ],
7401     "in_project_namespace": true,
7402     "kind": "theorem",
7403     "module": "KomorebiVerification.SingleOperatorGraph",
7404     "name": "Komorebi.SingleOperatorGraph.orbitFamily.eq_1",
7405     "runtime_only": false
7406   },
7407   {
7408     "axioms": [
7409       "propext",
7410       "Classical.choice",
7411       "Quot.sound"
7412     ],
7413     "in_project_namespace": true,
7414     "kind": "theorem",
7415     "module": "KomorebiVerification.PaperITransport",
7416     "name": "Komorebi.Foundation.conjugate_transferBlock",
7417     "runtime_only": false
7418   },
7419   {
7420     "axioms": [],
7421     "in_project_namespace": true,
7422     "kind": "definition",
7423     "module": "KomorebiVerification.ProjectorCore",
7424     "name": "Komorebi.Algebra.IsLowerTriangular",
7425     "runtime_only": false
7426   },
7427   {
7428     "axioms": [
7429       "propext",
7430       "Quot.sound"
7431     ],
7432     "in_project_namespace": true,
7433     "kind": "theorem",
7434     "module": "KomorebiVerification.PacketNaturalityCompletion",
7435     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083.eq_1",
7436     "runtime_only": false
7437   },
7438   {
7439     "axioms": [
7440       "propext",
7441       "Classical.choice",
7442       "Quot.sound"
7443     ],
7444     "in_project_namespace": true,
7445     "kind": "theorem",
7446     "module": "PaperICompletion6.PrimaryCyclicCriterion",
7447     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_nonzero_primary_cyclic",
7448     "runtime_only": false
7449   },
7450   {
7451     "axioms": [
7452       "propext",
7453       "Quot.sound"
7454     ],
7455     "in_project_namespace": true,
7456     "kind": "theorem",
7457     "module": "PaperIRelease.AlgebraClassGrouping",
7458     "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq._simp_1_1",
7459     "runtime_only": false
7460   },
7461   {
7462     "axioms": [],
7463     "in_project_namespace": true,
7464     "kind": "theorem",
7465     "module": "PaperIRelease.GrammarPaths",
7466     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil.sizeOf_spec",
7467     "runtime_only": false
7468   },
7469   {
7470     "axioms": [
7471       "propext",
7472       "Classical.choice",
7473       "Quot.sound"
7474     ],
7475     "in_project_namespace": true,
7476     "kind": "theorem",
7477     "module": "PaperIRelease.GrammarAlgebra",
7478     "name": "Komorebi.PaperIRelease.GrammarAlgebra.declared_relation",
7479     "runtime_only": false
7480   },
7481   {
7482     "axioms": [],
7483     "in_project_namespace": true,
7484     "kind": "theorem",
7485     "module": "KomorebiVerification.ProjectorCore",
7486     "name": "Komorebi.FiniteDifference.iteratedDiff.eq_2",
7487     "runtime_only": false
7488   },
7489   {
7490     "axioms": [
7491       "propext",
7492       "Classical.choice",
7493       "Quot.sound"
7494     ],
7495     "in_project_namespace": false,
7496     "kind": "definition",
7497     "module": "ReleaseBoundary",
7498     "name": "PaperIBlock08Tests.DH",
7499     "runtime_only": false
7500   },
7501   {
7502     "axioms": [
7503       "propext"
7504     ],
7505     "in_project_namespace": true,
7506     "kind": "theorem",
7507     "module": "KomorebiVerification.SingleOperatorGraph",
7508     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_3",
7509     "runtime_only": false
7510   },
7511   {
7512     "axioms": [
7513       "propext",
7514       "Classical.choice",
7515       "Quot.sound"
7516     ],
7517     "in_project_namespace": true,
7518     "kind": "theorem",
7519     "module": "KomorebiVerification.SeedRankBasics",
7520     "name": "Komorebi.SeedRankBasics.cyclic_iff_seedFinrank_eq_one",
7521     "runtime_only": false
7522   },
7523   {
7524     "axioms": [
7525       "propext",
7526       "Classical.choice",
7527       "Quot.sound"
7528     ],
7529     "in_project_namespace": true,
7530     "kind": "theorem",
7531     "module": "KomorebiVerification.PacketNaturalityCompletion",
7532     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB._proof_1",
7533     "runtime_only": false
7534   },
7535   {
7536     "axioms": [
7537       "propext",
7538       "Classical.choice",
7539       "Quot.sound"
7540     ],
7541     "in_project_namespace": true,
7542     "kind": "definition",
7543     "module": "PaperIRelease.GrammarIdeal",
7544     "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeToIdeal",
7545     "runtime_only": false
7546   },
7547   {
7548     "axioms": [
7549       "propext",
7550       "Classical.choice",
7551       "Quot.sound"
7552     ],
7553     "in_project_namespace": true,
7554     "kind": "theorem",
7555     "module": "PaperIRelease.TopologyCategories",
7556     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.inj",
7557     "runtime_only": false
7558   },
7559   {
7560     "axioms": [
7561       "propext",
7562       "Classical.choice",
7563       "Quot.sound"
7564     ],
7565     "in_project_namespace": true,
7566     "kind": "theorem",
7567     "module": "PaperIRelease.CategoryPackets",
7568     "name": "Komorebi.PaperIRelease.CategoryPackets.hull_natural",
7569     "runtime_only": false
7570   },
7571   {
7572     "axioms": [
7573       "propext",
7574       "Classical.choice",
7575       "Quot.sound"
7576     ],
7577     "in_project_namespace": true,
7578     "kind": "theorem",
7579     "module": "KomorebiVerification.PacketNaturalityCompletion",
7580     "name": "Komorebi.PacketNaturalityCompletion.Reachability.ReachableFrom.eq_1",
7581     "runtime_only": false
7582   },
7583   {
7584     "axioms": [
7585       "propext",
7586       "Classical.choice",
7587       "Quot.sound"
7588     ],
7589     "in_project_namespace": true,
7590     "kind": "theorem",
7591     "module": "PaperIRelease.GraphSourceCount",
7592     "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_2",
7593     "runtime_only": false
7594   },
7595   {
7596     "axioms": [],
7597     "in_project_namespace": false,
7598     "kind": "theorem",
7599     "module": "PaperIRelease.CategoryExport",
7600     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_7",
7601     "runtime_only": false
7602   },
7603   {
7604     "axioms": [
7605       "propext",
7606       "Classical.choice",
7607       "Quot.sound"
7608     ],
7609     "in_project_namespace": true,
7610     "kind": "theorem",
7611     "module": "PaperIRelease.PacketPureRank",
7612     "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_card",
7613     "runtime_only": false
7614   },
7615   {
7616     "axioms": [
7617       "propext",
7618       "Classical.choice",
7619       "Quot.sound"
7620     ],
7621     "in_project_namespace": true,
7622     "kind": "theorem",
7623     "module": "PaperICompletion7.ModuleTop",
7624     "name": "Komorebi.PaperICompletion7.ModuleTop.family_generates_iff",
7625     "runtime_only": false
7626   },
7627   {
7628     "axioms": [
7629       "propext",
7630       "Quot.sound"
7631     ],
7632     "in_project_namespace": true,
7633     "kind": "theorem",
7634     "module": "KomorebiVerification.SingleOperatorGraph",
7635     "name": "Komorebi.SingleOperatorGraph.complex_cycle_seedNumber_isLeast_two._proof_1_2",
7636     "runtime_only": false
7637   },
7638   {
7639     "axioms": [
7640       "propext",
7641       "Classical.choice",
7642       "Quot.sound"
7643     ],
7644     "in_project_namespace": true,
7645     "kind": "definition",
7646     "module": "PaperIRelease.GrammarEquivalence",
7647     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk._flat_ctor",
7648     "runtime_only": false
7649   },
7650   {
7651     "axioms": [
7652       "propext",
7653       "Classical.choice",
7654       "Quot.sound"
7655     ],
7656     "in_project_namespace": true,
7657     "kind": "theorem",
7658     "module": "KomorebiVerification.SingleOperatorGraph",
7659     "name": "Komorebi.SingleOperatorGraph.singleOperator_operatorAlgebra_seedRanks_eq_of_primary_decomposition",
7660     "runtime_only": false
7661   },
7662   {
7663     "axioms": [
7664       "propext",
7665       "Classical.choice",
7666       "Quot.sound"
7667     ],
7668     "in_project_namespace": true,
7669     "kind": "theorem",
7670     "module": "PaperICompletion.CyclicClassification",
7671     "name": "Komorebi.PaperICompletion.CyclicClassification.cyclic_four_way_without_polynomial_certificate",
7672     "runtime_only": false
7673   },
7674   {
7675     "axioms": [],
7676     "in_project_namespace": true,
7677     "kind": "definition",
7678     "module": "KomorebiVerification.ProjectorCore",
7679     "name": "Komorebi.Seed.OperatorExpr.recOn",
7680     "runtime_only": false
7681   },
7682   {
7683     "axioms": [
7684       "propext",
7685       "Classical.choice",
7686       "Quot.sound"
7687     ],
7688     "in_project_namespace": true,
7689     "kind": "theorem",
7690     "module": "PaperIRelease.GrammarTyped",
7691     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.inj",
7692     "runtime_only": false
7693   },
7694   {
7695     "axioms": [
7696       "propext",
7697       "Quot.sound"
7698     ],
7699     "in_project_namespace": true,
7700     "kind": "theorem",
7701     "module": "KomorebiVerification.FibreRefinement",
7702     "name": "Komorebi.Packet.fibreLinearProjectorFamily._proof_1",
7703     "runtime_only": false
7704   },
7705   {
7706     "axioms": [],
7707     "in_project_namespace": true,
7708     "kind": "theorem",
7709     "module": "PaperICompletion3.PrimarySeedFormula",
7710     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_1",
7711     "runtime_only": false
7712   },
7713   {
7714     "axioms": [
7715       "propext",
7716       "Classical.choice",
7717       "Quot.sound"
7718     ],
7719     "in_project_namespace": true,
7720     "kind": "theorem",
7721     "module": "PaperIRelease.AlgebraDiagonal",
7722     "name": "Komorebi.PaperIRelease.diagonalProjection_proj",
7723     "runtime_only": false
7724   },
7725   {
7726     "axioms": [
7727       "propext",
7728       "Classical.choice",
7729       "Quot.sound"
7730     ],
7731     "in_project_namespace": true,
7732     "kind": "definition",
7733     "module": "PaperICompletion7.Nakayama",
7734     "name": "Komorebi.PaperICompletion7.Nakayama.IdealTop",
7735     "runtime_only": false
7736   },
7737   {
7738     "axioms": [
7739       "propext",
7740       "Classical.choice",
7741       "Quot.sound"
7742     ],
7743     "in_project_namespace": true,
7744     "kind": "theorem",
7745     "module": "KomorebiVerification.SingleOperatorGraph",
7746     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_apply",
7747     "runtime_only": false
7748   },
7749   {
7750     "axioms": [
7751       "propext",
7752       "Classical.choice",
7753       "Quot.sound"
7754     ],
7755     "in_project_namespace": true,
7756     "kind": "theorem",
7757     "module": "KomorebiVerification.PaperIBlockCompletion",
7758     "name": "Komorebi.Foundation.transferBlock_reconstruction_end",
7759     "runtime_only": false
7760   },
7761   {
7762     "axioms": [
7763       "propext",
7764       "Quot.sound"
7765     ],
7766     "in_project_namespace": true,
7767     "kind": "definition",
7768     "module": "PaperIRelease.AlgebraTransfer",
7769     "name": "Komorebi.PaperIRelease.operatorWord._f",
7770     "runtime_only": false
7771   },
7772   {
7773     "axioms": [
7774       "propext",
7775       "Classical.choice",
7776       "Quot.sound"
7777     ],
7778     "in_project_namespace": false,
7779     "kind": "theorem",
7780     "module": "PaperIRelease.TopologyCountablePackets",
7781     "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_1",
7782     "runtime_only": false
7783   },
7784   {
7785     "axioms": [
7786       "propext",
7787       "Classical.choice",
7788       "Quot.sound"
7789     ],
7790     "in_project_namespace": true,
7791     "kind": "theorem",
7792     "module": "KomorebiVerification.EllipticAlgorithms",
7793     "name": "Komorebi.EllipticCoordinates.relationPolynomial.eq_1",
7794     "runtime_only": false
7795   },
7796   {
7797     "axioms": [
7798       "propext",
7799       "Classical.choice",
7800       "Quot.sound"
7801     ],
7802     "in_project_namespace": true,
7803     "kind": "definition",
7804     "module": "KomorebiVerification.PacketNaturalityCompletion",
7805     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks",
7806     "runtime_only": false
7807   },
7808   {
7809     "axioms": [
7810       "propext",
7811       "Classical.choice",
7812       "Quot.sound"
7813     ],
7814     "in_project_namespace": true,
7815     "kind": "theorem",
7816     "module": "KomorebiVerification.TopologicalCompletion",
7817     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.idempotentRange_eq_closure_map",
7818     "runtime_only": false
7819   },
7820   {
7821     "axioms": [
7822       "propext",
7823       "Classical.choice",
7824       "Quot.sound"
7825     ],
7826     "in_project_namespace": true,
7827     "kind": "theorem",
7828     "module": "PaperIRelease.GraphReachability",
7829     "name": "Komorebi.PaperIRelease.generatedAlgebra_le_reachability",
7830     "runtime_only": false
7831   },
7832   {
7833     "axioms": [
7834       "propext",
7835       "Quot.sound"
7836     ],
7837     "in_project_namespace": true,
7838     "kind": "definition",
7839     "module": "PaperIRelease.GrammarModules",
7840     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.ctorIdx",
7841     "runtime_only": false
7842   },
7843   {
7844     "axioms": [
7845       "propext",
7846       "Classical.choice",
7847       "Quot.sound"
7848     ],
7849     "in_project_namespace": true,
7850     "kind": "definition",
7851     "module": "PaperIRelease.GrammarAlgebra",
7852     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction",
7853     "runtime_only": false
7854   },
7855   {
7856     "axioms": [
7857       "propext",
7858       "Classical.choice",
7859       "Quot.sound"
7860     ],
7861     "in_project_namespace": true,
7862     "kind": "theorem",
7863     "module": "PaperICompletion7.Nakayama",
7864     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_smul",
7865     "runtime_only": false
7866   },
7867   {
7868     "axioms": [
7869       "propext",
7870       "Classical.choice",
7871       "Quot.sound"
7872     ],
7873     "in_project_namespace": true,
7874     "kind": "definition",
7875     "module": "PaperIRelease.GrammarEquivalence",
7876     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.noConfusionType",
7877     "runtime_only": false
7878   },
7879   {
7880     "axioms": [
7881       "propext",
7882       "Classical.choice",
7883       "Quot.sound"
7884     ],
7885     "in_project_namespace": true,
7886     "kind": "theorem",
7887     "module": "PaperIRelease.GraphSources",
7888     "name": "Komorebi.PaperIRelease.FiniteDigraph.exists_source_le",
7889     "runtime_only": false
7890   },
7891   {
7892     "axioms": [
7893       "propext",
7894       "Classical.choice",
7895       "Quot.sound"
7896     ],
7897     "in_project_namespace": true,
7898     "kind": "theorem",
7899     "module": "PaperIRelease.PacketCorners",
7900     "name": "Komorebi.PaperIRelease.cornerCompression._proof_4",
7901     "runtime_only": false
7902   },
7903   {
7904     "axioms": [
7905       "propext",
7906       "Classical.choice",
7907       "Quot.sound"
7908     ],
7909     "in_project_namespace": true,
7910     "kind": "theorem",
7911     "module": "KomorebiVerification.PathGraphKrylov",
7912     "name": "Komorebi.PathGraphKrylov.endpoint_isCyclic",
7913     "runtime_only": false
7914   },
7915   {
7916     "axioms": [
7917       "propext",
7918       "Classical.choice",
7919       "Quot.sound"
7920     ],
7921     "in_project_namespace": true,
7922     "kind": "theorem",
7923     "module": "PaperICompletion.SpectralCertificates",
7924     "name": "Komorebi.PaperICompletion.SpectralCertificates.real_symmetric_matrix_seedNumber_isLeast",
7925     "runtime_only": false
7926   },
7927   {
7928     "axioms": [
7929       "propext",
7930       "Classical.choice",
7931       "Quot.sound"
7932     ],
7933     "in_project_namespace": true,
7934     "kind": "definition",
7935     "module": "KomorebiVerification.PacketNaturalityCompletion",
7936     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.BlockMulClosed",
7937     "runtime_only": false
7938   },
7939   {
7940     "axioms": [
7941       "propext",
7942       "Classical.choice",
7943       "Quot.sound"
7944     ],
7945     "in_project_namespace": true,
7946     "kind": "theorem",
7947     "module": "PaperIRelease.PacketTopology",
7948     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient._proof_1",
7949     "runtime_only": false
7950   },
7951   {
7952     "axioms": [
7953       "propext",
7954       "Quot.sound"
7955     ],
7956     "in_project_namespace": true,
7957     "kind": "theorem",
7958     "module": "KomorebiVerification.SingleOperatorGraph",
7959     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_5",
7960     "runtime_only": false
7961   },
7962   {
7963     "axioms": [],
7964     "in_project_namespace": true,
7965     "kind": "definition",
7966     "module": "PaperIRelease.AlgebraPreorder",
7967     "name": "Komorebi.PaperIRelease.StrictPath",
7968     "runtime_only": false
7969   },
7970   {
7971     "axioms": [
7972       "propext",
7973       "Classical.choice",
7974       "Quot.sound"
7975     ],
7976     "in_project_namespace": true,
7977     "kind": "definition",
7978     "module": "PaperIRelease.CategoryPackets",
7979     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.noConfusion",
7980     "runtime_only": false
7981   },
7982   {
7983     "axioms": [
7984       "propext",
7985       "Classical.choice",
7986       "Quot.sound"
7987     ],
7988     "in_project_namespace": false,
7989     "kind": "definition",
7990     "module": "PaperIRelease.TopologyDenseCompletion",
7991     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv",
7992     "runtime_only": false
7993   },
7994   {
7995     "axioms": [
7996       "propext",
7997       "Classical.choice",
7998       "Quot.sound"
7999     ],
8000     "in_project_namespace": true,
8001     "kind": "theorem",
8002     "module": "PaperIRelease.CategoryPackets",
8003     "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_2",
8004     "runtime_only": false
8005   },
8006   {
8007     "axioms": [
8008       "propext",
8009       "Classical.choice",
8010       "Quot.sound"
8011     ],
8012     "in_project_namespace": true,
8013     "kind": "theorem",
8014     "module": "KomorebiVerification.SingleOperatorGraph",
8015     "name": "Komorebi.SingleOperatorGraph.operatorAlgebra_seedRank_eq_of_seedNumber_isLeast",
8016     "runtime_only": false
8017   },
8018   {
8019     "axioms": [
8020       "propext",
8021       "Classical.choice",
8022       "Quot.sound"
8023     ],
8024     "in_project_namespace": true,
8025     "kind": "theorem",
8026     "module": "PaperIRelease.GraphSourceProjection",
8027     "name": "Komorebi.PaperIRelease.componentProjection_packet",
8028     "runtime_only": false
8029   },
8030   {
8031     "axioms": [
8032       "propext",
8033       "Classical.choice",
8034       "Quot.sound"
8035     ],
8036     "in_project_namespace": true,
8037     "kind": "theorem",
8038     "module": "KomorebiVerification.ExactCoordinates",
8039     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_5",
8040     "runtime_only": false
8041   },
8042   {
8043     "axioms": [
8044       "propext",
8045       "Classical.choice",
8046       "Quot.sound"
8047     ],
8048     "in_project_namespace": true,
8049     "kind": "theorem",
8050     "module": "KomorebiVerification.SingleOperatorGraph",
8051     "name": "Komorebi.SingleOperatorGraph.finrank_le_card_of_generates_of_scalar_factor",
8052     "runtime_only": false
8053   },
8054   {
8055     "axioms": [
8056       "propext",
8057       "Classical.choice",
8058       "Quot.sound"
8059     ],
8060     "in_project_namespace": true,
8061     "kind": "theorem",
8062     "module": "KomorebiVerification.TopologicalCompletion",
8063     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.closure_le_ker_of_le_ker",
8064     "runtime_only": false
8065   },
8066   {
8067     "axioms": [],
8068     "in_project_namespace": true,
8069     "kind": "theorem",
8070     "module": "PaperICompletion8.RegularMultiplicity",
8071     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_3",
8072     "runtime_only": false
8073   },
8074   {
8075     "axioms": [
8076       "propext",
8077       "Quot.sound"
8078     ],
8079     "in_project_namespace": false,
8080     "kind": "theorem",
8081     "module": "PaperIRelease.TopologyDenseCompletion",
8082     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_1",
8083     "runtime_only": false
8084   },
8085   {
8086     "axioms": [
8087       "propext",
8088       "Classical.choice",
8089       "Quot.sound"
8090     ],
8091     "in_project_namespace": true,
8092     "kind": "theorem",
8093     "module": "KomorebiVerification.SingleOperatorGraph",
8094     "name": "Komorebi.SingleOperatorGraph.familyGenerates_iff_operatorAlgebra_familyGenerates",
8095     "runtime_only": false
8096   },
8097   {
8098     "axioms": [
8099       "propext",
8100       "Classical.choice",
8101       "Quot.sound"
8102     ],
8103     "in_project_namespace": true,
8104     "kind": "theorem",
8105     "module": "PaperIRelease.CoordinateTransport",
8106     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_9",
8107     "runtime_only": false
8108   },
8109   {
8110     "axioms": [],
8111     "in_project_namespace": true,
8112     "kind": "definition",
8113     "module": "PaperIRelease.CategoryExport",
8114     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorElimType",
8115     "runtime_only": false
8116   },
8117   {
8118     "axioms": [
8119       "propext",
8120       "Quot.sound"
8121     ],
8122     "in_project_namespace": true,
8123     "kind": "recursor",
8124     "module": "PaperIRelease.GrammarModules",
8125     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.rec",
8126     "runtime_only": false
8127   },
8128   {
8129     "axioms": [
8130       "propext",
8131       "Classical.choice",
8132       "Quot.sound"
8133     ],
8134     "in_project_namespace": true,
8135     "kind": "theorem",
8136     "module": "PaperIRelease.AlgebraTransfer",
8137     "name": "Komorebi.PaperIRelease.target_coordinate_sum",
8138     "runtime_only": false
8139   },
8140   {
8141     "axioms": [
8142       "propext",
8143       "Quot.sound"
8144     ],
8145     "in_project_namespace": true,
8146     "kind": "theorem",
8147     "module": "KomorebiVerification.SemisimpleSeedRank",
8148     "name": "Komorebi.SemisimpleSeedRank.RowsSpan.eq_1",
8149     "runtime_only": false
8150   },
8151   {
8152     "axioms": [
8153       "propext",
8154       "Quot.sound"
8155     ],
8156     "in_project_namespace": true,
8157     "kind": "recursor",
8158     "module": "PaperIRelease.GrammarModules",
8159     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.rec",
8160     "runtime_only": false
8161   },
8162   {
8163     "axioms": [
8164       "propext",
8165       "Classical.choice",
8166       "Quot.sound"
8167     ],
8168     "in_project_namespace": true,
8169     "kind": "definition",
8170     "module": "PaperICompletion4.OperatorIntrinsicFormula",
8171     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient",
8172     "runtime_only": false
8173   },
8174   {
8175     "axioms": [
8176       "propext",
8177       "Classical.choice",
8178       "Quot.sound"
8179     ],
8180     "in_project_namespace": true,
8181     "kind": "definition",
8182     "module": "PaperIRelease.PacketDescent",
8183     "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros",
8184     "runtime_only": false
8185   },
8186   {
8187     "axioms": [
8188       "propext",
8189       "Classical.choice",
8190       "Quot.sound"
8191     ],
8192     "in_project_namespace": true,
8193     "kind": "theorem",
8194     "module": "PaperIRelease.CoordinateTransport",
8195     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_3",
8196     "runtime_only": false
8197   },
8198   {
8199     "axioms": [
8200       "propext",
8201       "Classical.choice",
8202       "Quot.sound"
8203     ],
8204     "in_project_namespace": false,
8205     "kind": "theorem",
8206     "module": "PaperIRelease.TopologyFiniteCompletion",
8207     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_6",
8208     "runtime_only": false
8209   },
8210   {
8211     "axioms": [],
8212     "in_project_namespace": true,
8213     "kind": "constructor",
8214     "module": "PaperIRelease.GrammarPaths",
8215     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil",
8216     "runtime_only": false
8217   },
8218   {
8219     "axioms": [
8220       "propext",
8221       "Classical.choice",
8222       "Quot.sound"
8223     ],
8224     "in_project_namespace": true,
8225     "kind": "definition",
8226     "module": "PaperIRelease.PacketUniversal",
8227     "name": "Komorebi.PaperIRelease.PacketUniversal.assembleIn",
8228     "runtime_only": false
8229   },
8230   {
8231     "axioms": [
8232       "propext",
8233       "Quot.sound"
8234     ],
8235     "in_project_namespace": true,
8236     "kind": "theorem",
8237     "module": "KomorebiVerification.PacketNaturalityCompletion",
8238     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks._proof_1",
8239     "runtime_only": false
8240   },
8241   {
8242     "axioms": [],
8243     "in_project_namespace": true,
8244     "kind": "definition",
8245     "module": "KomorebiVerification.ProjectorCore",
8246     "name": "Komorebi.ClaimKind.numericalCertificate.elim",
8247     "runtime_only": false
8248   },
8249   {
8250     "axioms": [
8251       "propext",
8252       "Classical.choice",
8253       "Quot.sound"
8254     ],
8255     "in_project_namespace": true,
8256     "kind": "theorem",
8257     "module": "PaperICompletion4.OperatorIntrinsicFormula",
8258     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_card_of_component_decomposition._simp_1_2",
8259     "runtime_only": false
8260   },
8261   {
8262     "axioms": [
8263       "propext",
8264       "Classical.choice",
8265       "Quot.sound"
8266     ],
8267     "in_project_namespace": true,
8268     "kind": "definition",
8269     "module": "PaperIRelease.GrammarAlgebra",
8270     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action",
8271     "runtime_only": false
8272   },
8273   {
8274     "axioms": [
8275       "propext",
8276       "Classical.choice",
8277       "Quot.sound"
8278     ],
8279     "in_project_namespace": true,
8280     "kind": "theorem",
8281     "module": "KomorebiVerification.TopologicalCompletion",
8282     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet.eq_1",
8283     "runtime_only": false
8284   },
8285   {
8286     "axioms": [
8287       "propext",
8288       "Classical.choice",
8289       "Quot.sound"
8290     ],
8291     "in_project_namespace": true,
8292     "kind": "theorem",
8293     "module": "PaperIRelease.BoundedStar",
8294     "name": "Komorebi.PaperIRelease.BoundedSupport.adjoint_closed_iff_symmetric",
8295     "runtime_only": false
8296   },
8297   {
8298     "axioms": [
8299       "propext",
8300       "Classical.choice",
8301       "Quot.sound"
8302     ],
8303     "in_project_namespace": true,
8304     "kind": "theorem",
8305     "module": "PaperICompletion.CyclicClassification",
8306     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_8",
8307     "runtime_only": false
8308   },
8309   {
8310     "axioms": [
8311       "propext",
8312       "Classical.choice",
8313       "Quot.sound"
8314     ],
8315     "in_project_namespace": false,
8316     "kind": "theorem",
8317     "module": "PaperIRelease.AlgebraPreorder",
8318     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_lengths_bdd",
8319     "runtime_only": false
8320   },
8321   {
8322     "axioms": [
8323       "propext",
8324       "Classical.choice",
8325       "Quot.sound"
8326     ],
8327     "in_project_namespace": true,
8328     "kind": "definition",
8329     "module": "PaperIRelease.GrammarAlgebra",
8330     "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow",
8331     "runtime_only": false
8332   },
8333   {
8334     "axioms": [
8335       "propext",
8336       "Classical.choice",
8337       "Quot.sound"
8338     ],
8339     "in_project_namespace": false,
8340     "kind": "definition",
8341     "module": "PaperIRelease.TopologyUnconditional",
8342     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.noConfusion",
8343     "runtime_only": false
8344   },
8345   {
8346     "axioms": [
8347       "propext",
8348       "Classical.choice",
8349       "Quot.sound"
8350     ],
8351     "in_project_namespace": true,
8352     "kind": "theorem",
8353     "module": "PaperICompletion8.ProductPresentation",
8354     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_3",
8355     "runtime_only": false
8356   },
8357   {
8358     "axioms": [
8359       "propext",
8360       "Classical.choice",
8361       "Quot.sound"
8362     ],
8363     "in_project_namespace": true,
8364     "kind": "theorem",
8365     "module": "KomorebiVerification.PaperIBlockCompletion",
8366     "name": "Komorebi.Foundation.transferBlock_comp_end",
8367     "runtime_only": false
8368   },
8369   {
8370     "axioms": [
8371       "propext",
8372       "Classical.choice",
8373       "Quot.sound"
8374     ],
8375     "in_project_namespace": true,
8376     "kind": "theorem",
8377     "module": "PaperIRelease.PolynomialMonic",
8378     "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec._proof_2",
8379     "runtime_only": false
8380   },
8381   {
8382     "axioms": [
8383       "propext",
8384       "Classical.choice",
8385       "Quot.sound"
8386     ],
8387     "in_project_namespace": true,
8388     "kind": "definition",
8389     "module": "PaperICompletion8.RegularMultiplicity",
8390     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicityDirectSumEquiv",
8391     "runtime_only": false
8392   },
8393   {
8394     "axioms": [
8395       "propext",
8396       "Classical.choice",
8397       "Quot.sound"
8398     ],
8399     "in_project_namespace": true,
8400     "kind": "theorem",
8401     "module": "PaperIRelease.GrammarEquivalence",
8402     "name": "Komorebi.PaperIRelease.GrammarAlgebra.actionHom_vertex",
8403     "runtime_only": false
8404   },
8405   {
8406     "axioms": [
8407       "propext"
8408     ],
8409     "in_project_namespace": true,
8410     "kind": "theorem",
8411     "module": "KomorebiVerification.ProjectorCore",
8412     "name": "Komorebi.Seed.OperatorRelation.satisfied_refl._simp_1",
8413     "runtime_only": false
8414   },
8415   {
8416     "axioms": [],
8417     "in_project_namespace": true,
8418     "kind": "theorem",
8419     "module": "KomorebiVerification.ProjectorCore",
8420     "name": "Komorebi.instDecidableEqFormalizationStatus._proof_2",
8421     "runtime_only": false
8422   },
8423   {
8424     "axioms": [
8425       "propext",
8426       "Classical.choice",
8427       "Quot.sound"
8428     ],
8429     "in_project_namespace": true,
8430     "kind": "theorem",
8431     "module": "PaperIRelease.PolynomialModule",
8432     "name": "Komorebi.PaperIRelease.PolynomialModule.primary_internal_decomposition",
8433     "runtime_only": false
8434   },
8435   {
8436     "axioms": [
8437       "propext",
8438       "Classical.choice",
8439       "Quot.sound"
8440     ],
8441     "in_project_namespace": true,
8442     "kind": "theorem",
8443     "module": "PaperIRelease.PacketLocalRank",
8444     "name": "Komorebi.PaperIRelease.groupedProjection_mem_algebra",
8445     "runtime_only": false
8446   },
8447   {
8448     "axioms": [
8449       "propext",
8450       "Classical.choice",
8451       "Quot.sound"
8452     ],
8453     "in_project_namespace": true,
8454     "kind": "definition",
8455     "module": "PaperIRelease.GrammarEquivalence",
8456     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total",
8457     "runtime_only": false
8458   },
8459   {
8460     "axioms": [
8461       "propext",
8462       "Quot.sound"
8463     ],
8464     "in_project_namespace": true,
8465     "kind": "theorem",
8466     "module": "PaperICompletion6.OneInvariantFactor",
8467     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_7",
8468     "runtime_only": false
8469   },
8470   {
8471     "axioms": [
8472       "propext",
8473       "Quot.sound"
8474     ],
8475     "in_project_namespace": true,
8476     "kind": "definition",
8477     "module": "PaperIRelease.GrammarAlgebra",
8478     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.noConfusion",
8479     "runtime_only": false
8480   },
8481   {
8482     "axioms": [
8483       "propext",
8484       "Classical.choice",
8485       "Quot.sound"
8486     ],
8487     "in_project_namespace": true,
8488     "kind": "theorem",
8489     "module": "PaperIRelease.BoundedStar",
8490     "name": "Komorebi.PaperIRelease.BoundedSupport.star_subalgebra_iff_equivalence",
8491     "runtime_only": false
8492   },
8493   {
8494     "axioms": [
8495       "propext",
8496       "Classical.choice",
8497       "Quot.sound"
8498     ],
8499     "in_project_namespace": true,
8500     "kind": "constructor",
8501     "module": "PaperIRelease.TopologyCategories",
8502     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk",
8503     "runtime_only": false
8504   },
8505   {
8506     "axioms": [
8507       "propext",
8508       "Classical.choice",
8509       "Quot.sound"
8510     ],
8511     "in_project_namespace": true,
8512     "kind": "definition",
8513     "module": "PaperIRelease.PacketDescent",
8514     "name": "Komorebi.Foundation.LinearProjectorFamily.NonzeroIndex",
8515     "runtime_only": false
8516   },
8517   {
8518     "axioms": [
8519       "propext",
8520       "Classical.choice",
8521       "Quot.sound"
8522     ],
8523     "in_project_namespace": true,
8524     "kind": "theorem",
8525     "module": "PaperIRelease.GeneralNormedPackets",
8526     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis.eq_1",
8527     "runtime_only": false
8528   },
8529   {
8530     "axioms": [
8531       "propext",
8532       "Quot.sound"
8533     ],
8534     "in_project_namespace": true,
8535     "kind": "definition",
8536     "module": "KomorebiVerification.FibreRefinement",
8537     "name": "Komorebi.Packet.fibreLinearProj",
8538     "runtime_only": false
8539   },
8540   {
8541     "axioms": [
8542       "propext",
8543       "Classical.choice",
8544       "Quot.sound"
8545     ],
8546     "in_project_namespace": false,
8547     "kind": "definition",
8548     "module": "PaperIRelease.TopologyCountablePackets",
8549     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_3",
8550     "runtime_only": false
8551   },
8552   {
8553     "axioms": [
8554       "propext",
8555       "Classical.choice",
8556       "Quot.sound"
8557     ],
8558     "in_project_namespace": true,
8559     "kind": "definition",
8560     "module": "KomorebiVerification.ProjectorCore",
8561     "name": "Komorebi.Operator.blockApply",
8562     "runtime_only": false
8563   },
8564   {
8565     "axioms": [
8566       "propext",
8567       "Classical.choice",
8568       "Quot.sound"
8569     ],
8570     "in_project_namespace": false,
8571     "kind": "theorem",
8572     "module": "PaperIRelease.TopologyDenseCompletion",
8573     "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv.congr_simp",
8574     "runtime_only": false
8575   },
8576   {
8577     "axioms": [
8578       "propext",
8579       "Classical.choice",
8580       "Quot.sound"
8581     ],
8582     "in_project_namespace": true,
8583     "kind": "theorem",
8584     "module": "PaperICompletion.SpectralCertificates",
8585     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity.eq_1",
8586     "runtime_only": false
8587   },
8588   {
8589     "axioms": [],
8590     "in_project_namespace": true,
8591     "kind": "theorem",
8592     "module": "KomorebiVerification.ProjectorCore",
8593     "name": "Komorebi.FormalizationStatus.proofTermPresent.sizeOf_spec",
8594     "runtime_only": false
8595   },
8596   {
8597     "axioms": [],
8598     "in_project_namespace": true,
8599     "kind": "theorem",
8600     "module": "PaperICompletion7.Nakayama",
8601     "name": "Komorebi.PaperICompletion7.Nakayama.IdealTop._proof_1",
8602     "runtime_only": false
8603   },
8604   {
8605     "axioms": [
8606       "propext",
8607       "Quot.sound"
8608     ],
8609     "in_project_namespace": true,
8610     "kind": "theorem",
8611     "module": "KomorebiVerification.SingleOperatorGraph",
8612     "name": "Komorebi.SingleOperatorGraph.evalVector._proof_3",
8613     "runtime_only": false
8614   },
8615   {
8616     "axioms": [
8617       "propext",
8618       "Classical.choice",
8619       "Quot.sound"
8620     ],
8621     "in_project_namespace": true,
8622     "kind": "theorem",
8623     "module": "KomorebiVerification.TopologicalCompletion",
8624     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.dense_realization",
8625     "runtime_only": false
8626   },
8627   {
8628     "axioms": [
8629       "propext",
8630       "Classical.choice",
8631       "Quot.sound"
8632     ],
8633     "in_project_namespace": true,
8634     "kind": "definition",
8635     "module": "PaperIRelease.AlgebraDiagonal",
8636     "name": "Komorebi.PaperIRelease.blockDiagonalSubalgebra",
8637     "runtime_only": false
8638   },
8639   {
8640     "axioms": [
8641       "propext",
8642       "Classical.choice",
8643       "Quot.sound"
8644     ],
8645     "in_project_namespace": true,
8646     "kind": "definition",
8647     "module": "PaperIRelease.GeneralFiniteCompletion",
8648     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily",
8649     "runtime_only": false
8650   },
8651   {
8652     "axioms": [
8653       "propext",
8654       "Classical.choice",
8655       "Quot.sound"
8656     ],
8657     "in_project_namespace": true,
8658     "kind": "theorem",
8659     "module": "KomorebiVerification.PacketNaturalityCompletion",
8660     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.map_algebraOrbitSet",
8661     "runtime_only": false
8662   },
8663   {
8664     "axioms": [
8665       "propext",
8666       "Quot.sound"
8667     ],
8668     "in_project_namespace": true,
8669     "kind": "theorem",
8670     "module": "PaperIRelease.GrammarModules",
8671     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.injEq",
8672     "runtime_only": false
8673   },
8674   {
8675     "axioms": [
8676       "propext",
8677       "Quot.sound"
8678     ],
8679     "in_project_namespace": true,
8680     "kind": "theorem",
8681     "module": "PaperIRelease.GraphSourceBoundary",
8682     "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_components_distinct",
8683     "runtime_only": false
8684   },
8685   {
8686     "axioms": [
8687       "propext",
8688       "Classical.choice",
8689       "Quot.sound"
8690     ],
8691     "in_project_namespace": true,
8692     "kind": "theorem",
8693     "module": "KomorebiVerification.TopologicalCompletion",
8694     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis_apply",
8695     "runtime_only": false
8696   },
8697   {
8698     "axioms": [
8699       "propext",
8700       "Classical.choice",
8701       "Quot.sound"
8702     ],
8703     "in_project_namespace": true,
8704     "kind": "theorem",
8705     "module": "PaperIRelease.PacketAggregation",
8706     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_2",
8707     "runtime_only": false
8708   },
8709   {
8710     "axioms": [
8711       "propext",
8712       "Classical.choice",
8713       "Quot.sound"
8714     ],
8715     "in_project_namespace": true,
8716     "kind": "theorem",
8717     "module": "KomorebiVerification.EllipticAlgorithms",
8718     "name": "Komorebi.FiniteAlgorithms.orbitClosureStep_mono",
8719     "runtime_only": false
8720   },
8721   {
8722     "axioms": [
8723       "propext",
8724       "Classical.choice",
8725       "Quot.sound"
8726     ],
8727     "in_project_namespace": true,
8728     "kind": "definition",
8729     "module": "PaperIRelease.GrammarEquivalence",
8730     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedActionEquivalence",
8731     "runtime_only": false
8732   },
8733   {
8734     "axioms": [
8735       "propext",
8736       "Classical.choice",
8737       "Quot.sound"
8738     ],
8739     "in_project_namespace": true,
8740     "kind": "definition",
8741     "module": "PaperIRelease.GrammarAlgebra",
8742     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors",
8743     "runtime_only": false
8744   },
8745   {
8746     "axioms": [
8747       "propext",
8748       "Classical.choice",
8749       "Quot.sound"
8750     ],
8751     "in_project_namespace": true,
8752     "kind": "definition",
8753     "module": "PaperIRelease.GrammarIdeal",
8754     "name": "Komorebi.PaperIRelease.GrammarAlgebra.PathAlgebra",
8755     "runtime_only": false
8756   },
8757   {
8758     "axioms": [
8759       "propext",
8760       "Classical.choice",
8761       "Quot.sound"
8762     ],
8763     "in_project_namespace": true,
8764     "kind": "theorem",
8765     "module": "PaperIRelease.GrammarEquivalence",
8766     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_5",
8767     "runtime_only": false
8768   },
8769   {
8770     "axioms": [
8771       "propext",
8772       "Classical.choice",
8773       "Quot.sound"
8774     ],
8775     "in_project_namespace": true,
8776     "kind": "theorem",
8777     "module": "PaperICompletion6.ScalarExtension",
8778     "name": "Komorebi.PaperICompletion6.ScalarExtension.isBaseChange_endomorphisms",
8779     "runtime_only": false
8780   },
8781   {
8782     "axioms": [
8783       "propext",
8784       "Classical.choice",
8785       "Quot.sound"
8786     ],
8787     "in_project_namespace": true,
8788     "kind": "theorem",
8789     "module": "KomorebiVerification.SemisimpleCompletion",
8790     "name": "Komorebi.SemisimpleCompletion.seedRank_eq_maxCeilDiv_of_splitProduct_decomposition",
8791     "runtime_only": false
8792   },
8793   {
8794     "axioms": [
8795       "propext",
8796       "Classical.choice",
8797       "Quot.sound"
8798     ],
8799     "in_project_namespace": true,
8800     "kind": "definition",
8801     "module": "PaperIRelease.TensorPackets",
8802     "name": "Komorebi.PaperIRelease.tensorPacketDirectSumCoordinates",
8803     "runtime_only": false
8804   },
8805   {
8806     "axioms": [
8807       "propext",
8808       "Classical.choice",
8809       "Quot.sound"
8810     ],
8811     "in_project_namespace": false,
8812     "kind": "theorem",
8813     "module": "PaperIRelease.TopologyDenseCompletion",
8814     "name": "PaperIRelease.TopologyDenseCompletion.completedAction_apply_coe",
8815     "runtime_only": false
8816   },
8817   {
8818     "axioms": [
8819       "propext",
8820       "Classical.choice",
8821       "Quot.sound"
8822     ],
8823     "in_project_namespace": false,
8824     "kind": "theorem",
8825     "module": "PaperIRelease.TopologyCountablePackets",
8826     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_4",
8827     "runtime_only": false
8828   },
8829   {
8830     "axioms": [
8831       "propext",
8832       "Classical.choice",
8833       "Quot.sound"
8834     ],
8835     "in_project_namespace": true,
8836     "kind": "theorem",
8837     "module": "PaperIRelease.BoundedStar",
8838     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_10",
8839     "runtime_only": false
8840   },
8841   {
8842     "axioms": [],
8843     "in_project_namespace": true,
8844     "kind": "definition",
8845     "module": "KomorebiVerification.ProjectorCore",
8846     "name": "Komorebi.ClaimKind.theoremClaim.elim",
8847     "runtime_only": false
8848   },
8849   {
8850     "axioms": [
8851       "propext",
8852       "Classical.choice",
8853       "Quot.sound"
8854     ],
8855     "in_project_namespace": true,
8856     "kind": "theorem",
8857     "module": "PaperICompletion3.OperatorPrimaryAPI",
8858     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.operator_seedRank_eq_primaryGeneratorCount",
8859     "runtime_only": false
8860   },
8861   {
8862     "axioms": [
8863       "propext",
8864       "Classical.choice",
8865       "Quot.sound"
8866     ],
8867     "in_project_namespace": true,
8868     "kind": "definition",
8869     "module": "PaperICompletion.ConditionedCoordinates",
8870     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber",
8871     "runtime_only": false
8872   },
8873   {
8874     "axioms": [
8875       "propext",
8876       "Classical.choice",
8877       "Quot.sound"
8878     ],
8879     "in_project_namespace": true,
8880     "kind": "theorem",
8881     "module": "PaperICompletion6.ScalarExtension",
8882     "name": "Komorebi.PaperICompletion6.ScalarExtension.aeval_map_baseChange",
8883     "runtime_only": false
8884   },
8885   {
8886     "axioms": [
8887       "propext",
8888       "Classical.choice",
8889       "Quot.sound"
8890     ],
8891     "in_project_namespace": true,
8892     "kind": "theorem",
8893     "module": "PaperICompletion6.PrimaryCyclicCriterion",
8894     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.intrinsicMultiplicity_le_one_of_primary_cyclic",
8895     "runtime_only": false
8896   },
8897   {
8898     "axioms": [
8899       "propext",
8900       "Quot.sound"
8901     ],
8902     "in_project_namespace": true,
8903     "kind": "definition",
8904     "module": "PaperIRelease.GrammarModules",
8905     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom._sizeOf_1",
8906     "runtime_only": false
8907   },
8908   {
8909     "axioms": [
8910       "propext",
8911       "Classical.choice",
8912       "Quot.sound"
8913     ],
8914     "in_project_namespace": true,
8915     "kind": "recursor",
8916     "module": "PaperIRelease.TopologyCategories",
8917     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.rec",
8918     "runtime_only": false
8919   },
8920   {
8921     "axioms": [
8922       "propext",
8923       "Classical.choice",
8924       "Quot.sound"
8925     ],
8926     "in_project_namespace": true,
8927     "kind": "theorem",
8928     "module": "KomorebiVerification.SeedRankBasics",
8929     "name": "Komorebi.SeedRankBasics.familyGenerates_iff_surjective",
8930     "runtime_only": false
8931   },
8932   {
8933     "axioms": [
8934       "propext",
8935       "Classical.choice",
8936       "Quot.sound"
8937     ],
8938     "in_project_namespace": true,
8939     "kind": "theorem",
8940     "module": "KomorebiVerification.PacketNaturalityCompletion",
8941     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.seedRank_le_of_surjective_intertwining",
8942     "runtime_only": false
8943   },
8944   {
8945     "axioms": [
8946       "propext",
8947       "Classical.choice",
8948       "Quot.sound"
8949     ],
8950     "in_project_namespace": true,
8951     "kind": "theorem",
8952     "module": "PaperIRelease.PacketUniversal",
8953     "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut.eq_1",
8954     "runtime_only": false
8955   },
8956   {
8957     "axioms": [
8958       "propext",
8959       "Classical.choice",
8960       "Quot.sound"
8961     ],
8962     "in_project_namespace": true,
8963     "kind": "definition",
8964     "module": "KomorebiVerification.PacketNaturalityCompletion",
8965     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism._sizeOf_1",
8966     "runtime_only": false
8967   },
8968   {
8969     "axioms": [
8970       "propext",
8971       "Classical.choice",
8972       "Quot.sound"
8973     ],
8974     "in_project_namespace": true,
8975     "kind": "theorem",
8976     "module": "PaperIRelease.GeneralNormedPackets",
8977     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.topological_packet_isomorphism",
8978     "runtime_only": false
8979   },
8980   {
8981     "axioms": [
8982       "propext",
8983       "Classical.choice",
8984       "Quot.sound"
8985     ],
8986     "in_project_namespace": false,
8987     "kind": "theorem",
8988     "module": "PaperIRelease.TopologyUnconditional",
8989     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space.ext",
8990     "runtime_only": false
8991   },
8992   {
8993     "axioms": [],
8994     "in_project_namespace": true,
8995     "kind": "definition",
8996     "module": "KomorebiVerification.ProjectorCore",
8997     "name": "Komorebi.instReprClaimKind.repr",
8998     "runtime_only": false
8999   },
9000   {
9001     "axioms": [
9002       "propext",
9003       "Classical.choice",
9004       "Quot.sound"
9005     ],
9006     "in_project_namespace": true,
9007     "kind": "theorem",
9008     "module": "KomorebiVerification.PathGraphKrylov",
9009     "name": "Komorebi.PathGraphKrylov.pathAdjacency.eq_1",
9010     "runtime_only": false
9011   },
9012   {
9013     "axioms": [
9014       "propext",
9015       "Classical.choice",
9016       "Quot.sound"
9017     ],
9018     "in_project_namespace": true,
9019     "kind": "theorem",
9020     "module": "PaperIRelease.AlgebraDiagonal",
9021     "name": "Komorebi.PaperIRelease.diagonalProjection_idempotent",
9022     "runtime_only": false
9023   },
9024   {
9025     "axioms": [
9026       "propext",
9027       "Classical.choice",
9028       "Quot.sound"
9029     ],
9030     "in_project_namespace": true,
9031     "kind": "theorem",
9032     "module": "PaperIRelease.GeneralNormedPackets",
9033     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis._proof_1",
9034     "runtime_only": false
9035   },
9036   {
9037     "axioms": [],
9038     "in_project_namespace": true,
9039     "kind": "theorem",
9040     "module": "KomorebiVerification.ProjectorCore",
9041     "name": "Komorebi.ClaimKind.algorithmClaim.sizeOf_spec",
9042     "runtime_only": false
9043   },
9044   {
9045     "axioms": [
9046       "propext",
9047       "Classical.choice",
9048       "Quot.sound"
9049     ],
9050     "in_project_namespace": true,
9051     "kind": "theorem",
9052     "module": "PaperIRelease.GraphSourceProjection",
9053     "name": "Komorebi.PaperIRelease.sourceProjection_comp_eq",
9054     "runtime_only": false
9055   },
9056   {
9057     "axioms": [
9058       "propext",
9059       "Classical.choice",
9060       "Quot.sound"
9061     ],
9062     "in_project_namespace": false,
9063     "kind": "theorem",
9064     "module": "PaperIRelease.TopologyUnconditional",
9065     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_neg_val",
9066     "runtime_only": false
9067   },
9068   {
9069     "axioms": [
9070       "propext",
9071       "Classical.choice",
9072       "Quot.sound"
9073     ],
9074     "in_project_namespace": true,
9075     "kind": "theorem",
9076     "module": "PaperIRelease.GeneralNormedPackets",
9077     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_apply_coe",
9078     "runtime_only": false
9079   },
9080   {
9081     "axioms": [],
9082     "in_project_namespace": true,
9083     "kind": "definition",
9084     "module": "KomorebiVerification.ProjectorCore",
9085     "name": "Komorebi.Seed.OperatorRelation.mk.noConfusion",
9086     "runtime_only": false
9087   },
9088   {
9089     "axioms": [
9090       "propext",
9091       "Classical.choice",
9092       "Quot.sound"
9093     ],
9094     "in_project_namespace": true,
9095     "kind": "theorem",
9096     "module": "PaperIRelease.AlgebraClassGrouping",
9097     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_4",
9098     "runtime_only": false
9099   },
9100   {
9101     "axioms": [
9102       "propext",
9103       "Quot.sound"
9104     ],
9105     "in_project_namespace": true,
9106     "kind": "definition",
9107     "module": "PaperIRelease.GraphSources",
9108     "name": "Komorebi.PaperIRelease.FiniteDigraph.Source",
9109     "runtime_only": false
9110   },
9111   {
9112     "axioms": [
9113       "propext",
9114       "Classical.choice",
9115       "Quot.sound"
9116     ],
9117     "in_project_namespace": true,
9118     "kind": "definition",
9119     "module": "PaperIRelease.PacketTopology",
9120     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM",
9121     "runtime_only": false
9122   },
9123   {
9124     "axioms": [
9125       "propext",
9126       "Classical.choice",
9127       "Quot.sound"
9128     ],
9129     "in_project_namespace": true,
9130     "kind": "theorem",
9131     "module": "KomorebiVerification.SemisimpleCompletion",
9132     "name": "Komorebi.SemisimpleCompletion.semisimple_seedRank_eq_maxCeilDiv_of_equivalences",
9133     "runtime_only": false
9134   },
9135   {
9136     "axioms": [
9137       "propext",
9138       "Classical.choice",
9139       "Quot.sound"
9140     ],
9141     "in_project_namespace": true,
9142     "kind": "theorem",
9143     "module": "PaperICompletion8.ProductPresentation",
9144     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_8",
9145     "runtime_only": false
9146   },
9147   {
9148     "axioms": [
9149       "propext",
9150       "Quot.sound"
9151     ],
9152     "in_project_namespace": true,
9153     "kind": "theorem",
9154     "module": "PaperICompletion5.LinearPrimaryEigenspace",
9155     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_5",
9156     "runtime_only": false
9157   },
9158   {
9159     "axioms": [
9160       "propext",
9161       "Classical.choice",
9162       "Quot.sound"
9163     ],
9164     "in_project_namespace": true,
9165     "kind": "theorem",
9166     "module": "PaperIRelease.PacketDescent",
9167     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_2",
9168     "runtime_only": false
9169   },
9170   {
9171     "axioms": [
9172       "propext",
9173       "Quot.sound"
9174     ],
9175     "in_project_namespace": true,
9176     "kind": "definition",
9177     "module": "KomorebiVerification.PacketNaturalityCompletion",
9178     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds",
9179     "runtime_only": false
9180   },
9181   {
9182     "axioms": [
9183       "propext"
9184     ],
9185     "in_project_namespace": true,
9186     "kind": "definition",
9187     "module": "PaperIRelease.CategoryExport",
9188     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._unsafe_rec",
9189     "runtime_only": true
9190   },
9191   {
9192     "axioms": [],
9193     "in_project_namespace": true,
9194     "kind": "theorem",
9195     "module": "KomorebiVerification.ProjectorCore",
9196     "name": "Komorebi.ClaimKind.exampleClaim.sizeOf_spec",
9197     "runtime_only": false
9198   },
9199   {
9200     "axioms": [
9201       "propext",
9202       "Classical.choice",
9203       "Quot.sound"
9204     ],
9205     "in_project_namespace": true,
9206     "kind": "theorem",
9207     "module": "KomorebiVerification.FibreRefinement",
9208     "name": "Komorebi.Packet.fibreLinearProj_refinement",
9209     "runtime_only": false
9210   },
9211   {
9212     "axioms": [
9213       "propext",
9214       "Classical.choice",
9215       "Quot.sound"
9216     ],
9217     "in_project_namespace": true,
9218     "kind": "definition",
9219     "module": "KomorebiVerification.SemisimpleCompletion",
9220     "name": "Komorebi.SemisimpleCompletion.blockModuleAction",
9221     "runtime_only": false
9222   },
9223   {
9224     "axioms": [
9225       "propext",
9226       "Classical.choice",
9227       "Quot.sound"
9228     ],
9229     "in_project_namespace": true,
9230     "kind": "theorem",
9231     "module": "PaperIRelease.BoundedStar",
9232     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_4",
9233     "runtime_only": false
9234   },
9235   {
9236     "axioms": [
9237       "propext",
9238       "Classical.choice",
9239       "Quot.sound"
9240     ],
9241     "in_project_namespace": true,
9242     "kind": "definition",
9243     "module": "PaperIRelease.PacketTopology",
9244     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM",
9245     "runtime_only": false
9246   },
9247   {
9248     "axioms": [
9249       "propext",
9250       "Classical.choice",
9251       "Quot.sound"
9252     ],
9253     "in_project_namespace": false,
9254     "kind": "definition",
9255     "module": "PaperIRelease.TopologyDenseCompletion",
9256     "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv",
9257     "runtime_only": false
9258   },
9259   {
9260     "axioms": [
9261       "propext",
9262       "Classical.choice",
9263       "Quot.sound"
9264     ],
9265     "in_project_namespace": true,
9266     "kind": "theorem",
9267     "module": "KomorebiVerification.EllipticAlgorithms",
9268     "name": "Komorebi.EllipticCoordinates.P0_My",
9269     "runtime_only": false
9270   },
9271   {
9272     "axioms": [],
9273     "in_project_namespace": true,
9274     "kind": "definition",
9275     "module": "KomorebiVerification.ProjectorCore",
9276     "name": "Komorebi.ClaimRecord.recOn",
9277     "runtime_only": false
9278   },
9279   {
9280     "axioms": [
9281       "propext",
9282       "Classical.choice",
9283       "Quot.sound"
9284     ],
9285     "in_project_namespace": false,
9286     "kind": "theorem",
9287     "module": "PaperIRelease.TopologyUnconditional",
9288     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_5",
9289     "runtime_only": false
9290   },
9291   {
9292     "axioms": [
9293       "propext",
9294       "Classical.choice",
9295       "Quot.sound"
9296     ],
9297     "in_project_namespace": false,
9298     "kind": "theorem",
9299     "module": "PaperIRelease.TopologyUnconditional",
9300     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_sub_val",
9301     "runtime_only": false
9302   },
9303   {
9304     "axioms": [
9305       "propext",
9306       "Classical.choice",
9307       "Quot.sound"
9308     ],
9309     "in_project_namespace": true,
9310     "kind": "definition",
9311     "module": "KomorebiVerification.TopologicalCompletion",
9312     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.operatorHull",
9313     "runtime_only": false
9314   },
9315   {
9316     "axioms": [],
9317     "in_project_namespace": true,
9318     "kind": "definition",
9319     "module": "KomorebiVerification.ProjectorCore",
9320     "name": "Komorebi.ClaimRecord._sizeOf_1",
9321     "runtime_only": false
9322   },
9323   {
9324     "axioms": [
9325       "propext",
9326       "Classical.choice",
9327       "Quot.sound"
9328     ],
9329     "in_project_namespace": true,
9330     "kind": "theorem",
9331     "module": "PaperIRelease.PacketDescent",
9332     "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_1",
9333     "runtime_only": false
9334   },
9335   {
9336     "axioms": [
9337       "propext",
9338       "Classical.choice",
9339       "Quot.sound"
9340     ],
9341     "in_project_namespace": true,
9342     "kind": "theorem",
9343     "module": "PaperICompletion8.RegularMultiplicity",
9344     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_nonzero_generates",
9345     "runtime_only": false
9346   },
9347   {
9348     "axioms": [
9349       "propext",
9350       "Classical.choice",
9351       "Quot.sound"
9352     ],
9353     "in_project_namespace": true,
9354     "kind": "theorem",
9355     "module": "PaperICompletion4.OperatorIntrinsicFormula",
9356     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity._proof_1",
9357     "runtime_only": false
9358   },
9359   {
9360     "axioms": [
9361       "propext",
9362       "Classical.choice",
9363       "Quot.sound"
9364     ],
9365     "in_project_namespace": true,
9366     "kind": "theorem",
9367     "module": "KomorebiVerification.EllipticAlgorithms",
9368     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_3",
9369     "runtime_only": false
9370   },
9371   {
9372     "axioms": [
9373       "propext",
9374       "Classical.choice",
9375       "Quot.sound"
9376     ],
9377     "in_project_namespace": true,
9378     "kind": "definition",
9379     "module": "PaperIRelease.TopologyCategories",
9380     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.recOn",
9381     "runtime_only": false
9382   },
9383   {
9384     "axioms": [
9385       "propext",
9386       "Classical.choice",
9387       "Quot.sound"
9388     ],
9389     "in_project_namespace": true,
9390     "kind": "inductive",
9391     "module": "PaperIRelease.CategoryPackets",
9392     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject",
9393     "runtime_only": false
9394   },
9395   {
9396     "axioms": [
9397       "propext",
9398       "Classical.choice",
9399       "Quot.sound"
9400     ],
9401     "in_project_namespace": true,
9402     "kind": "definition",
9403     "module": "PaperIRelease.PacketTopology",
9404     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientLiftCLM",
9405     "runtime_only": false
9406   },
9407   {
9408     "axioms": [
9409       "propext",
9410       "Classical.choice",
9411       "Quot.sound"
9412     ],
9413     "in_project_namespace": true,
9414     "kind": "definition",
9415     "module": "PaperIRelease.CategoryPackets",
9416     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.noConfusion",
9417     "runtime_only": false
9418   },
9419   {
9420     "axioms": [
9421       "propext",
9422       "Classical.choice",
9423       "Quot.sound"
9424     ],
9425     "in_project_namespace": true,
9426     "kind": "definition",
9427     "module": "KomorebiVerification.TopologicalCompletion",
9428     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation._sizeOf_1",
9429     "runtime_only": false
9430   },
9431   {
9432     "axioms": [
9433       "propext",
9434       "Classical.choice",
9435       "Quot.sound"
9436     ],
9437     "in_project_namespace": true,
9438     "kind": "theorem",
9439     "module": "KomorebiVerification.ProjectorCore",
9440     "name": "Komorebi.Foundation.LinearProjectorFamily.analyze.eq_1",
9441     "runtime_only": false
9442   },
9443   {
9444     "axioms": [
9445       "propext",
9446       "Classical.choice",
9447       "Quot.sound"
9448     ],
9449     "in_project_namespace": true,
9450     "kind": "theorem",
9451     "module": "KomorebiVerification.PacketNaturalityCompletion",
9452     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation_eU\u2081",
9453     "runtime_only": false
9454   },
9455   {
9456     "axioms": [
9457       "propext",
9458       "Quot.sound"
9459     ],
9460     "in_project_namespace": false,
9461     "kind": "theorem",
9462     "module": "KomorebiVerification.SeedRankOperations",
9463     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.sharedSum_familyGenerates",
9464     "runtime_only": false
9465   },
9466   {
9467     "axioms": [
9468       "propext",
9469       "Classical.choice",
9470       "Quot.sound"
9471     ],
9472     "in_project_namespace": true,
9473     "kind": "definition",
9474     "module": "PaperIRelease.TopologyCategories",
9475     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.noConfusionType",
9476     "runtime_only": false
9477   },
9478   {
9479     "axioms": [
9480       "propext",
9481       "Classical.choice",
9482       "Quot.sound"
9483     ],
9484     "in_project_namespace": false,
9485     "kind": "theorem",
9486     "module": "ReleaseBoundary",
9487     "name": "PaperIBlock08Tests.mixed_product_not_three",
9488     "runtime_only": false
9489   },
9490   {
9491     "axioms": [
9492       "propext",
9493       "Classical.choice",
9494       "Quot.sound"
9495     ],
9496     "in_project_namespace": true,
9497     "kind": "theorem",
9498     "module": "PaperIRelease.TopologyCategories",
9499     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.operator_continuous",
9500     "runtime_only": false
9501   },
9502   {
9503     "axioms": [
9504       "propext",
9505       "Classical.choice",
9506       "Quot.sound"
9507     ],
9508     "in_project_namespace": true,
9509     "kind": "definition",
9510     "module": "PaperIRelease.GrammarAlgebra",
9511     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction",
9512     "runtime_only": false
9513   },
9514   {
9515     "axioms": [
9516       "propext",
9517       "Classical.choice",
9518       "Quot.sound"
9519     ],
9520     "in_project_namespace": true,
9521     "kind": "definition",
9522     "module": "PaperIRelease.GraphSources",
9523     "name": "Komorebi.PaperIRelease.FiniteDigraph.sccFintype",
9524     "runtime_only": false
9525   },
9526   {
9527     "axioms": [
9528       "propext",
9529       "Classical.choice",
9530       "Quot.sound"
9531     ],
9532     "in_project_namespace": true,
9533     "kind": "theorem",
9534     "module": "PaperIRelease.GrammarTyped",
9535     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_1",
9536     "runtime_only": false
9537   },
9538   {
9539     "axioms": [
9540       "propext",
9541       "Classical.choice",
9542       "Quot.sound"
9543     ],
9544     "in_project_namespace": true,
9545     "kind": "definition",
9546     "module": "PaperIRelease.GrammarTyped",
9547     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.noConfusion",
9548     "runtime_only": false
9549   },
9550   {
9551     "axioms": [
9552       "propext",
9553       "Classical.choice",
9554       "Quot.sound"
9555     ],
9556     "in_project_namespace": true,
9557     "kind": "theorem",
9558     "module": "PaperIRelease.GrammarAlgebra",
9559     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_quotient",
9560     "runtime_only": false
9561   },
9562   {
9563     "axioms": [
9564       "propext",
9565       "Classical.choice",
9566       "Quot.sound"
9567     ],
9568     "in_project_namespace": true,
9569     "kind": "theorem",
9570     "module": "PaperIRelease.PacketSourceLower",
9571     "name": "Komorebi.PaperIRelease.localNonzeroSeeds_generate_of_compression",
9572     "runtime_only": false
9573   },
9574   {
9575     "axioms": [],
9576     "in_project_namespace": true,
9577     "kind": "theorem",
9578     "module": "KomorebiVerification.ProjectorCore",
9579     "name": "Komorebi.FormalizationStatus.boundaryOnly.sizeOf_spec",
9580     "runtime_only": false
9581   },
9582   {
9583     "axioms": [
9584       "propext",
9585       "Classical.choice",
9586       "Quot.sound"
9587     ],
9588     "in_project_namespace": true,
9589     "kind": "theorem",
9590     "module": "PaperICompletion8.DivisionRows",
9591     "name": "Komorebi.PaperICompletion8.DivisionRows.exists_leftGenerators_iff",
9592     "runtime_only": false
9593   },
9594   {
9595     "axioms": [],
9596     "in_project_namespace": true,
9597     "kind": "theorem",
9598     "module": "PaperICompletion8.RegularMultiplicity",
9599     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_4",
9600     "runtime_only": false
9601   },
9602   {
9603     "axioms": [
9604       "propext",
9605       "Classical.choice",
9606       "Quot.sound"
9607     ],
9608     "in_project_namespace": true,
9609     "kind": "theorem",
9610     "module": "PaperICompletion5.GeometricSeedFormula",
9611     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum._simp_1_1",
9612     "runtime_only": false
9613   },
9614   {
9615     "axioms": [
9616       "propext",
9617       "Classical.choice",
9618       "Quot.sound"
9619     ],
9620     "in_project_namespace": true,
9621     "kind": "definition",
9622     "module": "PaperIRelease.TopologyCategories",
9623     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.identity",
9624     "runtime_only": false
9625   },
9626   {
9627     "axioms": [
9628       "propext",
9629       "Classical.choice",
9630       "Quot.sound"
9631     ],
9632     "in_project_namespace": true,
9633     "kind": "theorem",
9634     "module": "PaperIRelease.PacketCorners",
9635     "name": "Komorebi.PaperIRelease.corner_action_ambient",
9636     "runtime_only": false
9637   },
9638   {
9639     "axioms": [
9640       "propext",
9641       "Quot.sound"
9642     ],
9643     "in_project_namespace": true,
9644     "kind": "definition",
9645     "module": "PaperIRelease.GrammarTyped",
9646     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk._flat_ctor",
9647     "runtime_only": false
9648   },
9649   {
9650     "axioms": [
9651       "propext",
9652       "Quot.sound"
9653     ],
9654     "in_project_namespace": true,
9655     "kind": "theorem",
9656     "module": "PaperIRelease.AlgebraQuotient",
9657     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_1",
9658     "runtime_only": false
9659   },
9660   {
9661     "axioms": [
9662       "propext"
9663     ],
9664     "in_project_namespace": true,
9665     "kind": "theorem",
9666     "module": "PaperIRelease.CategoryExport",
9667     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate_transport",
9668     "runtime_only": false
9669   },
9670   {
9671     "axioms": [],
9672     "in_project_namespace": true,
9673     "kind": "definition",
9674     "module": "PaperIRelease.CategoryExport",
9675     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.noConfusion",
9676     "runtime_only": false
9677   },
9678   {
9679     "axioms": [
9680       "propext",
9681       "Classical.choice",
9682       "Quot.sound"
9683     ],
9684     "in_project_namespace": true,
9685     "kind": "definition",
9686     "module": "PaperIRelease.PolynomialMonic",
9687     "name": "Komorebi.PaperIRelease.PolynomialModule.instDecidableEqMonicIrreducibles",
9688     "runtime_only": false
9689   },
9690   {
9691     "axioms": [
9692       "propext",
9693       "Classical.choice",
9694       "Quot.sound"
9695     ],
9696     "in_project_namespace": true,
9697     "kind": "theorem",
9698     "module": "PaperIRelease.GrammarFactorization",
9699     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.seedRank_imageAlgebra_eq",
9700     "runtime_only": false
9701   },
9702   {
9703     "axioms": [
9704       "propext",
9705       "Classical.choice",
9706       "Quot.sound"
9707     ],
9708     "in_project_namespace": true,
9709     "kind": "theorem",
9710     "module": "PaperICompletion.CyclicClassification",
9711     "name": "Komorebi.PaperICompletion.CyclicClassification.singleton_generates_iff_orbitMap_surjective",
9712     "runtime_only": false
9713   },
9714   {
9715     "axioms": [],
9716     "in_project_namespace": true,
9717     "kind": "inductive",
9718     "module": "KomorebiVerification.ProjectorCore",
9719     "name": "Komorebi.Seed.OperatorExpr",
9720     "runtime_only": false
9721   },
9722   {
9723     "axioms": [
9724       "propext",
9725       "Quot.sound"
9726     ],
9727     "in_project_namespace": false,
9728     "kind": "theorem",
9729     "module": "PaperIRelease.AlgebraTransfer",
9730     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.eq_2",
9731     "runtime_only": false
9732   },
9733   {
9734     "axioms": [
9735       "propext",
9736       "Quot.sound"
9737     ],
9738     "in_project_namespace": true,
9739     "kind": "theorem",
9740     "module": "PaperICompletion3.PrimarySeedFormula",
9741     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_3",
9742     "runtime_only": false
9743   },
9744   {
9745     "axioms": [
9746       "propext",
9747       "Classical.choice",
9748       "Quot.sound"
9749     ],
9750     "in_project_namespace": true,
9751     "kind": "definition",
9752     "module": "KomorebiVerification.EllipticAlgorithms",
9753     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._sunfold",
9754     "runtime_only": false
9755   },
9756   {
9757     "axioms": [
9758       "propext",
9759       "Quot.sound"
9760     ],
9761     "in_project_namespace": true,
9762     "kind": "theorem",
9763     "module": "PaperIRelease.GrammarModules",
9764     "name": "Komorebi.PaperIRelease.GrammarModules.toModules_essSurj",
9765     "runtime_only": false
9766   },
9767   {
9768     "axioms": [
9769       "propext",
9770       "Classical.choice",
9771       "Quot.sound"
9772     ],
9773     "in_project_namespace": false,
9774     "kind": "theorem",
9775     "module": "PaperIRelease.TopologyCountablePackets",
9776     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_4",
9777     "runtime_only": false
9778   },
9779   {
9780     "axioms": [
9781       "propext",
9782       "Classical.choice",
9783       "Quot.sound"
9784     ],
9785     "in_project_namespace": true,
9786     "kind": "theorem",
9787     "module": "PaperICompletion.ConditionedCoordinates",
9788     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_nonneg",
9789     "runtime_only": false
9790   },
9791   {
9792     "axioms": [
9793       "propext",
9794       "Classical.choice",
9795       "Quot.sound"
9796     ],
9797     "in_project_namespace": true,
9798     "kind": "theorem",
9799     "module": "KomorebiVerification.SingleOperatorGraph",
9800     "name": "Komorebi.SingleOperatorGraph.complexCycleRoot.eq_1",
9801     "runtime_only": false
9802   },
9803   {
9804     "axioms": [
9805       "propext",
9806       "Classical.choice",
9807       "Quot.sound"
9808     ],
9809     "in_project_namespace": true,
9810     "kind": "theorem",
9811     "module": "PaperIRelease.AlgebraQuotient",
9812     "name": "Komorebi.PaperIRelease.diagonalClassHom_eq_zero_iff",
9813     "runtime_only": false
9814   },
9815   {
9816     "axioms": [
9817       "propext",
9818       "Quot.sound"
9819     ],
9820     "in_project_namespace": true,
9821     "kind": "theorem",
9822     "module": "KomorebiVerification.SeedRankBasics",
9823     "name": "Komorebi.SeedRankBasics.generates_univ",
9824     "runtime_only": false
9825   },
9826   {
9827     "axioms": [
9828       "propext",
9829       "Classical.choice",
9830       "Quot.sound"
9831     ],
9832     "in_project_namespace": true,
9833     "kind": "definition",
9834     "module": "KomorebiVerification.PacketNaturalityCompletion",
9835     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks",
9836     "runtime_only": false
9837   },
9838   {
9839     "axioms": [
9840       "propext",
9841       "Classical.choice",
9842       "Quot.sound"
9843     ],
9844     "in_project_namespace": false,
9845     "kind": "theorem",
9846     "module": "PaperIRelease.TopologyUnconditionalBridge",
9847     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_4",
9848     "runtime_only": false
9849   },
9850   {
9851     "axioms": [
9852       "propext",
9853       "Classical.choice",
9854       "Quot.sound"
9855     ],
9856     "in_project_namespace": true,
9857     "kind": "theorem",
9858     "module": "PaperICompletion4.OperatorIntrinsicFormula",
9859     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_zero_of_absent",
9860     "runtime_only": false
9861   },
9862   {
9863     "axioms": [
9864       "propext",
9865       "Classical.choice",
9866       "Quot.sound"
9867     ],
9868     "in_project_namespace": true,
9869     "kind": "theorem",
9870     "module": "PaperIRelease.GraphReachability",
9871     "name": "Komorebi.PaperIRelease.generatedAlgebra_block_zero",
9872     "runtime_only": false
9873   },
9874   {
9875     "axioms": [
9876       "propext",
9877       "Classical.choice",
9878       "Quot.sound"
9879     ],
9880     "in_project_namespace": true,
9881     "kind": "theorem",
9882     "module": "PaperICompletion8.RegularMultiplicity",
9883     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.natural_seedRank_eq_one",
9884     "runtime_only": false
9885   },
9886   {
9887     "axioms": [
9888       "propext",
9889       "Classical.choice",
9890       "Quot.sound"
9891     ],
9892     "in_project_namespace": false,
9893     "kind": "theorem",
9894     "module": "ReleaseBoundary",
9895     "name": "PaperIBlock08Tests.mixed_direct_sum_rank",
9896     "runtime_only": false
9897   },
9898   {
9899     "axioms": [
9900       "propext",
9901       "Classical.choice",
9902       "Quot.sound"
9903     ],
9904     "in_project_namespace": false,
9905     "kind": "theorem",
9906     "module": "PaperIRelease.TopologyDenseCompletion",
9907     "name": "PaperIRelease.TopologyDenseCompletion.completion_intertwines",
9908     "runtime_only": false
9909   },
9910   {
9911     "axioms": [
9912       "propext",
9913       "Quot.sound"
9914     ],
9915     "in_project_namespace": true,
9916     "kind": "theorem",
9917     "module": "KomorebiVerification.FibreRefinement",
9918     "name": "Komorebi.Packet.fibreLinearProj_apply",
9919     "runtime_only": false
9920   },
9921   {
9922     "axioms": [
9923       "propext",
9924       "Classical.choice",
9925       "Quot.sound"
9926     ],
9927     "in_project_namespace": true,
9928     "kind": "definition",
9929     "module": "PaperICompletion4.ResidueQuotient",
9930     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap",
9931     "runtime_only": false
9932   },
9933   {
9934     "axioms": [
9935       "propext",
9936       "Classical.choice",
9937       "Quot.sound"
9938     ],
9939     "in_project_namespace": true,
9940     "kind": "theorem",
9941     "module": "PaperIRelease.CategoryPackets",
9942     "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector_apply",
9943     "runtime_only": false
9944   },
9945   {
9946     "axioms": [
9947       "propext",
9948       "Classical.choice",
9949       "Quot.sound"
9950     ],
9951     "in_project_namespace": true,
9952     "kind": "theorem",
9953     "module": "KomorebiVerification.TopologicalCompletion",
9954     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic.eq_1",
9955     "runtime_only": false
9956   },
9957   {
9958     "axioms": [
9959       "propext",
9960       "Quot.sound"
9961     ],
9962     "in_project_namespace": true,
9963     "kind": "theorem",
9964     "module": "PaperICompletion8.RegularMultiplicity",
9965     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_2",
9966     "runtime_only": false
9967   },
9968   {
9969     "axioms": [
9970       "propext",
9971       "Classical.choice",
9972       "Quot.sound"
9973     ],
9974     "in_project_namespace": true,
9975     "kind": "definition",
9976     "module": "PaperIRelease.GrammarIdeal",
9977     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealGrammar",
9978     "runtime_only": false
9979   },
9980   {
9981     "axioms": [
9982       "propext",
9983       "Classical.choice",
9984       "Quot.sound"
9985     ],
9986     "in_project_namespace": true,
9987     "kind": "definition",
9988     "module": "PaperIRelease.GrammarTyped",
9989     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.casesOn",
9990     "runtime_only": false
9991   },
9992   {
9993     "axioms": [
9994       "propext",
9995       "Classical.choice",
9996       "Quot.sound"
9997     ],
9998     "in_project_namespace": true,
9999     "kind": "theorem",
10000     "module": "PaperICompletion8.RegularMultiplicity",
10001     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_3",
10002     "runtime_only": false
10003   },
10004   {
10005     "axioms": [
10006       "propext"
10007     ],
10008     "in_project_namespace": true,
10009     "kind": "theorem",
10010     "module": "PaperIRelease.CategoryExport",
10011     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_7",
10012     "runtime_only": false
10013   },
10014   {
10015     "axioms": [
10016       "propext",
10017       "Classical.choice",
10018       "Quot.sound"
10019     ],
10020     "in_project_namespace": true,
10021     "kind": "theorem",
10022     "module": "PaperIRelease.GrammarEquivalence",
10023     "name": "Komorebi.PaperIRelease.GrammarAlgebra.actionHom_arrow",
10024     "runtime_only": false
10025   },
10026   {
10027     "axioms": [],
10028     "in_project_namespace": true,
10029     "kind": "definition",
10030     "module": "KomorebiVerification.ProjectorCore",
10031     "name": "Komorebi.Seed.OperatorRelation.rhs",
10032     "runtime_only": false
10033   },
10034   {
10035     "axioms": [
10036       "propext",
10037       "Classical.choice",
10038       "Quot.sound"
10039     ],
10040     "in_project_namespace": true,
10041     "kind": "theorem",
10042     "module": "PaperIRelease.AlgebraPreorder",
10043     "name": "Komorebi.PaperIRelease.strictSupport_iff_same_class_zero",
10044     "runtime_only": false
10045   },
10046   {
10047     "axioms": [
10048       "propext",
10049       "Classical.choice",
10050       "Quot.sound"
10051     ],
10052     "in_project_namespace": true,
10053     "kind": "theorem",
10054     "module": "PaperIRelease.TopologyCategories",
10055     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.scalarContinuous",
10056     "runtime_only": false
10057   },
10058   {
10059     "axioms": [
10060       "propext",
10061       "Classical.choice",
10062       "Quot.sound"
10063     ],
10064     "in_project_namespace": true,
10065     "kind": "theorem",
10066     "module": "PaperIRelease.PacketTopology",
10067     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM._proof_1",
10068     "runtime_only": false
10069   },
10070   {
10071     "axioms": [
10072       "propext",
10073       "Quot.sound"
10074     ],
10075     "in_project_namespace": true,
10076     "kind": "definition",
10077     "module": "PaperIRelease.GrammarAlgebra",
10078     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar._sizeOf_inst",
10079     "runtime_only": false
10080   },
10081   {
10082     "axioms": [],
10083     "in_project_namespace": true,
10084     "kind": "theorem",
10085     "module": "KomorebiVerification.ProjectorCore",
10086     "name": "Komorebi.Polyphase.coeffSection.eq_1",
10087     "runtime_only": false
10088   },
10089   {
10090     "axioms": [
10091       "propext",
10092       "Classical.choice",
10093       "Quot.sound"
10094     ],
10095     "in_project_namespace": true,
10096     "kind": "theorem",
10097     "module": "PaperIRelease.PacketSourceLower",
10098     "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_1",
10099     "runtime_only": false
10100   },
10101   {
10102     "axioms": [
10103       "propext",
10104       "Classical.choice",
10105       "Quot.sound"
10106     ],
10107     "in_project_namespace": true,
10108     "kind": "theorem",
10109     "module": "PaperIRelease.PacketSourceLower",
10110     "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_2",
10111     "runtime_only": false
10112   },
10113   {
10114     "axioms": [
10115       "propext",
10116       "Classical.choice",
10117       "Quot.sound"
10118     ],
10119     "in_project_namespace": false,
10120     "kind": "definition",
10121     "module": "ReleaseBoundary",
10122     "name": "PaperIBlock08Tests.H",
10123     "runtime_only": false
10124   },
10125   {
10126     "axioms": [
10127       "propext",
10128       "Classical.choice",
10129       "Quot.sound"
10130     ],
10131     "in_project_namespace": true,
10132     "kind": "definition",
10133     "module": "PaperIRelease.CategoryPackets",
10134     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.casesOn",
10135     "runtime_only": false
10136   },
10137   {
10138     "axioms": [],
10139     "in_project_namespace": true,
10140     "kind": "definition",
10141     "module": "KomorebiVerification.ProjectorCore",
10142     "name": "Komorebi.FormalizationStatus.contextOnly.elim",
10143     "runtime_only": false
10144   },
10145   {
10146     "axioms": [
10147       "propext",
10148       "Classical.choice",
10149       "Quot.sound"
10150     ],
10151     "in_project_namespace": true,
10152     "kind": "theorem",
10153     "module": "KomorebiVerification.PacketNaturalityCompletion",
10154     "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_transferEdge_iff",
10155     "runtime_only": false
10156   },
10157   {
10158     "axioms": [
10159       "propext",
10160       "Classical.choice",
10161       "Quot.sound"
10162     ],
10163     "in_project_namespace": true,
10164     "kind": "definition",
10165     "module": "PaperICompletion8.DivisionBlock",
10166     "name": "Komorebi.PaperICompletion8.DivisionBlock.blockModuleAction",
10167     "runtime_only": false
10168   },
10169   {
10170     "axioms": [
10171       "propext",
10172       "Classical.choice",
10173       "Quot.sound"
10174     ],
10175     "in_project_namespace": true,
10176     "kind": "theorem",
10177     "module": "KomorebiVerification.EllipticAlgorithms",
10178     "name": "Komorebi.EllipticCoordinates.P0_add_P1",
10179     "runtime_only": false
10180   },
10181   {
10182     "axioms": [
10183       "propext",
10184       "Classical.choice",
10185       "Quot.sound"
10186     ],
10187     "in_project_namespace": true,
10188     "kind": "definition",
10189     "module": "PaperIRelease.CategoryExport",
10190     "name": "Komorebi.PaperIRelease.CategoryExport.transportLimit",
10191     "runtime_only": false
10192   },
10193   {
10194     "axioms": [
10195       "propext",
10196       "Classical.choice",
10197       "Quot.sound"
10198     ],
10199     "in_project_namespace": false,
10200     "kind": "definition",
10201     "module": "PaperIRelease.TopologyCountablePackets",
10202     "name": "PaperIRelease.TopologyCountablePackets.Projectors.recOn",
10203     "runtime_only": false
10204   },
10205   {
10206     "axioms": [
10207       "propext",
10208       "Classical.choice",
10209       "Quot.sound"
10210     ],
10211     "in_project_namespace": true,
10212     "kind": "recursor",
10213     "module": "KomorebiVerification.TopologicalCompletion",
10214     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.rec",
10215     "runtime_only": false
10216   },
10217   {
10218     "axioms": [
10219       "propext",
10220       "Classical.choice",
10221       "Quot.sound"
10222     ],
10223     "in_project_namespace": true,
10224     "kind": "theorem",
10225     "module": "PaperIRelease.PacketExactSequence",
10226     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_5",
10227     "runtime_only": false
10228   },
10229   {
10230     "axioms": [
10231       "propext",
10232       "Classical.choice",
10233       "Quot.sound"
10234     ],
10235     "in_project_namespace": true,
10236     "kind": "theorem",
10237     "module": "KomorebiVerification.EllipticAlgorithms",
10238     "name": "Komorebi.EllipticCoordinates.y.eq_1",
10239     "runtime_only": false
10240   },
10241   {
10242     "axioms": [
10243       "propext",
10244       "Classical.choice",
10245       "Quot.sound"
10246     ],
10247     "in_project_namespace": true,
10248     "kind": "theorem",
10249     "module": "KomorebiVerification.EllipticAlgorithms",
10250     "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity_le_exactGraphSeedRank",
10251     "runtime_only": false
10252   },
10253   {
10254     "axioms": [
10255       "propext",
10256       "Classical.choice",
10257       "Quot.sound"
10258     ],
10259     "in_project_namespace": true,
10260     "kind": "definition",
10261     "module": "PaperIRelease.CategoryPackets",
10262     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk._flat_ctor",
10263     "runtime_only": false
10264   },
10265   {
10266     "axioms": [
10267       "propext",
10268       "Classical.choice",
10269       "Quot.sound"
10270     ],
10271     "in_project_namespace": true,
10272     "kind": "theorem",
10273     "module": "PaperIRelease.PacketBoundaryTests",
10274     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.all_preserve_top",
10275     "runtime_only": false
10276   },
10277   {
10278     "axioms": [
10279       "propext",
10280       "Classical.choice",
10281       "Quot.sound"
10282     ],
10283     "in_project_namespace": true,
10284     "kind": "theorem",
10285     "module": "PaperIRelease.CategoryPackets",
10286     "name": "Komorebi.PaperIRelease.CategoryPackets.transferBlock_naturality_apply",
10287     "runtime_only": false
10288   },
10289   {
10290     "axioms": [
10291       "propext",
10292       "Classical.choice",
10293       "Quot.sound"
10294     ],
10295     "in_project_namespace": true,
10296     "kind": "theorem",
10297     "module": "KomorebiVerification.SingleOperatorGraph",
10298     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_map_adjacency",
10299     "runtime_only": false
10300   },
10301   {
10302     "axioms": [
10303       "propext",
10304       "Classical.choice",
10305       "Quot.sound"
10306     ],
10307     "in_project_namespace": false,
10308     "kind": "theorem",
10309     "module": "PaperIRelease.TopologyCountablePackets",
10310     "name": "PaperIRelease.TopologyCountablePackets.Projectors.complete",
10311     "runtime_only": false
10312   },
10313   {
10314     "axioms": [
10315       "propext",
10316       "Classical.choice",
10317       "Quot.sound"
10318     ],
10319     "in_project_namespace": false,
10320     "kind": "definition",
10321     "module": "ReleaseBoundary",
10322     "name": "PaperIBlock08Tests.qj",
10323     "runtime_only": false
10324   },
10325   {
10326     "axioms": [
10327       "propext",
10328       "Classical.choice",
10329       "Quot.sound"
10330     ],
10331     "in_project_namespace": true,
10332     "kind": "theorem",
10333     "module": "PaperIRelease.GeneralConditionedCoordinates",
10334     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear._proof_2",
10335     "runtime_only": false
10336   },
10337   {
10338     "axioms": [
10339       "propext",
10340       "Quot.sound"
10341     ],
10342     "in_project_namespace": true,
10343     "kind": "theorem",
10344     "module": "PaperIRelease.TensorPackets",
10345     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_4",
10346     "runtime_only": false
10347   },
10348   {
10349     "axioms": [
10350       "propext",
10351       "Classical.choice",
10352       "Quot.sound"
10353     ],
10354     "in_project_namespace": true,
10355     "kind": "theorem",
10356     "module": "PaperIRelease.TopologyCategories",
10357     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.map_hull",
10358     "runtime_only": false
10359   },
10360   {
10361     "axioms": [
10362       "propext",
10363       "Classical.choice",
10364       "Quot.sound"
10365     ],
10366     "in_project_namespace": true,
10367     "kind": "definition",
10368     "module": "KomorebiVerification.TopologicalCompletion",
10369     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2",
10370     "runtime_only": false
10371   },
10372   {
10373     "axioms": [
10374       "propext",
10375       "Classical.choice",
10376       "Quot.sound"
10377     ],
10378     "in_project_namespace": true,
10379     "kind": "theorem",
10380     "module": "PaperIRelease.AlgebraPreorder",
10381     "name": "Komorebi.PaperIRelease.strictSupportIdeal_pow_eq_bot",
10382     "runtime_only": false
10383   },
10384   {
10385     "axioms": [
10386       "propext",
10387       "Classical.choice",
10388       "Quot.sound"
10389     ],
10390     "in_project_namespace": true,
10391     "kind": "theorem",
10392     "module": "PaperIRelease.GrammarAlgebra",
10393     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_6",
10394     "runtime_only": false
10395   },
10396   {
10397     "axioms": [
10398       "propext",
10399       "Classical.choice",
10400       "Quot.sound"
10401     ],
10402     "in_project_namespace": true,
10403     "kind": "definition",
10404     "module": "KomorebiVerification.PacketNaturalityCompletion",
10405     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMul",
10406     "runtime_only": false
10407   },
10408   {
10409     "axioms": [
10410       "propext",
10411       "Classical.choice",
10412       "Quot.sound"
10413     ],
10414     "in_project_namespace": true,
10415     "kind": "theorem",
10416     "module": "PaperICompletion7.LocalResidue",
10417     "name": "Komorebi.PaperICompletion7.LocalResidue.maximal_left_ideal_unique",
10418     "runtime_only": false
10419   },
10420   {
10421     "axioms": [],
10422     "in_project_namespace": true,
10423     "kind": "definition",
10424     "module": "PaperIRelease.CategoryExport",
10425     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.casesOn",
10426     "runtime_only": false
10427   },
10428   {
10429     "axioms": [],
10430     "in_project_namespace": true,
10431     "kind": "definition",
10432     "module": "KomorebiVerification.ProjectorCore",
10433     "name": "Komorebi.FormalizationStatus.ctorElim",
10434     "runtime_only": false
10435   },
10436   {
10437     "axioms": [
10438       "propext",
10439       "Classical.choice",
10440       "Quot.sound"
10441     ],
10442     "in_project_namespace": true,
10443     "kind": "theorem",
10444     "module": "KomorebiVerification.TopologicalCompletion",
10445     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis_synthesis",
10446     "runtime_only": false
10447   },
10448   {
10449     "axioms": [
10450       "propext",
10451       "Quot.sound"
10452     ],
10453     "in_project_namespace": false,
10454     "kind": "theorem",
10455     "module": "PaperIRelease.TopologyDenseCompletion",
10456     "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding._proof_1",
10457     "runtime_only": false
10458   },
10459   {
10460     "axioms": [
10461       "propext",
10462       "Classical.choice",
10463       "Quot.sound"
10464     ],
10465     "in_project_namespace": false,
10466     "kind": "theorem",
10467     "module": "ReleaseBoundary",
10468     "name": "PaperIBlock08Tests.quaternion_every_nonzero_is_cyclic",
10469     "runtime_only": false
10470   },
10471   {
10472     "axioms": [
10473       "propext",
10474       "Classical.choice",
10475       "Quot.sound"
10476     ],
10477     "in_project_namespace": false,
10478     "kind": "theorem",
10479     "module": "PaperIRelease.TopologyDenseCompletion",
10480     "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_injective",
10481     "runtime_only": false
10482   },
10483   {
10484     "axioms": [
10485       "propext"
10486     ],
10487     "in_project_namespace": true,
10488     "kind": "theorem",
10489     "module": "PaperIRelease.CategoryExport",
10490     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_3",
10491     "runtime_only": false
10492   },
10493   {
10494     "axioms": [
10495       "propext",
10496       "Quot.sound"
10497     ],
10498     "in_project_namespace": true,
10499     "kind": "definition",
10500     "module": "PaperIRelease.GrammarModules",
10501     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.noConfusion",
10502     "runtime_only": false
10503   },
10504   {
10505     "axioms": [
10506       "propext",
10507       "Classical.choice",
10508       "Quot.sound"
10509     ],
10510     "in_project_namespace": false,
10511     "kind": "theorem",
10512     "module": "PaperIRelease.TopologyUnconditionalBridge",
10513     "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_3",
10514     "runtime_only": false
10515   },
10516   {
10517     "axioms": [
10518       "propext",
10519       "Classical.choice",
10520       "Quot.sound"
10521     ],
10522     "in_project_namespace": true,
10523     "kind": "theorem",
10524     "module": "PaperIRelease.PacketTopology",
10525     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSum_proj_modK",
10526     "runtime_only": false
10527   },
10528   {
10529     "axioms": [
10530       "propext",
10531       "Classical.choice",
10532       "Quot.sound"
10533     ],
10534     "in_project_namespace": true,
10535     "kind": "definition",
10536     "module": "KomorebiVerification.SemisimpleCompletion",
10537     "name": "Komorebi.SemisimpleCompletion.maxCeilDiv",
10538     "runtime_only": false
10539   },
10540   {
10541     "axioms": [
10542       "propext",
10543       "Classical.choice",
10544       "Quot.sound"
10545     ],
10546     "in_project_namespace": true,
10547     "kind": "theorem",
10548     "module": "KomorebiVerification.SingleOperatorGraph",
10549     "name": "Komorebi.SingleOperatorGraph.operator_mem_span_orbit_of_mem",
10550     "runtime_only": false
10551   },
10552   {
10553     "axioms": [
10554       "propext"
10555     ],
10556     "in_project_namespace": true,
10557     "kind": "theorem",
10558     "module": "KomorebiVerification.ProjectorCore",
10559     "name": "Komorebi.Polyphase.coeffSection_comp",
10560     "runtime_only": false
10561   },
10562   {
10563     "axioms": [
10564       "propext",
10565       "Classical.choice",
10566       "Quot.sound"
10567     ],
10568     "in_project_namespace": true,
10569     "kind": "theorem",
10570     "module": "PaperIRelease.GeneralFiniteCompletion",
10571     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_5",
10572     "runtime_only": false
10573   },
10574   {
10575     "axioms": [
10576       "propext",
10577       "Classical.choice",
10578       "Quot.sound"
10579     ],
10580     "in_project_namespace": true,
10581     "kind": "theorem",
10582     "module": "PaperIRelease.CategoryPackets",
10583     "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_3",
10584     "runtime_only": false
10585   },
10586   {
10587     "axioms": [
10588       "propext"
10589     ],
10590     "in_project_namespace": true,
10591     "kind": "theorem",
10592     "module": "KomorebiVerification.ProjectorCore",
10593     "name": "Komorebi.Seed.OperatorExpr.comp.injEq",
10594     "runtime_only": false
10595   },
10596   {
10597     "axioms": [
10598       "propext"
10599     ],
10600     "in_project_namespace": true,
10601     "kind": "definition",
10602     "module": "KomorebiVerification.ProjectorCore",
10603     "name": "Komorebi.instReprClaimRecord.repr",
10604     "runtime_only": false
10605   },
10606   {
10607     "axioms": [
10608       "propext",
10609       "Classical.choice",
10610       "Quot.sound"
10611     ],
10612     "in_project_namespace": true,
10613     "kind": "definition",
10614     "module": "KomorebiVerification.TopologicalCompletion",
10615     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily._sizeOf_inst",
10616     "runtime_only": false
10617   },
10618   {
10619     "axioms": [],
10620     "in_project_namespace": true,
10621     "kind": "definition",
10622     "module": "KomorebiVerification.ProjectorCore",
10623     "name": "Komorebi.Seed.OperatorExpr.atom.elim",
10624     "runtime_only": false
10625   },
10626   {
10627     "axioms": [
10628       "propext",
10629       "Classical.choice",
10630       "Quot.sound"
10631     ],
10632     "in_project_namespace": true,
10633     "kind": "definition",
10634     "module": "PaperIRelease.GrammarAlgebra",
10635     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk._flat_ctor",
10636     "runtime_only": false
10637   },
10638   {
10639     "axioms": [
10640       "propext",
10641       "Classical.choice",
10642       "Quot.sound"
10643     ],
10644     "in_project_namespace": true,
10645     "kind": "theorem",
10646     "module": "KomorebiVerification.SemisimpleCompletion",
10647     "name": "Komorebi.SemisimpleCompletion.fullMatrix_module_cyclic",
10648     "runtime_only": false
10649   },
10650   {
10651     "axioms": [
10652       "propext",
10653       "Classical.choice",
10654       "Quot.sound"
10655     ],
10656     "in_project_namespace": true,
10657     "kind": "definition",
10658     "module": "PaperIRelease.GeneralNormedPackets",
10659     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis",
10660     "runtime_only": false
10661   },
10662   {
10663     "axioms": [],
10664     "in_project_namespace": true,
10665     "kind": "theorem",
10666     "module": "KomorebiVerification.ProjectorCore",
10667     "name": "Komorebi.FormalizationStatus.partialFormalization.sizeOf_spec",
10668     "runtime_only": false
10669   },
10670   {
10671     "axioms": [
10672       "propext",
10673       "Classical.choice",
10674       "Quot.sound"
10675     ],
10676     "in_project_namespace": true,
10677     "kind": "theorem",
10678     "module": "PaperIRelease.GeneralNormedPackets",
10679     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv_apply",
10680     "runtime_only": false
10681   },
10682   {
10683     "axioms": [
10684       "propext",
10685       "Classical.choice",
10686       "Quot.sound"
10687     ],
10688     "in_project_namespace": true,
10689     "kind": "theorem",
10690     "module": "PaperICompletion8.DivisionRows",
10691     "name": "Komorebi.PaperICompletion8.DivisionRows.multiplicity_le_of_leftGenerates",
10692     "runtime_only": false
10693   },
10694   {
10695     "axioms": [
10696       "propext",
10697       "Classical.choice",
10698       "Quot.sound"
10699     ],
10700     "in_project_namespace": true,
10701     "kind": "theorem",
10702     "module": "KomorebiVerification.ProjectorCore",
10703     "name": "Komorebi.Operator.blockApply_zero",
10704     "runtime_only": false
10705   },
10706   {
10707     "axioms": [],
10708     "in_project_namespace": true,
10709     "kind": "theorem",
10710     "module": "KomorebiVerification.PathGraphKrylov",
10711     "name": "Komorebi.PathGraphKrylov.leftTerm._proof_2",
10712     "runtime_only": false
10713   },
10714   {
10715     "axioms": [
10716       "propext",
10717       "Quot.sound"
10718     ],
10719     "in_project_namespace": true,
10720     "kind": "theorem",
10721     "module": "KomorebiVerification.PacketNaturalityCompletion",
10722     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.linearMap_smul_of_intertwining",
10723     "runtime_only": false
10724   },
10725   {
10726     "axioms": [
10727       "propext",
10728       "Classical.choice",
10729       "Quot.sound"
10730     ],
10731     "in_project_namespace": true,
10732     "kind": "definition",
10733     "module": "PaperIRelease.AlgebraClassGrouping",
10734     "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv",
10735     "runtime_only": false
10736   },
10737   {
10738     "axioms": [
10739       "propext"
10740     ],
10741     "in_project_namespace": true,
10742     "kind": "theorem",
10743     "module": "PaperIRelease.PacketDescent",
10744     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range_preimage._abel_1_1",
10745     "runtime_only": false
10746   },
10747   {
10748     "axioms": [],
10749     "in_project_namespace": true,
10750     "kind": "definition",
10751     "module": "PaperIRelease.CategoryExport",
10752     "name": "Komorebi.PaperIRelease.CategoryExport.Expression._sizeOf_inst",
10753     "runtime_only": false
10754   },
10755   {
10756     "axioms": [
10757       "propext",
10758       "Quot.sound"
10759     ],
10760     "in_project_namespace": true,
10761     "kind": "theorem",
10762     "module": "KomorebiVerification.FibreRefinement",
10763     "name": "Komorebi.Packet.fibreLinearProj._proof_2",
10764     "runtime_only": false
10765   },
10766   {
10767     "axioms": [
10768       "propext",
10769       "Classical.choice",
10770       "Quot.sound"
10771     ],
10772     "in_project_namespace": true,
10773     "kind": "theorem",
10774     "module": "PaperIRelease.TopologyCategories",
10775     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.inj",
10776     "runtime_only": false
10777   },
10778   {
10779     "axioms": [
10780       "propext",
10781       "Quot.sound"
10782     ],
10783     "in_project_namespace": true,
10784     "kind": "inductive",
10785     "module": "PaperIRelease.GrammarModules",
10786     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom",
10787     "runtime_only": false
10788   },
10789   {
10790     "axioms": [],
10791     "in_project_namespace": true,
10792     "kind": "theorem",
10793     "module": "PaperICompletion4.ResidueQuotient",
10794     "name": "Komorebi.PaperICompletion4.ResidueQuotient.ScalarQuotient._proof_1",
10795     "runtime_only": false
10796   },
10797   {
10798     "axioms": [
10799       "propext",
10800       "Classical.choice",
10801       "Quot.sound"
10802     ],
10803     "in_project_namespace": true,
10804     "kind": "theorem",
10805     "module": "PaperIRelease.AlgebraDiagonal",
10806     "name": "Komorebi.PaperIRelease.diagonalProjection_commutes",
10807     "runtime_only": false
10808   },
10809   {
10810     "axioms": [
10811       "propext",
10812       "Classical.choice",
10813       "Quot.sound"
10814     ],
10815     "in_project_namespace": true,
10816     "kind": "theorem",
10817     "module": "KomorebiVerification.EllipticAlgorithms",
10818     "name": "Komorebi.FiniteAlgorithms.seeds_subset_orbitClosureIter",
10819     "runtime_only": false
10820   },
10821   {
10822     "axioms": [
10823       "propext",
10824       "Classical.choice",
10825       "Quot.sound"
10826     ],
10827     "in_project_namespace": true,
10828     "kind": "theorem",
10829     "module": "KomorebiVerification.PacketNaturalityCompletion",
10830     "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_2",
10831     "runtime_only": false
10832   },
10833   {
10834     "axioms": [
10835       "propext",
10836       "Classical.choice",
10837       "Quot.sound"
10838     ],
10839     "in_project_namespace": false,
10840     "kind": "theorem",
10841     "module": "PaperIRelease.AlgebraPreorder",
10842     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strict_mul_power_mem",
10843     "runtime_only": false
10844   },
10845   {
10846     "axioms": [
10847       "propext",
10848       "Classical.choice",
10849       "Quot.sound"
10850     ],
10851     "in_project_namespace": true,
10852     "kind": "theorem",
10853     "module": "KomorebiVerification.TopologicalCompletion",
10854     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetRange_eq_closure_map",
10855     "runtime_only": false
10856   },
10857   {
10858     "axioms": [
10859       "propext",
10860       "Classical.choice",
10861       "Quot.sound"
10862     ],
10863     "in_project_namespace": false,
10864     "kind": "definition",
10865     "module": "PaperIRelease.TopologyUnconditional",
10866     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm",
10867     "runtime_only": false
10868   },
10869   {
10870     "axioms": [
10871       "propext",
10872       "Classical.choice",
10873       "Quot.sound"
10874     ],
10875     "in_project_namespace": true,
10876     "kind": "theorem",
10877     "module": "PaperICompletion5.LinearPrimaryEigenspace",
10878     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap_surjective",
10879     "runtime_only": false
10880   },
10881   {
10882     "axioms": [
10883       "propext",
10884       "Quot.sound"
10885     ],
10886     "in_project_namespace": true,
10887     "kind": "theorem",
10888     "module": "PaperIRelease.GrammarModules",
10889     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_7",
10890     "runtime_only": false
10891   },
10892   {
10893     "axioms": [
10894       "propext",
10895       "Quot.sound"
10896     ],
10897     "in_project_namespace": true,
10898     "kind": "definition",
10899     "module": "KomorebiVerification.PathGraphKrylov",
10900     "name": "Komorebi.PathGraphKrylov.IsCyclic",
10901     "runtime_only": false
10902   },
10903   {
10904     "axioms": [
10905       "propext",
10906       "Classical.choice",
10907       "Quot.sound"
10908     ],
10909     "in_project_namespace": true,
10910     "kind": "definition",
10911     "module": "KomorebiVerification.PacketNaturalityCompletion",
10912     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation",
10913     "runtime_only": false
10914   },
10915   {
10916     "axioms": [
10917       "propext",
10918       "Quot.sound"
10919     ],
10920     "in_project_namespace": true,
10921     "kind": "theorem",
10922     "module": "KomorebiVerification.SingleOperatorGraph",
10923     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_4",
10924     "runtime_only": false
10925   },
10926   {
10927     "axioms": [
10928       "propext",
10929       "Classical.choice",
10930       "Quot.sound"
10931     ],
10932     "in_project_namespace": true,
10933     "kind": "theorem",
10934     "module": "PaperIRelease.BoundedStar",
10935     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_7",
10936     "runtime_only": false
10937   },
10938   {
10939     "axioms": [],
10940     "in_project_namespace": true,
10941     "kind": "theorem",
10942     "module": "KomorebiVerification.ProjectorCore",
10943     "name": "Komorebi.Seed.OperatorRelation.satisfied_trans",
10944     "runtime_only": false
10945   },
10946   {
10947     "axioms": [
10948       "propext",
10949       "Classical.choice",
10950       "Quot.sound"
10951     ],
10952     "in_project_namespace": true,
10953     "kind": "definition",
10954     "module": "KomorebiVerification.SeedRankBasics",
10955     "name": "Komorebi.SeedRankBasics.multiSeedMap",
10956     "runtime_only": false
10957   },
10958   {
10959     "axioms": [
10960       "propext",
10961       "Classical.choice",
10962       "Quot.sound"
10963     ],
10964     "in_project_namespace": true,
10965     "kind": "definition",
10966     "module": "PaperIRelease.CategoryPackets",
10967     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp",
10968     "runtime_only": false
10969   },
10970   {
10971     "axioms": [
10972       "propext",
10973       "Classical.choice",
10974       "Quot.sound"
10975     ],
10976     "in_project_namespace": true,
10977     "kind": "definition",
10978     "module": "KomorebiVerification.PacketNaturalityCompletion",
10979     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB",
10980     "runtime_only": false
10981   },
10982   {
10983     "axioms": [
10984       "propext",
10985       "Quot.sound"
10986     ],
10987     "in_project_namespace": false,
10988     "kind": "theorem",
10989     "module": "KomorebiVerification.SeedRankOperations",
10990     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.product_smul_mk",
10991     "runtime_only": false
10992   },
10993   {
10994     "axioms": [
10995       "propext",
10996       "Quot.sound"
10997     ],
10998     "in_project_namespace": false,
10999     "kind": "theorem",
11000     "module": "PaperIRelease.AlgebraTransfer",
11001     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.eq_1",
11002     "runtime_only": false
11003   },
11004   {
11005     "axioms": [
11006       "propext",
11007       "Classical.choice",
11008       "Quot.sound"
11009     ],
11010     "in_project_namespace": true,
11011     "kind": "theorem",
11012     "module": "PaperIRelease.PacketSourceUpper",
11013     "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_sum_local_of_generation",
11014     "runtime_only": false
11015   },
11016   {
11017     "axioms": [
11018       "propext",
11019       "Classical.choice",
11020       "Quot.sound"
11021     ],
11022     "in_project_namespace": true,
11023     "kind": "definition",
11024     "module": "KomorebiVerification.EllipticAlgorithms",
11025     "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity",
11026     "runtime_only": false
11027   },
11028   {
11029     "axioms": [],
11030     "in_project_namespace": true,
11031     "kind": "constructor",
11032     "module": "PaperIRelease.CategoryExport",
11033     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp",
11034     "runtime_only": false
11035   },
11036   {
11037     "axioms": [
11038       "propext",
11039       "Classical.choice",
11040       "Quot.sound"
11041     ],
11042     "in_project_namespace": true,
11043     "kind": "theorem",
11044     "module": "PaperIRelease.GrammarAlgebra",
11045     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ext_iff",
11046     "runtime_only": false
11047   },
11048   {
11049     "axioms": [],
11050     "in_project_namespace": true,
11051     "kind": "definition",
11052     "module": "KomorebiVerification.PacketNaturalityCompletion",
11053     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.U",
11054     "runtime_only": false
11055   },
11056   {
11057     "axioms": [
11058       "propext",
11059       "Classical.choice",
11060       "Quot.sound"
11061     ],
11062     "in_project_namespace": false,
11063     "kind": "theorem",
11064     "module": "PaperIRelease.TopologySemilinearRank",
11065     "name": "PaperIRelease.TopologySemilinearRank.generates_univ",
11066     "runtime_only": false
11067   },
11068   {
11069     "axioms": [
11070       "propext",
11071       "Classical.choice",
11072       "Quot.sound"
11073     ],
11074     "in_project_namespace": false,
11075     "kind": "definition",
11076     "module": "PaperIRelease.TopologyCountablePackets",
11077     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule",
11078     "runtime_only": false
11079   },
11080   {
11081     "axioms": [
11082       "propext",
11083       "Classical.choice",
11084       "Quot.sound"
11085     ],
11086     "in_project_namespace": true,
11087     "kind": "recursor",
11088     "module": "PaperIRelease.GeneralNormedPackets",
11089     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.rec",
11090     "runtime_only": false
11091   },
11092   {
11093     "axioms": [
11094       "propext",
11095       "Classical.choice",
11096       "Quot.sound"
11097     ],
11098     "in_project_namespace": true,
11099     "kind": "theorem",
11100     "module": "KomorebiVerification.SingleOperatorGraph",
11101     "name": "Komorebi.SingleOperatorGraph.SeedNumberLE.eq_1",
11102     "runtime_only": false
11103   },
11104   {
11105     "axioms": [
11106       "propext",
11107       "Classical.choice",
11108       "Quot.sound"
11109     ],
11110     "in_project_namespace": true,
11111     "kind": "theorem",
11112     "module": "PaperIRelease.PacketTopology",
11113     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseCLM._proof_1",
11114     "runtime_only": false
11115   },
11116   {
11117     "axioms": [
11118       "propext",
11119       "Classical.choice",
11120       "Quot.sound"
11121     ],
11122     "in_project_namespace": false,
11123     "kind": "theorem",
11124     "module": "PaperIRelease.TopologyCountablePackets",
11125     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_opNorm_le",
11126     "runtime_only": false
11127   },
11128   {
11129     "axioms": [
11130       "propext",
11131       "Quot.sound"
11132     ],
11133     "in_project_namespace": true,
11134     "kind": "theorem",
11135     "module": "PaperIRelease.GrammarTyped",
11136     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.injEq",
11137     "runtime_only": false
11138   },
11139   {
11140     "axioms": [
11141       "propext",
11142       "Classical.choice",
11143       "Quot.sound"
11144     ],
11145     "in_project_namespace": true,
11146     "kind": "definition",
11147     "module": "KomorebiVerification.SingleOperatorGraph",
11148     "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate",
11149     "runtime_only": false
11150   },
11151   {
11152     "axioms": [
11153       "propext",
11154       "Classical.choice",
11155       "Quot.sound"
11156     ],
11157     "in_project_namespace": false,
11158     "kind": "theorem",
11159     "module": "PaperIRelease.TopologyCountablePackets",
11160     "name": "PaperIRelease.TopologyCountablePackets.Projectors.nonneg_K",
11161     "runtime_only": false
11162   },
11163   {
11164     "axioms": [
11165       "propext",
11166       "Classical.choice",
11167       "Quot.sound"
11168     ],
11169     "in_project_namespace": true,
11170     "kind": "theorem",
11171     "module": "PaperICompletion4.OperatorIntrinsicFormula",
11172     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_5",
11173     "runtime_only": false
11174   },
11175   {
11176     "axioms": [
11177       "propext",
11178       "Classical.choice",
11179       "Quot.sound"
11180     ],
11181     "in_project_namespace": true,
11182     "kind": "theorem",
11183     "module": "KomorebiVerification.TopologicalCompletion",
11184     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta.eq_1",
11185     "runtime_only": false
11186   },
11187   {
11188     "axioms": [
11189       "propext",
11190       "Classical.choice",
11191       "Quot.sound"
11192     ],
11193     "in_project_namespace": true,
11194     "kind": "theorem",
11195     "module": "PaperICompletion7.ModuleTop",
11196     "name": "Komorebi.PaperICompletion7.ModuleTop.lifts_generate",
11197     "runtime_only": false
11198   },
11199   {
11200     "axioms": [],
11201     "in_project_namespace": false,
11202     "kind": "definition",
11203     "module": "KomorebiVerification.EllipticAlgorithms",
11204     "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.splitter",
11205     "runtime_only": false
11206   },
11207   {
11208     "axioms": [],
11209     "in_project_namespace": true,
11210     "kind": "definition",
11211     "module": "KomorebiVerification.ProjectorCore",
11212     "name": "Komorebi.FiniteDifference.iteratedDiff",
11213     "runtime_only": false
11214   },
11215   {
11216     "axioms": [
11217       "propext",
11218       "Quot.sound"
11219     ],
11220     "in_project_namespace": true,
11221     "kind": "theorem",
11222     "module": "PaperIRelease.ScalarExtension",
11223     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorActionsCommute",
11224     "runtime_only": false
11225   },
11226   {
11227     "axioms": [
11228       "propext",
11229       "Classical.choice",
11230       "Quot.sound"
11231     ],
11232     "in_project_namespace": true,
11233     "kind": "theorem",
11234     "module": "PaperICompletion4.OperatorIntrinsicFormula",
11235     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity.eq_1",
11236     "runtime_only": false
11237   },
11238   {
11239     "axioms": [
11240       "propext",
11241       "Quot.sound"
11242     ],
11243     "in_project_namespace": true,
11244     "kind": "definition",
11245     "module": "KomorebiVerification.PacketNaturalityCompletion",
11246     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2082",
11247     "runtime_only": false
11248   },
11249   {
11250     "axioms": [
11251       "propext",
11252       "Classical.choice",
11253       "Quot.sound"
11254     ],
11255     "in_project_namespace": true,
11256     "kind": "constructor",
11257     "module": "KomorebiVerification.TopologicalCompletion",
11258     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk",
11259     "runtime_only": false
11260   },
11261   {
11262     "axioms": [
11263       "propext",
11264       "Classical.choice",
11265       "Quot.sound"
11266     ],
11267     "in_project_namespace": true,
11268     "kind": "definition",
11269     "module": "PaperIRelease.PacketDescent",
11270     "name": "Komorebi.Foundation.LinearProjectorFamily.descendedPacketEquivSumQuotient",
11271     "runtime_only": false
11272   },
11273   {
11274     "axioms": [
11275       "propext",
11276       "Classical.choice",
11277       "Quot.sound"
11278     ],
11279     "in_project_namespace": true,
11280     "kind": "theorem",
11281     "module": "PaperICompletion.CyclicClassification",
11282     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_5",
11283     "runtime_only": false
11284   },
11285   {
11286     "axioms": [
11287       "propext",
11288       "Quot.sound"
11289     ],
11290     "in_project_namespace": true,
11291     "kind": "theorem",
11292     "module": "PaperIRelease.GrammarEquivalence",
11293     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_2",
11294     "runtime_only": false
11295   },
11296   {
11297     "axioms": [
11298       "propext",
11299       "Classical.choice",
11300       "Quot.sound"
11301     ],
11302     "in_project_namespace": true,
11303     "kind": "theorem",
11304     "module": "PaperICompletion3.PrimarySeedFormula",
11305     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity_le_of_generates",
11306     "runtime_only": false
11307   },
11308   {
11309     "axioms": [
11310       "propext",
11311       "Quot.sound"
11312     ],
11313     "in_project_namespace": true,
11314     "kind": "theorem",
11315     "module": "PaperIRelease.AlgebraClassGrouping",
11316     "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_1",
11317     "runtime_only": false
11318   },
11319   {
11320     "axioms": [
11321       "propext",
11322       "Classical.choice",
11323       "Quot.sound"
11324     ],
11325     "in_project_namespace": true,
11326     "kind": "definition",
11327     "module": "PaperICompletion3.OperatorPrimaryAPI",
11328     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.equiv",
11329     "runtime_only": false
11330   },
11331   {
11332     "axioms": [
11333       "propext",
11334       "Classical.choice",
11335       "Quot.sound"
11336     ],
11337     "in_project_namespace": true,
11338     "kind": "theorem",
11339     "module": "PaperIRelease.SeedOperations",
11340     "name": "Komorebi.PaperIRelease.SeedOperations.regular_seedRank",
11341     "runtime_only": false
11342   },
11343   {
11344     "axioms": [
11345       "propext",
11346       "Quot.sound"
11347     ],
11348     "in_project_namespace": true,
11349     "kind": "definition",
11350     "module": "KomorebiVerification.PathGraphKrylov",
11351     "name": "Komorebi.PathGraphKrylov.krylov._sunfold",
11352     "runtime_only": false
11353   },
11354   {
11355     "axioms": [
11356       "propext",
11357       "Classical.choice",
11358       "Quot.sound"
11359     ],
11360     "in_project_namespace": true,
11361     "kind": "theorem",
11362     "module": "KomorebiVerification.PaperITransport",
11363     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_2",
11364     "runtime_only": false
11365   },
11366   {
11367     "axioms": [
11368       "propext",
11369       "Quot.sound"
11370     ],
11371     "in_project_namespace": true,
11372     "kind": "theorem",
11373     "module": "PaperIRelease.AlgebraPreorder",
11374     "name": "Komorebi.PaperIRelease.strictIdeal_power_mem._simp_1_1",
11375     "runtime_only": false
11376   },
11377   {
11378     "axioms": [
11379       "propext",
11380       "Classical.choice",
11381       "Quot.sound"
11382     ],
11383     "in_project_namespace": true,
11384     "kind": "definition",
11385     "module": "KomorebiVerification.PacketNaturalityCompletion",
11386     "name": "Komorebi.PacketNaturalityCompletion.Reachability.VectorSupported",
11387     "runtime_only": false
11388   },
11389   {
11390     "axioms": [
11391       "propext",
11392       "Classical.choice",
11393       "Quot.sound"
11394     ],
11395     "in_project_namespace": false,
11396     "kind": "theorem",
11397     "module": "KomorebiVerification.TopologicalCompletion",
11398     "name": "ContinuousLinearMap.codRestrict.congr_simp",
11399     "runtime_only": false
11400   },
11401   {
11402     "axioms": [
11403       "propext",
11404       "Classical.choice",
11405       "Quot.sound"
11406     ],
11407     "in_project_namespace": true,
11408     "kind": "definition",
11409     "module": "PaperIRelease.CategoryPackets",
11410     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ctorIdx",
11411     "runtime_only": false
11412   },
11413   {
11414     "axioms": [
11415       "propext",
11416       "Classical.choice",
11417       "Quot.sound"
11418     ],
11419     "in_project_namespace": true,
11420     "kind": "theorem",
11421     "module": "PaperIRelease.PolynomialMonic",
11422     "name": "Komorebi.PaperIRelease.PolynomialModule.monicSpectrumEquiv._proof_1",
11423     "runtime_only": false
11424   },
11425   {
11426     "axioms": [
11427       "propext",
11428       "Quot.sound"
11429     ],
11430     "in_project_namespace": false,
11431     "kind": "theorem",
11432     "module": "PaperIRelease.TopologySemilinearRank",
11433     "name": "PaperIRelease.TopologySemilinearRank.map_mem_span",
11434     "runtime_only": false
11435   },
11436   {
11437     "axioms": [
11438       "propext",
11439       "Classical.choice",
11440       "Quot.sound"
11441     ],
11442     "in_project_namespace": true,
11443     "kind": "theorem",
11444     "module": "PaperIRelease.GrammarEquivalence",
11445     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_1",
11446     "runtime_only": false
11447   },
11448   {
11449     "axioms": [
11450       "propext",
11451       "Classical.choice",
11452       "Quot.sound"
11453     ],
11454     "in_project_namespace": true,
11455     "kind": "theorem",
11456     "module": "PaperIRelease.PacketExactSequence",
11457     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion._proof_2",
11458     "runtime_only": false
11459   },
11460   {
11461     "axioms": [
11462       "propext",
11463       "Classical.choice",
11464       "Quot.sound"
11465     ],
11466     "in_project_namespace": true,
11467     "kind": "theorem",
11468     "module": "PaperIRelease.GrammarEquivalence",
11469     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_3",
11470     "runtime_only": false
11471   },
11472   {
11473     "axioms": [
11474       "propext",
11475       "Classical.choice",
11476       "Quot.sound"
11477     ],
11478     "in_project_namespace": true,
11479     "kind": "definition",
11480     "module": "PaperIRelease.GrammarAlgebra",
11481     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.noConfusion",
11482     "runtime_only": false
11483   },
11484   {
11485     "axioms": [
11486       "propext",
11487       "Quot.sound"
11488     ],
11489     "in_project_namespace": true,
11490     "kind": "theorem",
11491     "module": "PaperIRelease.GraphSources",
11492     "name": "Komorebi.PaperIRelease.FiniteDigraph.component_le_iff._simp_1",
11493     "runtime_only": false
11494   },
11495   {
11496     "axioms": [
11497       "propext",
11498       "Classical.choice",
11499       "Quot.sound"
11500     ],
11501     "in_project_namespace": true,
11502     "kind": "theorem",
11503     "module": "PaperIRelease.AlgebraSupport",
11504     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_2",
11505     "runtime_only": false
11506   },
11507   {
11508     "axioms": [
11509       "propext",
11510       "Classical.choice",
11511       "Quot.sound"
11512     ],
11513     "in_project_namespace": true,
11514     "kind": "theorem",
11515     "module": "PaperICompletion4.OperatorIntrinsicFormula",
11516     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_5",
11517     "runtime_only": false
11518   },
11519   {
11520     "axioms": [
11521       "propext",
11522       "Quot.sound"
11523     ],
11524     "in_project_namespace": true,
11525     "kind": "theorem",
11526     "module": "PaperICompletion.CyclicClassification",
11527     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_2",
11528     "runtime_only": false
11529   },
11530   {
11531     "axioms": [
11532       "propext",
11533       "Classical.choice",
11534       "Quot.sound"
11535     ],
11536     "in_project_namespace": true,
11537     "kind": "definition",
11538     "module": "PaperIRelease.TopologyCategories",
11539     "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory",
11540     "runtime_only": false
11541   },
11542   {
11543     "axioms": [
11544       "propext",
11545       "Classical.choice",
11546       "Quot.sound"
11547     ],
11548     "in_project_namespace": true,
11549     "kind": "theorem",
11550     "module": "KomorebiVerification.PacketNaturalityCompletion",
11551     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR._proof_1",
11552     "runtime_only": false
11553   },
11554   {
11555     "axioms": [
11556       "propext",
11557       "Classical.choice",
11558       "Quot.sound"
11559     ],
11560     "in_project_namespace": true,
11561     "kind": "theorem",
11562     "module": "PaperIRelease.PacketAggregation",
11563     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_2",
11564     "runtime_only": false
11565   },
11566   {
11567     "axioms": [],
11568     "in_project_namespace": true,
11569     "kind": "inductive",
11570     "module": "KomorebiVerification.ProjectorCore",
11571     "name": "Komorebi.ClaimRecord",
11572     "runtime_only": false
11573   },
11574   {
11575     "axioms": [],
11576     "in_project_namespace": true,
11577     "kind": "constructor",
11578     "module": "KomorebiVerification.ProjectorCore",
11579     "name": "Komorebi.ClaimKind.corollaryClaim",
11580     "runtime_only": false
11581   },
11582   {
11583     "axioms": [
11584       "propext",
11585       "Classical.choice",
11586       "Quot.sound"
11587     ],
11588     "in_project_namespace": true,
11589     "kind": "theorem",
11590     "module": "PaperICompletion5.LinearPrimaryEigenspace",
11591     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel_mk",
11592     "runtime_only": false
11593   },
11594   {
11595     "axioms": [
11596       "propext",
11597       "Classical.choice",
11598       "Quot.sound"
11599     ],
11600     "in_project_namespace": false,
11601     "kind": "definition",
11602     "module": "PaperIRelease.TopologyUnconditional",
11603     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences",
11604     "runtime_only": false
11605   },
11606   {
11607     "axioms": [],
11608     "in_project_namespace": true,
11609     "kind": "definition",
11610     "module": "KomorebiVerification.ProjectorCore",
11611     "name": "Komorebi.FormalizationStatus.queued.elim",
11612     "runtime_only": false
11613   },
11614   {
11615     "axioms": [
11616       "propext",
11617       "Classical.choice",
11618       "Quot.sound"
11619     ],
11620     "in_project_namespace": false,
11621     "kind": "theorem",
11622     "module": "PaperIRelease.TopologyDenseCompletion",
11623     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_5",
11624     "runtime_only": false
11625   },
11626   {
11627     "axioms": [
11628       "propext",
11629       "Quot.sound"
11630     ],
11631     "in_project_namespace": false,
11632     "kind": "theorem",
11633     "module": "PaperIRelease.TopologyPresentations",
11634     "name": "PaperIRelease.TopologyDenseCompletion.completedRestrictedQuotient._proof_1",
11635     "runtime_only": false
11636   },
11637   {
11638     "axioms": [
11639       "propext",
11640       "Quot.sound"
11641     ],
11642     "in_project_namespace": true,
11643     "kind": "definition",
11644     "module": "KomorebiVerification.SeedRankOperations",
11645     "name": "Komorebi.SeedRankOperations.tensorOperatorModule",
11646     "runtime_only": false
11647   },
11648   {
11649     "axioms": [
11650       "propext",
11651       "Classical.choice",
11652       "Quot.sound"
11653     ],
11654     "in_project_namespace": true,
11655     "kind": "theorem",
11656     "module": "PaperIRelease.PacketTopology",
11657     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM_toLinearMap",
11658     "runtime_only": false
11659   },
11660   {
11661     "axioms": [
11662       "propext",
11663       "Classical.choice",
11664       "Quot.sound"
11665     ],
11666     "in_project_namespace": true,
11667     "kind": "definition",
11668     "module": "KomorebiVerification.PacketNaturalityCompletion",
11669     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.noConfusionType",
11670     "runtime_only": false
11671   },
11672   {
11673     "axioms": [],
11674     "in_project_namespace": true,
11675     "kind": "constructor",
11676     "module": "KomorebiVerification.ProjectorCore",
11677     "name": "Komorebi.FormalizationStatus.encodedDefinition",
11678     "runtime_only": false
11679   },
11680   {
11681     "axioms": [
11682       "propext",
11683       "Classical.choice",
11684       "Quot.sound"
11685     ],
11686     "in_project_namespace": true,
11687     "kind": "theorem",
11688     "module": "KomorebiVerification.PacketNaturalityCompletion",
11689     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_5",
11690     "runtime_only": false
11691   },
11692   {
11693     "axioms": [
11694       "propext",
11695       "Classical.choice",
11696       "Quot.sound"
11697     ],
11698     "in_project_namespace": true,
11699     "kind": "theorem",
11700     "module": "PaperIRelease.AlgebraQuotient",
11701     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_5",
11702     "runtime_only": false
11703   },
11704   {
11705     "axioms": [
11706       "propext",
11707       "Classical.choice",
11708       "Quot.sound"
11709     ],
11710     "in_project_namespace": true,
11711     "kind": "theorem",
11712     "module": "PaperIRelease.GrammarPaths",
11713     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_def",
11714     "runtime_only": false
11715   },
11716   {
11717     "axioms": [],
11718     "in_project_namespace": true,
11719     "kind": "theorem",
11720     "module": "KomorebiVerification.ProjectorCore",
11721     "name": "Komorebi.Seed.OperatorRelation.satisfied_postcomp",
11722     "runtime_only": false
11723   },
11724   {
11725     "axioms": [
11726       "propext",
11727       "Classical.choice",
11728       "Quot.sound"
11729     ],
11730     "in_project_namespace": true,
11731     "kind": "theorem",
11732     "module": "KomorebiVerification.EllipticAlgorithms",
11733     "name": "Komorebi.EllipticCoordinates.Mx._proof_2",
11734     "runtime_only": false
11735   },
11736   {
11737     "axioms": [
11738       "propext",
11739       "Classical.choice",
11740       "Quot.sound"
11741     ],
11742     "in_project_namespace": true,
11743     "kind": "theorem",
11744     "module": "KomorebiVerification.PaperITransport",
11745     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_4",
11746     "runtime_only": false
11747   },
11748   {
11749     "axioms": [
11750       "propext",
11751       "Classical.choice",
11752       "Quot.sound"
11753     ],
11754     "in_project_namespace": true,
11755     "kind": "theorem",
11756     "module": "PaperIRelease.AlgebraPreorder",
11757     "name": "Komorebi.PaperIRelease.maximalStrictSteps_attained",
11758     "runtime_only": false
11759   },
11760   {
11761     "axioms": [
11762       "propext",
11763       "Classical.choice",
11764       "Quot.sound"
11765     ],
11766     "in_project_namespace": true,
11767     "kind": "theorem",
11768     "module": "KomorebiVerification.SingleOperatorGraph",
11769     "name": "Komorebi.SingleOperatorGraph.cyclic_matrix_criterion_of_primary_decomposition",
11770     "runtime_only": false
11771   },
11772   {
11773     "axioms": [
11774       "propext",
11775       "Classical.choice",
11776       "Quot.sound"
11777     ],
11778     "in_project_namespace": true,
11779     "kind": "theorem",
11780     "module": "KomorebiVerification.TopologicalCompletion",
11781     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.sizeOf_spec",
11782     "runtime_only": false
11783   },
11784   {
11785     "axioms": [
11786       "propext",
11787       "Classical.choice",
11788       "Quot.sound"
11789     ],
11790     "in_project_namespace": true,
11791     "kind": "definition",
11792     "module": "PaperIRelease.TopologyCategories",
11793     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.topology",
11794     "runtime_only": false
11795   },
11796   {
11797     "axioms": [
11798       "propext",
11799       "Classical.choice",
11800       "Quot.sound"
11801     ],
11802     "in_project_namespace": true,
11803     "kind": "theorem",
11804     "module": "KomorebiVerification.EllipticAlgorithms",
11805     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_3",
11806     "runtime_only": false
11807   },
11808   {
11809     "axioms": [
11810       "propext",
11811       "Classical.choice",
11812       "Quot.sound"
11813     ],
11814     "in_project_namespace": true,
11815     "kind": "theorem",
11816     "module": "KomorebiVerification.EllipticAlgorithms",
11817     "name": "Komorebi.EllipticCoordinates.Mx_pow_My_pow_unitSeed",
11818     "runtime_only": false
11819   },
11820   {
11821     "axioms": [
11822       "propext",
11823       "Classical.choice",
11824       "Quot.sound"
11825     ],
11826     "in_project_namespace": true,
11827     "kind": "theorem",
11828     "module": "PaperIRelease.GeneralNormedPackets",
11829     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis.eq_1",
11830     "runtime_only": false
11831   },
11832   {
11833     "axioms": [],
11834     "in_project_namespace": true,
11835     "kind": "definition",
11836     "module": "KomorebiVerification.ProjectorCore",
11837     "name": "Komorebi.Seed.OperatorExpr.id.elim",
11838     "runtime_only": false
11839   },
11840   {
11841     "axioms": [],
11842     "in_project_namespace": true,
11843     "kind": "theorem",
11844     "module": "KomorebiVerification.SeedRankBasics",
11845     "name": "Komorebi.SeedRankBasics.oneSeedMap_apply",
11846     "runtime_only": false
11847   },
11848   {
11849     "axioms": [
11850       "propext",
11851       "Classical.choice",
11852       "Quot.sound"
11853     ],
11854     "in_project_namespace": true,
11855     "kind": "definition",
11856     "module": "PaperIRelease.AlgebraTransfer",
11857     "name": "Komorebi.PaperIRelease.activeTargets",
11858     "runtime_only": false
11859   },
11860   {
11861     "axioms": [
11862       "propext",
11863       "Classical.choice",
11864       "Quot.sound"
11865     ],
11866     "in_project_namespace": true,
11867     "kind": "definition",
11868     "module": "PaperICompletion5.GeometricSeedFormula",
11869     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralSeedMaximum",
11870     "runtime_only": false
11871   },
11872   {
11873     "axioms": [
11874       "propext",
11875       "Classical.choice",
11876       "Quot.sound"
11877     ],
11878     "in_project_namespace": true,
11879     "kind": "theorem",
11880     "module": "KomorebiVerification.TopologicalCompletion",
11881     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.inj",
11882     "runtime_only": false
11883   },
11884   {
11885     "axioms": [],
11886     "in_project_namespace": true,
11887     "kind": "definition",
11888     "module": "KomorebiVerification.ProjectorCore",
11889     "name": "Komorebi.Seed.OperatorExpr._sizeOf_inst",
11890     "runtime_only": false
11891   },
11892   {
11893     "axioms": [
11894       "propext",
11895       "Classical.choice",
11896       "Quot.sound"
11897     ],
11898     "in_project_namespace": true,
11899     "kind": "theorem",
11900     "module": "PaperIRelease.GeneralFiniteCompletion",
11901     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_6",
11902     "runtime_only": false
11903   },
11904   {
11905     "axioms": [
11906       "propext",
11907       "Classical.choice",
11908       "Quot.sound"
11909     ],
11910     "in_project_namespace": true,
11911     "kind": "theorem",
11912     "module": "PaperIRelease.PacketCorners",
11913     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_7",
11914     "runtime_only": false
11915   },
11916   {
11917     "axioms": [
11918       "propext",
11919       "Classical.choice",
11920       "Quot.sound"
11921     ],
11922     "in_project_namespace": true,
11923     "kind": "theorem",
11924     "module": "PaperIRelease.PacketBoundaryTests",
11925     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.quotient_by_whole_is_zero",
11926     "runtime_only": false
11927   },
11928   {
11929     "axioms": [
11930       "propext",
11931       "Quot.sound"
11932     ],
11933     "in_project_namespace": true,
11934     "kind": "theorem",
11935     "module": "PaperICompletion.CyclicClassification",
11936     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_3",
11937     "runtime_only": false
11938   },
11939   {
11940     "axioms": [
11941       "propext",
11942       "Classical.choice",
11943       "Quot.sound"
11944     ],
11945     "in_project_namespace": true,
11946     "kind": "definition",
11947     "module": "PaperIRelease.PacketPureRank",
11948     "name": "Komorebi.PaperIRelease.packetPureSeedRank",
11949     "runtime_only": false
11950   },
11951   {
11952     "axioms": [
11953       "propext",
11954       "Quot.sound"
11955     ],
11956     "in_project_namespace": true,
11957     "kind": "theorem",
11958     "module": "KomorebiVerification.PaperITransport",
11959     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_1",
11960     "runtime_only": false
11961   },
11962   {
11963     "axioms": [
11964       "propext",
11965       "Classical.choice",
11966       "Quot.sound"
11967     ],
11968     "in_project_namespace": true,
11969     "kind": "theorem",
11970     "module": "PaperIRelease.AlgebraTransfer",
11971     "name": "Komorebi.PaperIRelease.packetSupport_image_eq_of_single_active",
11972     "runtime_only": false
11973   },
11974   {
11975     "axioms": [
11976       "propext",
11977       "Classical.choice",
11978       "Quot.sound"
11979     ],
11980     "in_project_namespace": true,
11981     "kind": "definition",
11982     "module": "PaperIRelease.GraphReachability",
11983     "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra",
11984     "runtime_only": false
11985   },
11986   {
11987     "axioms": [
11988       "propext",
11989       "Quot.sound"
11990     ],
11991     "in_project_namespace": true,
11992     "kind": "theorem",
11993     "module": "KomorebiVerification.SingleOperatorGraph",
11994     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency.eq_1",
11995     "runtime_only": false
11996   },
11997   {
11998     "axioms": [
11999       "propext",
12000       "Classical.choice",
12001       "Quot.sound"
12002     ],
12003     "in_project_namespace": true,
12004     "kind": "theorem",
12005     "module": "PaperIRelease.GraphSourceCount",
12006     "name": "Komorebi.PaperIRelease.source_count_le_packetPureSeedRank",
12007     "runtime_only": false
12008   },
12009   {
12010     "axioms": [
12011       "propext",
12012       "Classical.choice",
12013       "Quot.sound"
12014     ],
12015     "in_project_namespace": true,
12016     "kind": "theorem",
12017     "module": "PaperIRelease.CategoryBoundaries",
12018     "name": "Komorebi.PaperIRelease.CategoryBoundaries.merge_is_not_injective",
12019     "runtime_only": false
12020   },
12021   {
12022     "axioms": [],
12023     "in_project_namespace": true,
12024     "kind": "definition",
12025     "module": "KomorebiVerification.PacketNaturalityCompletion",
12026     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply.match_1",
12027     "runtime_only": false
12028   },
12029   {
12030     "axioms": [
12031       "propext",
12032       "Classical.choice",
12033       "Quot.sound"
12034     ],
12035     "in_project_namespace": true,
12036     "kind": "theorem",
12037     "module": "PaperIRelease.GrammarAlgebra",
12038     "name": "Komorebi.PaperIRelease.GrammarAlgebra.action_ofAction",
12039     "runtime_only": false
12040   },
12041   {
12042     "axioms": [
12043       "propext",
12044       "Classical.choice",
12045       "Quot.sound"
12046     ],
12047     "in_project_namespace": true,
12048     "kind": "theorem",
12049     "module": "PaperIRelease.GeneralConditionedCoordinates",
12050     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.one_le_packet_conditionNumber",
12051     "runtime_only": false
12052   },
12053   {
12054     "axioms": [
12055       "propext",
12056       "Quot.sound"
12057     ],
12058     "in_project_namespace": true,
12059     "kind": "definition",
12060     "module": "PaperIRelease.GrammarAlgebra",
12061     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.target",
12062     "runtime_only": false
12063   },
12064   {
12065     "axioms": [
12066       "propext",
12067       "Classical.choice",
12068       "Quot.sound"
12069     ],
12070     "in_project_namespace": false,
12071     "kind": "definition",
12072     "module": "PaperIRelease.TopologyUnconditionalBridge",
12073     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv",
12074     "runtime_only": false
12075   },
12076   {
12077     "axioms": [
12078       "propext",
12079       "Classical.choice",
12080       "Quot.sound"
12081     ],
12082     "in_project_namespace": false,
12083     "kind": "theorem",
12084     "module": "PaperIRelease.TopologyCountablePackets",
12085     "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_2",
12086     "runtime_only": false
12087   },
12088   {
12089     "axioms": [
12090       "propext",
12091       "Classical.choice",
12092       "Quot.sound"
12093     ],
12094     "in_project_namespace": true,
12095     "kind": "theorem",
12096     "module": "KomorebiVerification.EllipticAlgorithms",
12097     "name": "Komorebi.EllipticCoordinates.My_eq_multiplication",
12098     "runtime_only": false
12099   },
12100   {
12101     "axioms": [
12102       "propext",
12103       "Classical.choice",
12104       "Quot.sound"
12105     ],
12106     "in_project_namespace": true,
12107     "kind": "theorem",
12108     "module": "KomorebiVerification.EllipticAlgorithms",
12109     "name": "Komorebi.EllipticCoordinates.normalFormToQuotient.eq_1",
12110     "runtime_only": false
12111   },
12112   {
12113     "axioms": [
12114       "propext",
12115       "Classical.choice",
12116       "Quot.sound"
12117     ],
12118     "in_project_namespace": true,
12119     "kind": "theorem",
12120     "module": "KomorebiVerification.SemisimpleSeedRank",
12121     "name": "Komorebi.SemisimpleSeedRank.multiplicity_le_of_leftGenerates",
12122     "runtime_only": false
12123   },
12124   {
12125     "axioms": [
12126       "propext",
12127       "Classical.choice",
12128       "Quot.sound"
12129     ],
12130     "in_project_namespace": true,
12131     "kind": "definition",
12132     "module": "KomorebiVerification.TopologicalCompletion",
12133     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.noConfusionType",
12134     "runtime_only": false
12135   },
12136   {
12137     "axioms": [
12138       "propext",
12139       "Classical.choice",
12140       "Quot.sound"
12141     ],
12142     "in_project_namespace": true,
12143     "kind": "theorem",
12144     "module": "KomorebiVerification.SemisimpleCompletion",
12145     "name": "Komorebi.SemisimpleCompletion.oneBlock_seedRank_eq_ceilDiv",
12146     "runtime_only": false
12147   },
12148   {
12149     "axioms": [
12150       "propext",
12151       "Classical.choice",
12152       "Quot.sound"
12153     ],
12154     "in_project_namespace": true,
12155     "kind": "theorem",
12156     "module": "KomorebiVerification.PacketNaturalityCompletion",
12157     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_2",
12158     "runtime_only": false
12159   },
12160   {
12161     "axioms": [
12162       "propext",
12163       "Classical.choice",
12164       "Quot.sound"
12165     ],
12166     "in_project_namespace": true,
12167     "kind": "theorem",
12168     "module": "KomorebiVerification.PacketNaturalityCompletion",
12169     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.generatedHull_natural",
12170     "runtime_only": false
12171   },
12172   {
12173     "axioms": [
12174       "propext",
12175       "Classical.choice",
12176       "Quot.sound"
12177     ],
12178     "in_project_namespace": true,
12179     "kind": "theorem",
12180     "module": "PaperIRelease.CategoryBoundaries",
12181     "name": "Komorebi.Packet.fibreLinearProjectorFamily.eq_1",
12182     "runtime_only": false
12183   },
12184   {
12185     "axioms": [
12186       "propext",
12187       "Classical.choice",
12188       "Quot.sound"
12189     ],
12190     "in_project_namespace": true,
12191     "kind": "theorem",
12192     "module": "PaperIRelease.CategoryPackets",
12193     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_3",
12194     "runtime_only": false
12195   },
12196   {
12197     "axioms": [
12198       "propext",
12199       "Classical.choice",
12200       "Quot.sound"
12201     ],
12202     "in_project_namespace": true,
12203     "kind": "definition",
12204     "module": "PaperIRelease.AlgebraClassGrouping",
12205     "name": "Komorebi.PaperIRelease.classPacketFamily",
12206     "runtime_only": false
12207   },
12208   {
12209     "axioms": [
12210       "propext",
12211       "Classical.choice",
12212       "Quot.sound"
12213     ],
12214     "in_project_namespace": true,
12215     "kind": "theorem",
12216     "module": "PaperIRelease.GrammarTyped",
12217     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_right",
12218     "runtime_only": false
12219   },
12220   {
12221     "axioms": [],
12222     "in_project_namespace": true,
12223     "kind": "definition",
12224     "module": "KomorebiVerification.ProjectorCore",
12225     "name": "Komorebi.Seed.OperatorExpr.eval._f",
12226     "runtime_only": false
12227   },
12228   {
12229     "axioms": [
12230       "propext",
12231       "Classical.choice",
12232       "Quot.sound"
12233     ],
12234     "in_project_namespace": false,
12235     "kind": "theorem",
12236     "module": "PaperIRelease.TopologyCountablePackets",
12237     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedSpace._proof_1",
12238     "runtime_only": false
12239   },
12240   {
12241     "axioms": [
12242       "propext",
12243       "Classical.choice",
12244       "Quot.sound"
12245     ],
12246     "in_project_namespace": true,
12247     "kind": "theorem",
12248     "module": "PaperICompletion5.CyclicGeometricCriterion",
12249     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_pos",
12250     "runtime_only": false
12251   },
12252   {
12253     "axioms": [
12254       "propext",
12255       "Classical.choice",
12256       "Quot.sound"
12257     ],
12258     "in_project_namespace": true,
12259     "kind": "definition",
12260     "module": "KomorebiVerification.PacketNaturalityCompletion",
12261     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.MappedOrbitSet",
12262     "runtime_only": false
12263   },
12264   {
12265     "axioms": [
12266       "propext",
12267       "Classical.choice",
12268       "Quot.sound"
12269     ],
12270     "in_project_namespace": true,
12271     "kind": "theorem",
12272     "module": "PaperICompletion.SpectralCertificates",
12273     "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis_is_eigenbasis",
12274     "runtime_only": false
12275   },
12276   {
12277     "axioms": [],
12278     "in_project_namespace": true,
12279     "kind": "definition",
12280     "module": "KomorebiVerification.ProjectorCore",
12281     "name": "Komorebi.Seed.OperatorExpr.atom.noConfusion",
12282     "runtime_only": false
12283   },
12284   {
12285     "axioms": [],
12286     "in_project_namespace": true,
12287     "kind": "definition",
12288     "module": "KomorebiVerification.ProjectorCore",
12289     "name": "Komorebi.ClaimKind.ctorElim",
12290     "runtime_only": false
12291   },
12292   {
12293     "axioms": [
12294       "propext",
12295       "Classical.choice",
12296       "Quot.sound"
12297     ],
12298     "in_project_namespace": true,
12299     "kind": "inductive",
12300     "module": "PaperIRelease.GrammarEquivalence",
12301     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom",
12302     "runtime_only": false
12303   },
12304   {
12305     "axioms": [
12306       "propext",
12307       "Classical.choice",
12308       "Quot.sound"
12309     ],
12310     "in_project_namespace": true,
12311     "kind": "theorem",
12312     "module": "PaperIRelease.CategoryPackets",
12313     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.injEq",
12314     "runtime_only": false
12315   },
12316   {
12317     "axioms": [
12318       "propext",
12319       "Classical.choice",
12320       "Quot.sound"
12321     ],
12322     "in_project_namespace": false,
12323     "kind": "theorem",
12324     "module": "PaperIRelease.TopologyUnconditional",
12325     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.closed",
12326     "runtime_only": false
12327   },
12328   {
12329     "axioms": [
12330       "propext",
12331       "Classical.choice",
12332       "Quot.sound"
12333     ],
12334     "in_project_namespace": false,
12335     "kind": "theorem",
12336     "module": "PaperIRelease.TopologyCountablePackets",
12337     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_20",
12338     "runtime_only": false
12339   },
12340   {
12341     "axioms": [
12342       "propext",
12343       "Classical.choice",
12344       "Quot.sound"
12345     ],
12346     "in_project_namespace": false,
12347     "kind": "theorem",
12348     "module": "PaperIRelease.TopologyUnconditionalBridge",
12349     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_7",
12350     "runtime_only": false
12351   },
12352   {
12353     "axioms": [
12354       "propext",
12355       "Classical.choice",
12356       "Quot.sound"
12357     ],
12358     "in_project_namespace": true,
12359     "kind": "theorem",
12360     "module": "KomorebiVerification.SingleOperatorGraph",
12361     "name": "Komorebi.SingleOperatorGraph.cycleSeeds.eq_1",
12362     "runtime_only": false
12363   },
12364   {
12365     "axioms": [],
12366     "in_project_namespace": true,
12367     "kind": "theorem",
12368     "module": "KomorebiVerification.ProjectorCore",
12369     "name": "Komorebi.ClaimKind.remarkClaim.sizeOf_spec",
12370     "runtime_only": false
12371   },
12372   {
12373     "axioms": [
12374       "propext",
12375       "Classical.choice",
12376       "Quot.sound"
12377     ],
12378     "in_project_namespace": true,
12379     "kind": "theorem",
12380     "module": "KomorebiVerification.SeedRankBasics",
12381     "name": "Komorebi.SeedRankBasics.range_oneSeedMap",
12382     "runtime_only": false
12383   },
12384   {
12385     "axioms": [
12386       "propext",
12387       "Classical.choice",
12388       "Quot.sound"
12389     ],
12390     "in_project_namespace": true,
12391     "kind": "theorem",
12392     "module": "KomorebiVerification.PacketNaturalityCompletion",
12393     "name": "Komorebi.PacketNaturalityCompletion.Packets.transferBlock_pow_zero",
12394     "runtime_only": false
12395   },
12396   {
12397     "axioms": [
12398       "propext",
12399       "Classical.choice",
12400       "Quot.sound"
12401     ],
12402     "in_project_namespace": true,
12403     "kind": "theorem",
12404     "module": "PaperIRelease.AlgebraTransfer",
12405     "name": "Komorebi.PaperIRelease.packetWordSum.eq_2",
12406     "runtime_only": false
12407   },
12408   {
12409     "axioms": [
12410       "propext",
12411       "Classical.choice",
12412       "Quot.sound"
12413     ],
12414     "in_project_namespace": true,
12415     "kind": "definition",
12416     "module": "PaperIRelease.AlgebraTransfer",
12417     "name": "Komorebi.PaperIRelease.packetSupport",
12418     "runtime_only": false
12419   },
12420   {
12421     "axioms": [],
12422     "in_project_namespace": true,
12423     "kind": "definition",
12424     "module": "KomorebiVerification.ProjectorCore",
12425     "name": "Komorebi.Seed.OperatorExpr.eval",
12426     "runtime_only": false
12427   },
12428   {
12429     "axioms": [
12430       "propext",
12431       "Classical.choice",
12432       "Quot.sound"
12433     ],
12434     "in_project_namespace": true,
12435     "kind": "definition",
12436     "module": "PaperICompletion6.OneInvariantFactor",
12437     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientCompanionBasis",
12438     "runtime_only": false
12439   },
12440   {
12441     "axioms": [
12442       "propext",
12443       "Classical.choice",
12444       "Quot.sound"
12445     ],
12446     "in_project_namespace": false,
12447     "kind": "definition",
12448     "module": "PaperIRelease.TopologyCountablePackets",
12449     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues",
12450     "runtime_only": false
12451   },
12452   {
12453     "axioms": [],
12454     "in_project_namespace": true,
12455     "kind": "constructor",
12456     "module": "KomorebiVerification.ProjectorCore",
12457     "name": "Komorebi.ClaimKind.classicalInput",
12458     "runtime_only": false
12459   },
12460   {
12461     "axioms": [
12462       "propext",
12463       "Classical.choice",
12464       "Quot.sound"
12465     ],
12466     "in_project_namespace": true,
12467     "kind": "theorem",
12468     "module": "PaperIRelease.PacketLocalRank",
12469     "name": "Komorebi.PaperIRelease.packetPure_discardZeros_iff",
12470     "runtime_only": false
12471   },
12472   {
12473     "axioms": [
12474       "propext",
12475       "Classical.choice",
12476       "Quot.sound"
12477     ],
12478     "in_project_namespace": true,
12479     "kind": "theorem",
12480     "module": "PaperICompletion8.ProductPresentation",
12481     "name": "Komorebi.PaperICompletion8.ProductPresentation.simple_equiv_natural",
12482     "runtime_only": false
12483   },
12484   {
12485     "axioms": [],
12486     "in_project_namespace": true,
12487     "kind": "definition",
12488     "module": "KomorebiVerification.ProjectorCore",
12489     "name": "Komorebi.instInhabitedClaimRecord.default",
12490     "runtime_only": false
12491   },
12492   {
12493     "axioms": [
12494       "propext",
12495       "Classical.choice",
12496       "Quot.sound"
12497     ],
12498     "in_project_namespace": true,
12499     "kind": "theorem",
12500     "module": "PaperIRelease.CategoryPackets",
12501     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_1",
12502     "runtime_only": false
12503   },
12504   {
12505     "axioms": [
12506       "propext",
12507       "Classical.choice",
12508       "Quot.sound"
12509     ],
12510     "in_project_namespace": true,
12511     "kind": "definition",
12512     "module": "PaperICompletion8.RegularMultiplicity",
12513     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv",
12514     "runtime_only": false
12515   },
12516   {
12517     "axioms": [
12518       "propext",
12519       "Classical.choice",
12520       "Quot.sound"
12521     ],
12522     "in_project_namespace": true,
12523     "kind": "theorem",
12524     "module": "KomorebiVerification.TopologicalCompletion",
12525     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.inj",
12526     "runtime_only": false
12527   },
12528   {
12529     "axioms": [
12530       "propext",
12531       "Classical.choice",
12532       "Quot.sound"
12533     ],
12534     "in_project_namespace": true,
12535     "kind": "theorem",
12536     "module": "KomorebiVerification.PacketNaturalityCompletion",
12537     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv._proof_2",
12538     "runtime_only": false
12539   },
12540   {
12541     "axioms": [
12542       "propext",
12543       "Classical.choice",
12544       "Quot.sound"
12545     ],
12546     "in_project_namespace": true,
12547     "kind": "theorem",
12548     "module": "PaperICompletion.ConditionedCoordinates",
12549     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber._proof_1",
12550     "runtime_only": false
12551   },
12552   {
12553     "axioms": [
12554       "propext",
12555       "Classical.choice",
12556       "Quot.sound"
12557     ],
12558     "in_project_namespace": true,
12559     "kind": "definition",
12560     "module": "PaperIRelease.CategoryPackets",
12561     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.comp",
12562     "runtime_only": false
12563   },
12564   {
12565     "axioms": [
12566       "propext"
12567     ],
12568     "in_project_namespace": true,
12569     "kind": "theorem",
12570     "module": "KomorebiVerification.SingleOperatorGraph",
12571     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_3",
12572     "runtime_only": false
12573   },
12574   {
12575     "axioms": [
12576       "propext",
12577       "Classical.choice",
12578       "Quot.sound"
12579     ],
12580     "in_project_namespace": true,
12581     "kind": "constructor",
12582     "module": "PaperIRelease.GrammarAlgebra",
12583     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.declared",
12584     "runtime_only": false
12585   },
12586   {
12587     "axioms": [
12588       "propext",
12589       "Classical.choice",
12590       "Quot.sound"
12591     ],
12592     "in_project_namespace": true,
12593     "kind": "theorem",
12594     "module": "PaperIRelease.CategoryPackets",
12595     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.inj",
12596     "runtime_only": false
12597   },
12598   {
12599     "axioms": [
12600       "propext",
12601       "Quot.sound"
12602     ],
12603     "in_project_namespace": true,
12604     "kind": "theorem",
12605     "module": "PaperIRelease.GrammarModules",
12606     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.sizeOf_spec",
12607     "runtime_only": false
12608   },
12609   {
12610     "axioms": [
12611       "propext",
12612       "Classical.choice",
12613       "Quot.sound"
12614     ],
12615     "in_project_namespace": true,
12616     "kind": "theorem",
12617     "module": "KomorebiVerification.TopologicalCompletion",
12618     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.topological_packet_isomorphism",
12619     "runtime_only": false
12620   },
12621   {
12622     "axioms": [
12623       "propext",
12624       "Classical.choice",
12625       "Quot.sound"
12626     ],
12627     "in_project_namespace": true,
12628     "kind": "theorem",
12629     "module": "PaperIRelease.GrammarEquivalence",
12630     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_11",
12631     "runtime_only": false
12632   },
12633   {
12634     "axioms": [],
12635     "in_project_namespace": true,
12636     "kind": "inductive",
12637     "module": "KomorebiVerification.ProjectorCore",
12638     "name": "Komorebi.FormalizationStatus",
12639     "runtime_only": false
12640   },
12641   {
12642     "axioms": [
12643       "propext",
12644       "Classical.choice",
12645       "Quot.sound"
12646     ],
12647     "in_project_namespace": true,
12648     "kind": "theorem",
12649     "module": "KomorebiVerification.SeedRankBasics",
12650     "name": "Komorebi.SeedRankBasics.seedRank_eq_seedFinrank",
12651     "runtime_only": false
12652   },
12653   {
12654     "axioms": [
12655       "propext",
12656       "Classical.choice",
12657       "Quot.sound"
12658     ],
12659     "in_project_namespace": true,
12660     "kind": "theorem",
12661     "module": "KomorebiVerification.EllipticAlgorithms",
12662     "name": "Komorebi.FiniteAlgorithms.transferBlock_algorithm_correct",
12663     "runtime_only": false
12664   },
12665   {
12666     "axioms": [
12667       "propext",
12668       "Classical.choice",
12669       "Quot.sound"
12670     ],
12671     "in_project_namespace": false,
12672     "kind": "theorem",
12673     "module": "PaperIRelease.TopologyUnconditional",
12674     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_21",
12675     "runtime_only": false
12676   },
12677   {
12678     "axioms": [
12679       "propext",
12680       "Classical.choice",
12681       "Quot.sound"
12682     ],
12683     "in_project_namespace": true,
12684     "kind": "definition",
12685     "module": "PaperIRelease.GrammarTyped",
12686     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.noConfusion",
12687     "runtime_only": false
12688   },
12689   {
12690     "axioms": [
12691       "propext",
12692       "Quot.sound"
12693     ],
12694     "in_project_namespace": true,
12695     "kind": "definition",
12696     "module": "PaperIRelease.ScalarExtension",
12697     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModuleInstance",
12698     "runtime_only": false
12699   },
12700   {
12701     "axioms": [
12702       "propext",
12703       "Classical.choice",
12704       "Quot.sound"
12705     ],
12706     "in_project_namespace": true,
12707     "kind": "theorem",
12708     "module": "PaperIRelease.AlgebraClassGrouping",
12709     "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_1",
12710     "runtime_only": false
12711   },
12712   {
12713     "axioms": [
12714       "propext",
12715       "Quot.sound"
12716     ],
12717     "in_project_namespace": true,
12718     "kind": "theorem",
12719     "module": "PaperIRelease.GrammarModules",
12720     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_4",
12721     "runtime_only": false
12722   },
12723   {
12724     "axioms": [
12725       "propext",
12726       "Classical.choice",
12727       "Quot.sound"
12728     ],
12729     "in_project_namespace": true,
12730     "kind": "definition",
12731     "module": "PaperIRelease.TensorPackets",
12732     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv",
12733     "runtime_only": false
12734   },
12735   {
12736     "axioms": [
12737       "propext",
12738       "Quot.sound"
12739     ],
12740     "in_project_namespace": true,
12741     "kind": "theorem",
12742     "module": "KomorebiVerification.PacketNaturalityCompletion",
12743     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2081.eq_1",
12744     "runtime_only": false
12745   },
12746   {
12747     "axioms": [
12748       "propext",
12749       "Classical.choice",
12750       "Quot.sound"
12751     ],
12752     "in_project_namespace": true,
12753     "kind": "theorem",
12754     "module": "KomorebiVerification.TopologicalCompletion",
12755     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv_apply",
12756     "runtime_only": false
12757   },
12758   {
12759     "axioms": [
12760       "propext",
12761       "Classical.choice",
12762       "Quot.sound"
12763     ],
12764     "in_project_namespace": true,
12765     "kind": "theorem",
12766     "module": "KomorebiVerification.PacketNaturalityCompletion",
12767     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMulClosed_of_transitive",
12768     "runtime_only": false
12769   },
12770   {
12771     "axioms": [
12772       "propext",
12773       "Classical.choice",
12774       "Quot.sound"
12775     ],
12776     "in_project_namespace": true,
12777     "kind": "definition",
12778     "module": "PaperIRelease.CategoryExport",
12779     "name": "Komorebi.PaperIRelease.CategoryExport.transportColimit",
12780     "runtime_only": false
12781   },
12782   {
12783     "axioms": [
12784       "propext",
12785       "Classical.choice",
12786       "Quot.sound"
12787     ],
12788     "in_project_namespace": true,
12789     "kind": "theorem",
12790     "module": "PaperICompletion.ConditionedCoordinates",
12791     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber._proof_1",
12792     "runtime_only": false
12793   },
12794   {
12795     "axioms": [
12796       "propext",
12797       "Classical.choice",
12798       "Quot.sound"
12799     ],
12800     "in_project_namespace": true,
12801     "kind": "theorem",
12802     "module": "KomorebiVerification.EllipticAlgorithms",
12803     "name": "Komorebi.EllipticCoordinates.P1_not_full_algebra_linear",
12804     "runtime_only": false
12805   },
12806   {
12807     "axioms": [
12808       "propext",
12809       "Classical.choice",
12810       "Quot.sound"
12811     ],
12812     "in_project_namespace": true,
12813     "kind": "theorem",
12814     "module": "KomorebiVerification.ProjectorCore",
12815     "name": "Komorebi.Foundation.transferBlock_comp",
12816     "runtime_only": false
12817   },
12818   {
12819     "axioms": [],
12820     "in_project_namespace": false,
12821     "kind": "theorem",
12822     "module": "ReleaseBoundary",
12823     "name": "_private.ReleaseBoundary.0.PaperIBlock08Tests.dims_pos",
12824     "runtime_only": false
12825   },
12826   {
12827     "axioms": [
12828       "propext",
12829       "Classical.choice",
12830       "Quot.sound"
12831     ],
12832     "in_project_namespace": true,
12833     "kind": "definition",
12834     "module": "PaperIRelease.GeneralConditionedCoordinates",
12835     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packetAnalysis",
12836     "runtime_only": false
12837   },
12838   {
12839     "axioms": [
12840       "propext",
12841       "Classical.choice",
12842       "Quot.sound"
12843     ],
12844     "in_project_namespace": true,
12845     "kind": "theorem",
12846     "module": "PaperICompletion.CyclicClassification",
12847     "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_operatorAlgebra_cyclic",
12848     "runtime_only": false
12849   },
12850   {
12851     "axioms": [
12852       "propext",
12853       "Classical.choice",
12854       "Quot.sound"
12855     ],
12856     "in_project_namespace": true,
12857     "kind": "theorem",
12858     "module": "KomorebiVerification.SingleOperatorGraph",
12859     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun",
12860     "runtime_only": false
12861   },
12862   {
12863     "axioms": [
12864       "propext",
12865       "Classical.choice",
12866       "Quot.sound"
12867     ],
12868     "in_project_namespace": true,
12869     "kind": "definition",
12870     "module": "PaperIRelease.TensorPackets",
12871     "name": "Komorebi.PaperIRelease.dualPacketDirectSumCoordinates",
12872     "runtime_only": false
12873   },
12874   {
12875     "axioms": [
12876       "propext",
12877       "Classical.choice",
12878       "Quot.sound"
12879     ],
12880     "in_project_namespace": true,
12881     "kind": "definition",
12882     "module": "KomorebiVerification.EllipticAlgorithms",
12883     "name": "Komorebi.EllipticCoordinates.y",
12884     "runtime_only": false
12885   },
12886   {
12887     "axioms": [],
12888     "in_project_namespace": true,
12889     "kind": "definition",
12890     "module": "KomorebiVerification.ProjectorCore",
12891     "name": "Komorebi.Seed.OperatorExpr.ctorElim",
12892     "runtime_only": false
12893   },
12894   {
12895     "axioms": [
12896       "propext",
12897       "Classical.choice",
12898       "Quot.sound"
12899     ],
12900     "in_project_namespace": false,
12901     "kind": "theorem",
12902     "module": "PaperIRelease.TopologyCountablePackets",
12903     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_8",
12904     "runtime_only": false
12905   },
12906   {
12907     "axioms": [],
12908     "in_project_namespace": true,
12909     "kind": "constructor",
12910     "module": "KomorebiVerification.ProjectorCore",
12911     "name": "Komorebi.ClaimKind.boundary",
12912     "runtime_only": false
12913   },
12914   {
12915     "axioms": [
12916       "propext",
12917       "Classical.choice",
12918       "Quot.sound"
12919     ],
12920     "in_project_namespace": true,
12921     "kind": "definition",
12922     "module": "PaperIRelease.GrammarPaths",
12923     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap",
12924     "runtime_only": false
12925   },
12926   {
12927     "axioms": [
12928       "propext",
12929       "Classical.choice",
12930       "Quot.sound"
12931     ],
12932     "in_project_namespace": true,
12933     "kind": "definition",
12934     "module": "PaperIRelease.TopologyCategories",
12935     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism._sizeOf_inst",
12936     "runtime_only": false
12937   },
12938   {
12939     "axioms": [
12940       "propext",
12941       "Classical.choice",
12942       "Quot.sound"
12943     ],
12944     "in_project_namespace": true,
12945     "kind": "theorem",
12946     "module": "PaperICompletion6.PrimaryCyclicCriterion",
12947     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.primary_cyclic_of_hasCyclicVector",
12948     "runtime_only": false
12949   },
12950   {
12951     "axioms": [
12952       "propext",
12953       "Classical.choice",
12954       "Quot.sound"
12955     ],
12956     "in_project_namespace": true,
12957     "kind": "theorem",
12958     "module": "PaperICompletion4.IntrinsicPrimary",
12959     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal_surjective",
12960     "runtime_only": false
12961   },
12962   {
12963     "axioms": [],
12964     "in_project_namespace": true,
12965     "kind": "constructor",
12966     "module": "PaperIRelease.GrammarPaths",
12967     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons",
12968     "runtime_only": false
12969   },
12970   {
12971     "axioms": [
12972       "propext",
12973       "Quot.sound"
12974     ],
12975     "in_project_namespace": true,
12976     "kind": "definition",
12977     "module": "PaperIRelease.GrammarPaths",
12978     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1",
12979     "runtime_only": false
12980   },
12981   {
12982     "axioms": [
12983       "propext",
12984       "Classical.choice",
12985       "Quot.sound"
12986     ],
12987     "in_project_namespace": true,
12988     "kind": "theorem",
12989     "module": "PaperICompletion8.RegularMultiplicity",
12990     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicity_seedRank",
12991     "runtime_only": false
12992   },
12993   {
12994     "axioms": [
12995       "propext",
12996       "Classical.choice",
12997       "Quot.sound"
12998     ],
12999     "in_project_namespace": false,
13000     "kind": "theorem",
13001     "module": "PaperIRelease.TopologyUnconditionalBridge",
13002     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countable_analysis_norm_le",
13003     "runtime_only": false
13004   },
13005   {
13006     "axioms": [
13007       "propext",
13008       "Classical.choice",
13009       "Quot.sound"
13010     ],
13011     "in_project_namespace": true,
13012     "kind": "definition",
13013     "module": "PaperIRelease.GrammarModules",
13014     "name": "Komorebi.PaperIRelease.GrammarModules.actionModuleEquivalence",
13015     "runtime_only": false
13016   },
13017   {
13018     "axioms": [
13019       "propext",
13020       "Classical.choice",
13021       "Quot.sound"
13022     ],
13023     "in_project_namespace": true,
13024     "kind": "theorem",
13025     "module": "KomorebiVerification.PacketNaturalityCompletion",
13026     "name": "Komorebi.PacketNaturalityCompletion.Packets.transferBlock_pow_eq_packetPathSum",
13027     "runtime_only": false
13028   },
13029   {
13030     "axioms": [],
13031     "in_project_namespace": true,
13032     "kind": "theorem",
13033     "module": "PaperIRelease.CategoryExport",
13034     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.sizeOf_spec",
13035     "runtime_only": false
13036   },
13037   {
13038     "axioms": [
13039       "propext",
13040       "Classical.choice",
13041       "Quot.sound"
13042     ],
13043     "in_project_namespace": true,
13044     "kind": "definition",
13045     "module": "PaperIRelease.GrammarEquivalence",
13046     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory",
13047     "runtime_only": false
13048   },
13049   {
13050     "axioms": [
13051       "propext",
13052       "Classical.choice",
13053       "Quot.sound"
13054     ],
13055     "in_project_namespace": true,
13056     "kind": "theorem",
13057     "module": "PaperIRelease.PacketDescent",
13058     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range",
13059     "runtime_only": false
13060   },
13061   {
13062     "axioms": [
13063       "propext",
13064       "Quot.sound"
13065     ],
13066     "in_project_namespace": true,
13067     "kind": "definition",
13068     "module": "KomorebiVerification.SemisimpleSeedRank",
13069     "name": "Komorebi.SemisimpleSeedRank.RowsSpan",
13070     "runtime_only": false
13071   },
13072   {
13073     "axioms": [
13074       "propext",
13075       "Classical.choice",
13076       "Quot.sound"
13077     ],
13078     "in_project_namespace": true,
13079     "kind": "theorem",
13080     "module": "PaperIRelease.PacketBoundaryTests",
13081     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_restriction_has_no_nonzero_packets",
13082     "runtime_only": false
13083   },
13084   {
13085     "axioms": [
13086       "propext",
13087       "Classical.choice",
13088       "Quot.sound"
13089     ],
13090     "in_project_namespace": true,
13091     "kind": "theorem",
13092     "module": "PaperIRelease.AlgebraClassGrouping",
13093     "name": "Komorebi.PaperIRelease.class_maximalStrictSteps",
13094     "runtime_only": false
13095   },
13096   {
13097     "axioms": [
13098       "propext",
13099       "Classical.choice",
13100       "Quot.sound"
13101     ],
13102     "in_project_namespace": false,
13103     "kind": "definition",
13104     "module": "PaperIRelease.TopologyCountablePackets",
13105     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_14",
13106     "runtime_only": false
13107   },
13108   {
13109     "axioms": [
13110       "propext",
13111       "Classical.choice",
13112       "Quot.sound"
13113     ],
13114     "in_project_namespace": true,
13115     "kind": "definition",
13116     "module": "KomorebiVerification.EllipticAlgorithms",
13117     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv",
13118     "runtime_only": false
13119   },
13120   {
13121     "axioms": [
13122       "propext",
13123       "Classical.choice",
13124       "Quot.sound"
13125     ],
13126     "in_project_namespace": true,
13127     "kind": "theorem",
13128     "module": "PaperIRelease.TensorPackets",
13129     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_5",
13130     "runtime_only": false
13131   },
13132   {
13133     "axioms": [
13134       "propext",
13135       "Classical.choice",
13136       "Quot.sound"
13137     ],
13138     "in_project_namespace": true,
13139     "kind": "theorem",
13140     "module": "KomorebiVerification.PacketNaturalityCompletion",
13141     "name": "Komorebi.PacketNaturalityCompletion.Reachability.unreachable_nonzero_packet_obstruction",
13142     "runtime_only": false
13143   },
13144   {
13145     "axioms": [],
13146     "in_project_namespace": true,
13147     "kind": "definition",
13148     "module": "KomorebiVerification.ProjectorCore",
13149     "name": "Komorebi.Seed.instReprOperatorExpr",
13150     "runtime_only": false
13151   },
13152   {
13153     "axioms": [
13154       "propext",
13155       "Classical.choice",
13156       "Quot.sound"
13157     ],
13158     "in_project_namespace": true,
13159     "kind": "theorem",
13160     "module": "KomorebiVerification.SeedRankBasics",
13161     "name": "Komorebi.SeedRankBasics.seedFinrank.eq_1",
13162     "runtime_only": false
13163   },
13164   {
13165     "axioms": [
13166       "propext",
13167       "Classical.choice",
13168       "Quot.sound"
13169     ],
13170     "in_project_namespace": true,
13171     "kind": "theorem",
13172     "module": "PaperIRelease.PacketExactSequence",
13173     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient_natural",
13174     "runtime_only": false
13175   },
13176   {
13177     "axioms": [
13178       "propext",
13179       "Classical.choice",
13180       "Quot.sound"
13181     ],
13182     "in_project_namespace": true,
13183     "kind": "theorem",
13184     "module": "KomorebiVerification.SemisimpleSeedRank",
13185     "name": "Komorebi.SemisimpleSeedRank.leftGenerates_iff_rowsSpan",
13186     "runtime_only": false
13187   },
13188   {
13189     "axioms": [
13190       "propext",
13191       "Classical.choice",
13192       "Quot.sound"
13193     ],
13194     "in_project_namespace": true,
13195     "kind": "theorem",
13196     "module": "KomorebiVerification.PacketNaturalityCompletion",
13197     "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull_le_reachable_support",
13198     "runtime_only": false
13199   },
13200   {
13201     "axioms": [
13202       "propext",
13203       "Quot.sound"
13204     ],
13205     "in_project_namespace": true,
13206     "kind": "definition",
13207     "module": "PaperICompletion8.DivisionRows",
13208     "name": "Komorebi.PaperICompletion8.DivisionRows.RowsSpan",
13209     "runtime_only": false
13210   },
13211   {
13212     "axioms": [
13213       "propext",
13214       "Classical.choice",
13215       "Quot.sound"
13216     ],
13217     "in_project_namespace": true,
13218     "kind": "inductive",
13219     "module": "PaperIRelease.GeneralNormedPackets",
13220     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily",
13221     "runtime_only": false
13222   },
13223   {
13224     "axioms": [],
13225     "in_project_namespace": true,
13226     "kind": "definition",
13227     "module": "KomorebiVerification.ProjectorCore",
13228     "name": "Komorebi.ClaimKind.boundary.elim",
13229     "runtime_only": false
13230   },
13231   {
13232     "axioms": [
13233       "propext",
13234       "Classical.choice",
13235       "Quot.sound"
13236     ],
13237     "in_project_namespace": true,
13238     "kind": "theorem",
13239     "module": "PaperIRelease.PacketTopologyGeneral",
13240     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.banach_packet_shortExact",
13241     "runtime_only": false
13242   },
13243   {
13244     "axioms": [
13245       "propext",
13246       "Classical.choice",
13247       "Quot.sound"
13248     ],
13249     "in_project_namespace": true,
13250     "kind": "theorem",
13251     "module": "PaperIRelease.PacketExactSequence",
13252     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion_injective",
13253     "runtime_only": false
13254   },
13255   {
13256     "axioms": [
13257       "propext",
13258       "Quot.sound"
13259     ],
13260     "in_project_namespace": true,
13261     "kind": "theorem",
13262     "module": "PaperIRelease.PacketExactSequence",
13263     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_3",
13264     "runtime_only": false
13265   },
13266   {
13267     "axioms": [
13268       "propext",
13269       "Classical.choice",
13270       "Quot.sound"
13271     ],
13272     "in_project_namespace": true,
13273     "kind": "theorem",
13274     "module": "PaperICompletion8.SemisimpleFormula",
13275     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.radicalTop_seedRank_of_decompositions",
13276     "runtime_only": false
13277   },
13278   {
13279     "axioms": [],
13280     "in_project_namespace": true,
13281     "kind": "theorem",
13282     "module": "PaperICompletion4.ResidueQuotient",
13283     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_1",
13284     "runtime_only": false
13285   },
13286   {
13287     "axioms": [],
13288     "in_project_namespace": true,
13289     "kind": "constructor",
13290     "module": "PaperIRelease.CategoryExport",
13291     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero",
13292     "runtime_only": false
13293   },
13294   {
13295     "axioms": [
13296       "propext",
13297       "Classical.choice",
13298       "Quot.sound"
13299     ],
13300     "in_project_namespace": true,
13301     "kind": "theorem",
13302     "module": "PaperIRelease.GrammarEquivalence",
13303     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_5",
13304     "runtime_only": false
13305   },
13306   {
13307     "axioms": [
13308       "propext",
13309       "Quot.sound"
13310     ],
13311     "in_project_namespace": true,
13312     "kind": "theorem",
13313     "module": "PaperIRelease.GrammarModules",
13314     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_3",
13315     "runtime_only": false
13316   },
13317   {
13318     "axioms": [],
13319     "in_project_namespace": true,
13320     "kind": "definition",
13321     "module": "KomorebiVerification.ProjectorCore",
13322     "name": "Komorebi.ClaimRecord.difficulty",
13323     "runtime_only": false
13324   },
13325   {
13326     "axioms": [
13327       "propext",
13328       "Classical.choice",
13329       "Quot.sound"
13330     ],
13331     "in_project_namespace": true,
13332     "kind": "theorem",
13333     "module": "PaperIRelease.AlgebraDiagonal",
13334     "name": "Komorebi.PaperIRelease.offdiagonal_zero_of_commutes",
13335     "runtime_only": false
13336   },
13337   {
13338     "axioms": [
13339       "propext",
13340       "Classical.choice",
13341       "Quot.sound"
13342     ],
13343     "in_project_namespace": true,
13344     "kind": "definition",
13345     "module": "PaperIRelease.PacketTopology",
13346     "name": "Komorebi.Foundation.LinearProjectorFamily.projectToPacketQuotient",
13347     "runtime_only": false
13348   },
13349   {
13350     "axioms": [
13351       "propext",
13352       "Classical.choice",
13353       "Quot.sound"
13354     ],
13355     "in_project_namespace": true,
13356     "kind": "theorem",
13357     "module": "PaperIRelease.PacketLocalRank",
13358     "name": "Komorebi.PaperIRelease.packetPureSeedRank_discardZeros",
13359     "runtime_only": false
13360   },
13361   {
13362     "axioms": [
13363       "propext",
13364       "Quot.sound"
13365     ],
13366     "in_project_namespace": true,
13367     "kind": "theorem",
13368     "module": "PaperIRelease.ScalarExtension",
13369     "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease._proof_1",
13370     "runtime_only": false
13371   },
13372   {
13373     "axioms": [
13374       "propext",
13375       "Classical.choice",
13376       "Quot.sound"
13377     ],
13378     "in_project_namespace": true,
13379     "kind": "theorem",
13380     "module": "KomorebiVerification.PacketNaturalityCompletion",
13381     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_surjective",
13382     "runtime_only": false
13383   },
13384   {
13385     "axioms": [
13386       "propext",
13387       "Quot.sound"
13388     ],
13389     "in_project_namespace": true,
13390     "kind": "definition",
13391     "module": "PaperIRelease.GrammarModules",
13392     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.moduleObject",
13393     "runtime_only": false
13394   },
13395   {
13396     "axioms": [
13397       "propext",
13398       "Classical.choice",
13399       "Quot.sound"
13400     ],
13401     "in_project_namespace": true,
13402     "kind": "theorem",
13403     "module": "PaperICompletion4.OperatorIntrinsicFormula",
13404     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues_bddAbove",
13405     "runtime_only": false
13406   },
13407   {
13408     "axioms": [
13409       "propext",
13410       "Quot.sound"
13411     ],
13412     "in_project_namespace": true,
13413     "kind": "definition",
13414     "module": "PaperIRelease.AlgebraTransfer",
13415     "name": "Komorebi.PaperIRelease.operatorWord._unsafe_rec",
13416     "runtime_only": true
13417   },
13418   {
13419     "axioms": [
13420       "propext",
13421       "Classical.choice",
13422       "Quot.sound"
13423     ],
13424     "in_project_namespace": true,
13425     "kind": "definition",
13426     "module": "PaperIRelease.TensorPackets",
13427     "name": "Komorebi.PaperIRelease.dualPacketCoordinates",
13428     "runtime_only": false
13429   },
13430   {
13431     "axioms": [],
13432     "in_project_namespace": true,
13433     "kind": "definition",
13434     "module": "PaperIRelease.CategoryExport",
13435     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.elim",
13436     "runtime_only": false
13437   },
13438   {
13439     "axioms": [
13440       "propext",
13441       "Quot.sound"
13442     ],
13443     "in_project_namespace": true,
13444     "kind": "definition",
13445     "module": "PaperIRelease.GrammarAlgebra",
13446     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.recOn",
13447     "runtime_only": false
13448   },
13449   {
13450     "axioms": [
13451       "propext",
13452       "Classical.choice",
13453       "Quot.sound"
13454     ],
13455     "in_project_namespace": true,
13456     "kind": "definition",
13457     "module": "PaperIRelease.PacketTopologyGeneral",
13458     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorCLM",
13459     "runtime_only": false
13460   },
13461   {
13462     "axioms": [
13463       "propext",
13464       "Classical.choice",
13465       "Quot.sound"
13466     ],
13467     "in_project_namespace": true,
13468     "kind": "theorem",
13469     "module": "KomorebiVerification.TopologicalCompletion",
13470     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower._proof_1",
13471     "runtime_only": false
13472   },
13473   {
13474     "axioms": [
13475       "propext",
13476       "Quot.sound"
13477     ],
13478     "in_project_namespace": true,
13479     "kind": "inductive",
13480     "module": "PaperIRelease.GrammarAlgebra",
13481     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar",
13482     "runtime_only": false
13483   },
13484   {
13485     "axioms": [
13486       "propext",
13487       "Classical.choice",
13488       "Quot.sound"
13489     ],
13490     "in_project_namespace": true,
13491     "kind": "theorem",
13492     "module": "PaperIRelease.GrammarAlgebra",
13493     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_4",
13494     "runtime_only": false
13495   },
13496   {
13497     "axioms": [
13498       "propext",
13499       "Classical.choice",
13500       "Quot.sound"
13501     ],
13502     "in_project_namespace": true,
13503     "kind": "theorem",
13504     "module": "PaperIRelease.GrammarAlgebra",
13505     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_complete",
13506     "runtime_only": false
13507   },
13508   {
13509     "axioms": [
13510       "propext",
13511       "Classical.choice",
13512       "Quot.sound"
13513     ],
13514     "in_project_namespace": true,
13515     "kind": "theorem",
13516     "module": "PaperIRelease.AlgebraClassGrouping",
13517     "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_3",
13518     "runtime_only": false
13519   },
13520   {
13521     "axioms": [],
13522     "in_project_namespace": true,
13523     "kind": "definition",
13524     "module": "KomorebiVerification.SemisimpleCompletion",
13525     "name": "Komorebi.SemisimpleCompletion.BlockAlgebra",
13526     "runtime_only": false
13527   },
13528   {
13529     "axioms": [
13530       "propext",
13531       "Classical.choice",
13532       "Quot.sound"
13533     ],
13534     "in_project_namespace": true,
13535     "kind": "definition",
13536     "module": "PaperIRelease.PolynomialModule",
13537     "name": "Komorebi.PaperIRelease.PolynomialModule.instDecidableEqHeightOneSpectrumPolynomial_paperIRelease",
13538     "runtime_only": false
13539   },
13540   {
13541     "axioms": [
13542       "propext",
13543       "Classical.choice",
13544       "Quot.sound"
13545     ],
13546     "in_project_namespace": true,
13547     "kind": "theorem",
13548     "module": "PaperIRelease.ExactSequences",
13549     "name": "Komorebi.PaperIRelease.shortExact_seedRank_bounds",
13550     "runtime_only": false
13551   },
13552   {
13553     "axioms": [
13554       "propext",
13555       "Classical.choice",
13556       "Quot.sound"
13557     ],
13558     "in_project_namespace": true,
13559     "kind": "theorem",
13560     "module": "PaperIRelease.BoundedStar",
13561     "name": "Komorebi.PaperIRelease.BoundedSupport.directed_two_packet_boundary",
13562     "runtime_only": false
13563   },
13564   {
13565     "axioms": [
13566       "propext"
13567     ],
13568     "in_project_namespace": true,
13569     "kind": "theorem",
13570     "module": "KomorebiVerification.ProjectorCore",
13571     "name": "Komorebi.ClaimRecord.mk.injEq",
13572     "runtime_only": false
13573   },
13574   {
13575     "axioms": [
13576       "propext",
13577       "Classical.choice",
13578       "Quot.sound"
13579     ],
13580     "in_project_namespace": true,
13581     "kind": "definition",
13582     "module": "PaperICompletion8.RegularMultiplicity",
13583     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simpleModule",
13584     "runtime_only": false
13585   },
13586   {
13587     "axioms": [
13588       "propext",
13589       "Quot.sound"
13590     ],
13591     "in_project_namespace": true,
13592     "kind": "theorem",
13593     "module": "PaperIRelease.ScalarExtension",
13594     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorLeftTower",
13595     "runtime_only": false
13596   },
13597   {
13598     "axioms": [],
13599     "in_project_namespace": true,
13600     "kind": "definition",
13601     "module": "KomorebiVerification.ProjectorCore",
13602     "name": "Komorebi.ClaimRecord.ordinal",
13603     "runtime_only": false
13604   },
13605   {
13606     "axioms": [
13607       "propext",
13608       "Classical.choice",
13609       "Quot.sound"
13610     ],
13611     "in_project_namespace": true,
13612     "kind": "theorem",
13613     "module": "PaperICompletion4.OperatorIntrinsicFormula",
13614     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicSeedMaximum_attained",
13615     "runtime_only": false
13616   },
13617   {
13618     "axioms": [],
13619     "in_project_namespace": true,
13620     "kind": "definition",
13621     "module": "PaperIRelease.GrammarPaths",
13622     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.below",
13623     "runtime_only": false
13624   },
13625   {
13626     "axioms": [
13627       "propext",
13628       "Classical.choice",
13629       "Quot.sound"
13630     ],
13631     "in_project_namespace": true,
13632     "kind": "theorem",
13633     "module": "PaperIRelease.PacketDescent",
13634     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range_preimage",
13635     "runtime_only": false
13636   },
13637   {
13638     "axioms": [
13639       "propext",
13640       "Classical.choice",
13641       "Quot.sound"
13642     ],
13643     "in_project_namespace": false,
13644     "kind": "theorem",
13645     "module": "PaperIRelease.TopologyCountablePackets",
13646     "name": "PaperIRelease.TopologyCountablePackets.Projectors.norm_le_K_synthesis",
13647     "runtime_only": false
13648   },
13649   {
13650     "axioms": [
13651       "propext",
13652       "Classical.choice",
13653       "Quot.sound"
13654     ],
13655     "in_project_namespace": true,
13656     "kind": "theorem",
13657     "module": "PaperIRelease.PacketPureBoundaryTests",
13658     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infinite_single_packet_rank",
13659     "runtime_only": false
13660   },
13661   {
13662     "axioms": [
13663       "propext",
13664       "Quot.sound"
13665     ],
13666     "in_project_namespace": true,
13667     "kind": "theorem",
13668     "module": "PaperIRelease.SeedOperations",
13669     "name": "Komorebi.PaperIRelease.SeedOperations.annihilator_two_sided_iff",
13670     "runtime_only": false
13671   },
13672   {
13673     "axioms": [
13674       "propext",
13675       "Classical.choice",
13676       "Quot.sound"
13677     ],
13678     "in_project_namespace": true,
13679     "kind": "theorem",
13680     "module": "PaperICompletion5.CyclicGeometricCriterion",
13681     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_5",
13682     "runtime_only": false
13683   },
13684   {
13685     "axioms": [
13686       "propext",
13687       "Classical.choice",
13688       "Quot.sound"
13689     ],
13690     "in_project_namespace": true,
13691     "kind": "theorem",
13692     "module": "KomorebiVerification.EllipticAlgorithms",
13693     "name": "Komorebi.FiniteAlgorithms.transferGraph_iff_block_ne_zero",
13694     "runtime_only": false
13695   },
13696   {
13697     "axioms": [
13698       "propext",
13699       "Quot.sound"
13700     ],
13701     "in_project_namespace": true,
13702     "kind": "constructor",
13703     "module": "PaperIRelease.GrammarAlgebra",
13704     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk",
13705     "runtime_only": false
13706   },
13707   {
13708     "axioms": [
13709       "propext",
13710       "Classical.choice",
13711       "Quot.sound"
13712     ],
13713     "in_project_namespace": false,
13714     "kind": "theorem",
13715     "module": "PaperIRelease.TopologyUnconditional",
13716     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_cauchy",
13717     "runtime_only": false
13718   },
13719   {
13720     "axioms": [
13721       "propext",
13722       "Classical.choice",
13723       "Quot.sound"
13724     ],
13725     "in_project_namespace": false,
13726     "kind": "theorem",
13727     "module": "PaperIRelease.TopologyCountablePackets",
13728     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_1",
13729     "runtime_only": false
13730   },
13731   {
13732     "axioms": [
13733       "propext",
13734       "Classical.choice",
13735       "Quot.sound"
13736     ],
13737     "in_project_namespace": true,
13738     "kind": "theorem",
13739     "module": "PaperIRelease.CategoryPackets",
13740     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_2",
13741     "runtime_only": false
13742   },
13743   {
13744     "axioms": [
13745       "propext",
13746       "Classical.choice",
13747       "Quot.sound"
13748     ],
13749     "in_project_namespace": true,
13750     "kind": "theorem",
13751     "module": "PaperIRelease.AlgebraClassGrouping",
13752     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_6",
13753     "runtime_only": false
13754   },
13755   {
13756     "axioms": [
13757       "propext",
13758       "Classical.choice",
13759       "Quot.sound"
13760     ],
13761     "in_project_namespace": true,
13762     "kind": "theorem",
13763     "module": "PaperIRelease.GraphSourceCount",
13764     "name": "Komorebi.PaperIRelease.packetPureSeedRank_eq_source_count",
13765     "runtime_only": false
13766   },
13767   {
13768     "axioms": [
13769       "propext",
13770       "Classical.choice",
13771       "Quot.sound"
13772     ],
13773     "in_project_namespace": true,
13774     "kind": "theorem",
13775     "module": "PaperIRelease.PacketTopology",
13776     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_2",
13777     "runtime_only": false
13778   },
13779   {
13780     "axioms": [
13781       "propext",
13782       "Classical.choice",
13783       "Quot.sound"
13784     ],
13785     "in_project_namespace": true,
13786     "kind": "theorem",
13787     "module": "KomorebiVerification.PaperIBlockCompletion",
13788     "name": "Komorebi.Foundation.transferBlock_comp_linearMap",
13789     "runtime_only": false
13790   },
13791   {
13792     "axioms": [
13793       "propext",
13794       "Quot.sound"
13795     ],
13796     "in_project_namespace": true,
13797     "kind": "theorem",
13798     "module": "PaperIRelease.AlgebraClassGrouping",
13799     "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_2",
13800     "runtime_only": false
13801   },
13802   {
13803     "axioms": [
13804       "propext",
13805       "Classical.choice",
13806       "Quot.sound"
13807     ],
13808     "in_project_namespace": true,
13809     "kind": "theorem",
13810     "module": "PaperIRelease.AlgebraPreorder",
13811     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_6",
13812     "runtime_only": false
13813   },
13814   {
13815     "axioms": [
13816       "propext",
13817       "Classical.choice",
13818       "Quot.sound"
13819     ],
13820     "in_project_namespace": true,
13821     "kind": "theorem",
13822     "module": "KomorebiVerification.PacketNaturalityCompletion",
13823     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA_eU\u2081",
13824     "runtime_only": false
13825   },
13826   {
13827     "axioms": [
13828       "propext",
13829       "Classical.choice",
13830       "Quot.sound"
13831     ],
13832     "in_project_namespace": true,
13833     "kind": "theorem",
13834     "module": "PaperIRelease.PacketTopologyGeneral",
13835     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorNormedHom._proof_1",
13836     "runtime_only": false
13837   },
13838   {
13839     "axioms": [
13840       "propext",
13841       "Classical.choice",
13842       "Quot.sound"
13843     ],
13844     "in_project_namespace": true,
13845     "kind": "theorem",
13846     "module": "PaperIRelease.TensorPackets",
13847     "name": "Komorebi.PaperIRelease.tensorPackets._proof_2",
13848     "runtime_only": false
13849   },
13850   {
13851     "axioms": [],
13852     "in_project_namespace": true,
13853     "kind": "constructor",
13854     "module": "PaperIRelease.CategoryExport",
13855     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add",
13856     "runtime_only": false
13857   },
13858   {
13859     "axioms": [
13860       "propext",
13861       "Classical.choice",
13862       "Quot.sound"
13863     ],
13864     "in_project_namespace": true,
13865     "kind": "definition",
13866     "module": "PaperIRelease.GrammarAlgebra",
13867     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.noConfusion",
13868     "runtime_only": false
13869   },
13870   {
13871     "axioms": [
13872       "propext",
13873       "Classical.choice",
13874       "Quot.sound"
13875     ],
13876     "in_project_namespace": true,
13877     "kind": "definition",
13878     "module": "PaperICompletion6.OneInvariantFactor",
13879     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.companionMatrix",
13880     "runtime_only": false
13881   },
13882   {
13883     "axioms": [
13884       "propext",
13885       "Classical.choice",
13886       "Quot.sound"
13887     ],
13888     "in_project_namespace": true,
13889     "kind": "theorem",
13890     "module": "PaperIRelease.PacketDescent",
13891     "name": "Komorebi.Foundation.LinearProjectorFamily.proj_eq_self_of_mem_range",
13892     "runtime_only": false
13893   },
13894   {
13895     "axioms": [
13896       "propext",
13897       "Classical.choice",
13898       "Quot.sound"
13899     ],
13900     "in_project_namespace": true,
13901     "kind": "theorem",
13902     "module": "PaperICompletion8.RegularMultiplicity",
13903     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.directSum_seedRank",
13904     "runtime_only": false
13905   },
13906   {
13907     "axioms": [
13908       "propext",
13909       "Classical.choice",
13910       "Quot.sound"
13911     ],
13912     "in_project_namespace": true,
13913     "kind": "theorem",
13914     "module": "KomorebiVerification.SemisimpleCompletion",
13915     "name": "Komorebi.SemisimpleCompletion.fullMatrix_isCyclic_iff_generates",
13916     "runtime_only": false
13917   },
13918   {
13919     "axioms": [
13920       "propext",
13921       "Classical.choice",
13922       "Quot.sound"
13923     ],
13924     "in_project_namespace": true,
13925     "kind": "theorem",
13926     "module": "PaperIRelease.PacketDescent",
13927     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_unique",
13928     "runtime_only": false
13929   },
13930   {
13931     "axioms": [],
13932     "in_project_namespace": true,
13933     "kind": "theorem",
13934     "module": "KomorebiVerification.PathGraphKrylov",
13935     "name": "Komorebi.PathGraphKrylov.rightTerm._proof_1",
13936     "runtime_only": false
13937   },
13938   {
13939     "axioms": [
13940       "propext",
13941       "Quot.sound"
13942     ],
13943     "in_project_namespace": true,
13944     "kind": "theorem",
13945     "module": "PaperIRelease.GrammarModules",
13946     "name": "Komorebi.PaperIRelease.GrammarModules.toModules_faithful",
13947     "runtime_only": false
13948   },
13949   {
13950     "axioms": [
13951       "propext",
13952       "Quot.sound"
13953     ],
13954     "in_project_namespace": true,
13955     "kind": "definition",
13956     "module": "PaperIRelease.SeedOperations",
13957     "name": "Komorebi.PaperIRelease.SeedOperations.vectorAnnihilator",
13958     "runtime_only": false
13959   },
13960   {
13961     "axioms": [
13962       "propext",
13963       "Classical.choice",
13964       "Quot.sound"
13965     ],
13966     "in_project_namespace": true,
13967     "kind": "theorem",
13968     "module": "KomorebiVerification.PacketNaturalityCompletion",
13969     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds_generate",
13970     "runtime_only": false
13971   },
13972   {
13973     "axioms": [
13974       "propext",
13975       "Classical.choice",
13976       "Quot.sound"
13977     ],
13978     "in_project_namespace": true,
13979     "kind": "theorem",
13980     "module": "KomorebiVerification.TopologicalCompletion",
13981     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_6",
13982     "runtime_only": false
13983   },
13984   {
13985     "axioms": [
13986       "propext",
13987       "Classical.choice",
13988       "Quot.sound"
13989     ],
13990     "in_project_namespace": true,
13991     "kind": "theorem",
13992     "module": "PaperIRelease.PolynomialModule",
13993     "name": "Komorebi.PaperIRelease.PolynomialModule.polynomialModule_isTorsion",
13994     "runtime_only": false
13995   },
13996   {
13997     "axioms": [
13998       "propext",
13999       "Classical.choice",
14000       "Quot.sound"
14001     ],
14002     "in_project_namespace": true,
14003     "kind": "theorem",
14004     "module": "KomorebiVerification.TopologicalCompletion",
14005     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis.eq_1",
14006     "runtime_only": false
14007   },
14008   {
14009     "axioms": [
14010       "propext",
14011       "Classical.choice",
14012       "Quot.sound"
14013     ],
14014     "in_project_namespace": true,
14015     "kind": "theorem",
14016     "module": "KomorebiVerification.ProjectorCore",
14017     "name": "Komorebi.Foundation.LinearProjectorFamily.idempotent",
14018     "runtime_only": false
14019   },
14020   {
14021     "axioms": [
14022       "propext",
14023       "Classical.choice",
14024       "Quot.sound"
14025     ],
14026     "in_project_namespace": true,
14027     "kind": "definition",
14028     "module": "PaperIRelease.GrammarAlgebra",
14029     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow",
14030     "runtime_only": false
14031   },
14032   {
14033     "axioms": [
14034       "propext",
14035       "Quot.sound"
14036     ],
14037     "in_project_namespace": true,
14038     "kind": "theorem",
14039     "module": "PaperIRelease.GrammarTyped",
14040     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.sizeOf_spec",
14041     "runtime_only": false
14042   },
14043   {
14044     "axioms": [
14045       "propext",
14046       "Classical.choice",
14047       "Quot.sound"
14048     ],
14049     "in_project_namespace": true,
14050     "kind": "theorem",
14051     "module": "KomorebiVerification.TopologicalCompletion",
14052     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_7",
14053     "runtime_only": false
14054   },
14055   {
14056     "axioms": [
14057       "propext",
14058       "Classical.choice",
14059       "Quot.sound"
14060     ],
14061     "in_project_namespace": true,
14062     "kind": "theorem",
14063     "module": "PaperIRelease.AlgebraClassGrouping",
14064     "name": "Komorebi.PaperIRelease.groupedProjection_original",
14065     "runtime_only": false
14066   },
14067   {
14068     "axioms": [
14069       "propext",
14070       "Classical.choice",
14071       "Quot.sound"
14072     ],
14073     "in_project_namespace": true,
14074     "kind": "definition",
14075     "module": "PaperIRelease.CategoryPackets",
14076     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packetMap",
14077     "runtime_only": false
14078   },
14079   {
14080     "axioms": [
14081       "propext",
14082       "Classical.choice",
14083       "Quot.sound"
14084     ],
14085     "in_project_namespace": true,
14086     "kind": "theorem",
14087     "module": "PaperIRelease.TensorPackets",
14088     "name": "Komorebi.PaperIRelease.tensorPackets._proof_3",
14089     "runtime_only": false
14090   },
14091   {
14092     "axioms": [
14093       "propext",
14094       "Classical.choice",
14095       "Quot.sound"
14096     ],
14097     "in_project_namespace": true,
14098     "kind": "definition",
14099     "module": "PaperIRelease.CategoryUniversal",
14100     "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial",
14101     "runtime_only": false
14102   },
14103   {
14104     "axioms": [
14105       "propext",
14106       "Quot.sound"
14107     ],
14108     "in_project_namespace": true,
14109     "kind": "theorem",
14110     "module": "PaperIRelease.PacketPureRank",
14111     "name": "Komorebi.PaperIRelease.PureGenerates._proof_1",
14112     "runtime_only": false
14113   },
14114   {
14115     "axioms": [
14116       "propext",
14117       "Classical.choice",
14118       "Quot.sound"
14119     ],
14120     "in_project_namespace": false,
14121     "kind": "theorem",
14122     "module": "PaperIRelease.TopologyCountablePackets",
14123     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_2",
14124     "runtime_only": false
14125   },
14126   {
14127     "axioms": [
14128       "propext",
14129       "Classical.choice",
14130       "Quot.sound"
14131     ],
14132     "in_project_namespace": true,
14133     "kind": "definition",
14134     "module": "KomorebiVerification.FullMatrixCyclicity",
14135     "name": "Komorebi.FullMatrixCyclicity.IsCyclic",
14136     "runtime_only": false
14137   },
14138   {
14139     "axioms": [
14140       "propext",
14141       "Classical.choice",
14142       "Quot.sound"
14143     ],
14144     "in_project_namespace": true,
14145     "kind": "definition",
14146     "module": "PaperIRelease.CategoryPackets",
14147     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.recOn",
14148     "runtime_only": false
14149   },
14150   {
14151     "axioms": [
14152       "propext",
14153       "Classical.choice",
14154       "Quot.sound"
14155     ],
14156     "in_project_namespace": true,
14157     "kind": "theorem",
14158     "module": "KomorebiVerification.SeedRankBasics",
14159     "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv._proof_1",
14160     "runtime_only": false
14161   },
14162   {
14163     "axioms": [
14164       "propext",
14165       "Classical.choice",
14166       "Quot.sound"
14167     ],
14168     "in_project_namespace": true,
14169     "kind": "definition",
14170     "module": "PaperIRelease.PacketDescent",
14171     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo",
14172     "runtime_only": false
14173   },
14174   {
14175     "axioms": [
14176       "propext",
14177       "Classical.choice",
14178       "Quot.sound"
14179     ],
14180     "in_project_namespace": true,
14181     "kind": "theorem",
14182     "module": "PaperIRelease.PacketCorners",
14183     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_8",
14184     "runtime_only": false
14185   },
14186   {
14187     "axioms": [
14188       "propext",
14189       "Quot.sound"
14190     ],
14191     "in_project_namespace": true,
14192     "kind": "definition",
14193     "module": "PaperIRelease.GrammarModules",
14194     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject._sizeOf_1",
14195     "runtime_only": false
14196   },
14197   {
14198     "axioms": [
14199       "propext",
14200       "Classical.choice",
14201       "Quot.sound"
14202     ],
14203     "in_project_namespace": true,
14204     "kind": "theorem",
14205     "module": "PaperICompletion7.Nakayama",
14206     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_apply",
14207     "runtime_only": false
14208   },
14209   {
14210     "axioms": [
14211       "propext",
14212       "Quot.sound"
14213     ],
14214     "in_project_namespace": true,
14215     "kind": "definition",
14216     "module": "PaperIRelease.GrammarTyped",
14217     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData._sizeOf_1",
14218     "runtime_only": false
14219   },
14220   {
14221     "axioms": [
14222       "propext",
14223       "Quot.sound"
14224     ],
14225     "in_project_namespace": true,
14226     "kind": "theorem",
14227     "module": "KomorebiVerification.SingleOperatorGraph",
14228     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_10",
14229     "runtime_only": false
14230   },
14231   {
14232     "axioms": [
14233       "propext",
14234       "Classical.choice",
14235       "Quot.sound"
14236     ],
14237     "in_project_namespace": true,
14238     "kind": "theorem",
14239     "module": "PaperICompletion6.OneInvariantFactor",
14240     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_8",
14241     "runtime_only": false
14242   },
14243   {
14244     "axioms": [
14245       "propext",
14246       "Classical.choice",
14247       "Quot.sound"
14248     ],
14249     "in_project_namespace": true,
14250     "kind": "theorem",
14251     "module": "PaperIRelease.GrammarEquivalence",
14252     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_7",
14253     "runtime_only": false
14254   },
14255   {
14256     "axioms": [
14257       "propext",
14258       "Classical.choice",
14259       "Quot.sound"
14260     ],
14261     "in_project_namespace": true,
14262     "kind": "definition",
14263     "module": "KomorebiVerification.SeedRankBasics",
14264     "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquivRange",
14265     "runtime_only": false
14266   },
14267   {
14268     "axioms": [],
14269     "in_project_namespace": true,
14270     "kind": "definition",
14271     "module": "KomorebiVerification.ProjectorCore",
14272     "name": "Komorebi.Seed.OperatorRelation.lhs",
14273     "runtime_only": false
14274   },
14275   {
14276     "axioms": [
14277       "propext",
14278       "Quot.sound"
14279     ],
14280     "in_project_namespace": true,
14281     "kind": "theorem",
14282     "module": "PaperIRelease.GrammarModules",
14283     "name": "Komorebi.PaperIRelease.GrammarModules.toModules_full",
14284     "runtime_only": false
14285   },
14286   {
14287     "axioms": [
14288       "propext",
14289       "Classical.choice",
14290       "Quot.sound"
14291     ],
14292     "in_project_namespace": true,
14293     "kind": "theorem",
14294     "module": "KomorebiVerification.PacketNaturalityCompletion",
14295     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_natural_algebra",
14296     "runtime_only": false
14297   },
14298   {
14299     "axioms": [
14300       "propext",
14301       "Quot.sound"
14302     ],
14303     "in_project_namespace": true,
14304     "kind": "definition",
14305     "module": "KomorebiVerification.SingleOperatorGraph",
14306     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency",
14307     "runtime_only": false
14308   },
14309   {
14310     "axioms": [
14311       "propext",
14312       "Classical.choice",
14313       "Quot.sound"
14314     ],
14315     "in_project_namespace": true,
14316     "kind": "theorem",
14317     "module": "KomorebiVerification.TopologicalCompletion",
14318     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis._proof_2",
14319     "runtime_only": false
14320   },
14321   {
14322     "axioms": [
14323       "propext",
14324       "Classical.choice",
14325       "Quot.sound"
14326     ],
14327     "in_project_namespace": true,
14328     "kind": "theorem",
14329     "module": "PaperIRelease.PacketTopology",
14330     "name": "Komorebi.Foundation.LinearProjectorFamily.packet_sequence_complete",
14331     "runtime_only": false
14332   },
14333   {
14334     "axioms": [
14335       "propext",
14336       "Classical.choice",
14337       "Quot.sound"
14338     ],
14339     "in_project_namespace": false,
14340     "kind": "definition",
14341     "module": "PaperIRelease.TopologyPresentations",
14342     "name": "PaperIRelease.TopologyDenseCompletion.completedFreePresentation",
14343     "runtime_only": false
14344   },
14345   {
14346     "axioms": [
14347       "propext",
14348       "Classical.choice",
14349       "Quot.sound"
14350     ],
14351     "in_project_namespace": true,
14352     "kind": "theorem",
14353     "module": "PaperIRelease.PacketExactSequence",
14354     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion._proof_1",
14355     "runtime_only": false
14356   },
14357   {
14358     "axioms": [
14359       "propext",
14360       "Classical.choice",
14361       "Quot.sound"
14362     ],
14363     "in_project_namespace": true,
14364     "kind": "definition",
14365     "module": "KomorebiVerification.TopologicalCompletion",
14366     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv",
14367     "runtime_only": false
14368   },
14369   {
14370     "axioms": [],
14371     "in_project_namespace": true,
14372     "kind": "recursor",
14373     "module": "KomorebiVerification.ProjectorCore",
14374     "name": "Komorebi.ClaimKind.rec",
14375     "runtime_only": false
14376   },
14377   {
14378     "axioms": [],
14379     "in_project_namespace": true,
14380     "kind": "definition",
14381     "module": "PaperIRelease.AlgebraClassGrouping",
14382     "name": "Komorebi.PaperIRelease.PreorderClasses",
14383     "runtime_only": false
14384   },
14385   {
14386     "axioms": [
14387       "propext",
14388       "Classical.choice",
14389       "Quot.sound"
14390     ],
14391     "in_project_namespace": false,
14392     "kind": "definition",
14393     "module": "PaperIRelease.TopologyUnconditional",
14394     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.casesOn",
14395     "runtime_only": false
14396   },
14397   {
14398     "axioms": [
14399       "propext",
14400       "Classical.choice",
14401       "Quot.sound"
14402     ],
14403     "in_project_namespace": true,
14404     "kind": "theorem",
14405     "module": "PaperIRelease.AlgebraPreorder",
14406     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_4",
14407     "runtime_only": false
14408   },
14409   {
14410     "axioms": [
14411       "propext",
14412       "Classical.choice",
14413       "Quot.sound"
14414     ],
14415     "in_project_namespace": true,
14416     "kind": "theorem",
14417     "module": "KomorebiVerification.EllipticAlgorithms",
14418     "name": "Komorebi.EllipticCoordinates.My_sq_eq_Mx_cube_sub_Mx",
14419     "runtime_only": false
14420   },
14421   {
14422     "axioms": [
14423       "propext",
14424       "Classical.choice",
14425       "Quot.sound"
14426     ],
14427     "in_project_namespace": true,
14428     "kind": "theorem",
14429     "module": "PaperIRelease.BoundedStar",
14430     "name": "Komorebi.PaperIRelease.BoundedSupport.supported_rankOne",
14431     "runtime_only": false
14432   },
14433   {
14434     "axioms": [],
14435     "in_project_namespace": true,
14436     "kind": "definition",
14437     "module": "PaperICompletion8.DivisionProduct",
14438     "name": "Komorebi.PaperICompletion8.DivisionProduct.DivisionProductAlgebra",
14439     "runtime_only": false
14440   },
14441   {
14442     "axioms": [
14443       "propext",
14444       "Classical.choice",
14445       "Quot.sound"
14446     ],
14447     "in_project_namespace": true,
14448     "kind": "theorem",
14449     "module": "KomorebiVerification.PathGraphKrylov",
14450     "name": "Komorebi.PathGraphKrylov.pathAdjacency_pow_mulVec_endpoint",
14451     "runtime_only": false
14452   },
14453   {
14454     "axioms": [
14455       "propext",
14456       "Classical.choice",
14457       "Quot.sound"
14458     ],
14459     "in_project_namespace": true,
14460     "kind": "theorem",
14461     "module": "KomorebiVerification.SemisimpleCompletion",
14462     "name": "Komorebi.SemisimpleCompletion.fullMatrix_every_nonzero_vector_generates",
14463     "runtime_only": false
14464   },
14465   {
14466     "axioms": [
14467       "propext",
14468       "Classical.choice",
14469       "Quot.sound"
14470     ],
14471     "in_project_namespace": true,
14472     "kind": "theorem",
14473     "module": "KomorebiVerification.SeedRankOperations",
14474     "name": "Komorebi.SeedRankOperations.cyclic_iff_seedRank_eq_one",
14475     "runtime_only": false
14476   },
14477   {
14478     "axioms": [
14479       "propext",
14480       "Classical.choice",
14481       "Quot.sound"
14482     ],
14483     "in_project_namespace": false,
14484     "kind": "definition",
14485     "module": "PaperIRelease.TopologyCountablePackets",
14486     "name": "PaperIRelease.TopologyCountablePackets.Projectors._sizeOf_inst",
14487     "runtime_only": false
14488   },
14489   {
14490     "axioms": [
14491       "propext",
14492       "Classical.choice",
14493       "Quot.sound"
14494     ],
14495     "in_project_namespace": true,
14496     "kind": "theorem",
14497     "module": "KomorebiVerification.SingleOperatorGraph",
14498     "name": "Komorebi.SingleOperatorGraph.operatorAlgebra_seedFinrank_eq_of_seedNumber_isLeast",
14499     "runtime_only": false
14500   },
14501   {
14502     "axioms": [
14503       "propext"
14504     ],
14505     "in_project_namespace": true,
14506     "kind": "theorem",
14507     "module": "PaperICompletion4.ResidueQuotient",
14508     "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff._simp_1_2",
14509     "runtime_only": false
14510   },
14511   {
14512     "axioms": [
14513       "propext",
14514       "Classical.choice",
14515       "Quot.sound"
14516     ],
14517     "in_project_namespace": true,
14518     "kind": "definition",
14519     "module": "KomorebiVerification.PacketNaturalityCompletion",
14520     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA",
14521     "runtime_only": false
14522   },
14523   {
14524     "axioms": [
14525       "propext",
14526       "Classical.choice",
14527       "Quot.sound"
14528     ],
14529     "in_project_namespace": true,
14530     "kind": "theorem",
14531     "module": "KomorebiVerification.SingleOperatorGraph",
14532     "name": "Komorebi.SingleOperatorGraph.paddedBlockSum.eq_1",
14533     "runtime_only": false
14534   },
14535   {
14536     "axioms": [
14537       "propext",
14538       "Classical.choice",
14539       "Quot.sound"
14540     ],
14541     "in_project_namespace": true,
14542     "kind": "theorem",
14543     "module": "PaperIRelease.AlgebraClassGrouping",
14544     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_3",
14545     "runtime_only": false
14546   },
14547   {
14548     "axioms": [
14549       "propext",
14550       "Quot.sound"
14551     ],
14552     "in_project_namespace": true,
14553     "kind": "theorem",
14554     "module": "PaperIRelease.GrammarTyped",
14555     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator._proof_1",
14556     "runtime_only": false
14557   },
14558   {
14559     "axioms": [
14560       "propext",
14561       "Classical.choice",
14562       "Quot.sound"
14563     ],
14564     "in_project_namespace": false,
14565     "kind": "theorem",
14566     "module": "PaperIRelease.TopologyDenseCompletion",
14567     "name": "PaperIRelease.TopologyDenseCompletion.completedAction.eq_1",
14568     "runtime_only": false
14569   },
14570   {
14571     "axioms": [
14572       "propext",
14573       "Classical.choice",
14574       "Quot.sound"
14575     ],
14576     "in_project_namespace": true,
14577     "kind": "definition",
14578     "module": "PaperICompletion5.LinearPrimaryEigenspace",
14579     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel",
14580     "runtime_only": false
14581   },
14582   {
14583     "axioms": [
14584       "propext",
14585       "Classical.choice",
14586       "Quot.sound"
14587     ],
14588     "in_project_namespace": true,
14589     "kind": "theorem",
14590     "module": "KomorebiVerification.SingleOperatorGraph",
14591     "name": "Komorebi.SingleOperatorGraph.diagonalizable_seedNumber_isLeast_of_distinct_eigenvalues",
14592     "runtime_only": false
14593   },
14594   {
14595     "axioms": [
14596       "propext",
14597       "Classical.choice",
14598       "Quot.sound"
14599     ],
14600     "in_project_namespace": false,
14601     "kind": "definition",
14602     "module": "PaperIRelease.TopologyCountablePackets",
14603     "name": "PaperIRelease.TopologyCountablePackets.Projectors.K",
14604     "runtime_only": false
14605   },
14606   {
14607     "axioms": [
14608       "propext",
14609       "Classical.choice",
14610       "Quot.sound"
14611     ],
14612     "in_project_namespace": true,
14613     "kind": "definition",
14614     "module": "PaperIRelease.CategoryPackets",
14615     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity",
14616     "runtime_only": false
14617   },
14618   {
14619     "axioms": [
14620       "propext",
14621       "Classical.choice",
14622       "Quot.sound"
14623     ],
14624     "in_project_namespace": false,
14625     "kind": "theorem",
14626     "module": "PaperIRelease.TopologyCountablePackets",
14627     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_analysis",
14628     "runtime_only": false
14629   },
14630   {
14631     "axioms": [],
14632     "in_project_namespace": true,
14633     "kind": "theorem",
14634     "module": "KomorebiVerification.ProjectorCore",
14635     "name": "Komorebi.FormalizationStatus.encodedDefinition.sizeOf_spec",
14636     "runtime_only": false
14637   },
14638   {
14639     "axioms": [
14640       "propext",
14641       "Classical.choice",
14642       "Quot.sound"
14643     ],
14644     "in_project_namespace": true,
14645     "kind": "theorem",
14646     "module": "PaperIRelease.CoordinateTransport",
14647     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_10",
14648     "runtime_only": false
14649   },
14650   {
14651     "axioms": [
14652       "propext",
14653       "Classical.choice",
14654       "Quot.sound"
14655     ],
14656     "in_project_namespace": true,
14657     "kind": "theorem",
14658     "module": "KomorebiVerification.ProjectorCore",
14659     "name": "Komorebi.Foundation.LinearProjectorFamily.eq_of_projectors_eq",
14660     "runtime_only": false
14661   },
14662   {
14663     "axioms": [],
14664     "in_project_namespace": true,
14665     "kind": "constructor",
14666     "module": "KomorebiVerification.ProjectorCore",
14667     "name": "Komorebi.ClaimKind.remarkClaim",
14668     "runtime_only": false
14669   },
14670   {
14671     "axioms": [],
14672     "in_project_namespace": true,
14673     "kind": "definition",
14674     "module": "KomorebiVerification.ProjectorCore",
14675     "name": "Komorebi.Seed.OperatorRelation.ctorIdx",
14676     "runtime_only": false
14677   },
14678   {
14679     "axioms": [
14680       "propext",
14681       "Classical.choice",
14682       "Quot.sound"
14683     ],
14684     "in_project_namespace": true,
14685     "kind": "theorem",
14686     "module": "PaperICompletion7.LocalResidue",
14687     "name": "Komorebi.PaperICompletion7.LocalResidue.jacobson_isMaximal",
14688     "runtime_only": false
14689   },
14690   {
14691     "axioms": [
14692       "propext",
14693       "Quot.sound"
14694     ],
14695     "in_project_namespace": true,
14696     "kind": "theorem",
14697     "module": "PaperIRelease.SeedOperations",
14698     "name": "Komorebi.PaperIRelease.SeedOperations.mem_vectorAnnihilator._simp_1",
14699     "runtime_only": false
14700   },
14701   {
14702     "axioms": [
14703       "propext",
14704       "Quot.sound"
14705     ],
14706     "in_project_namespace": true,
14707     "kind": "theorem",
14708     "module": "PaperIRelease.PacketExactSequence",
14709     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_1",
14710     "runtime_only": false
14711   },
14712   {
14713     "axioms": [
14714       "propext"
14715     ],
14716     "in_project_namespace": true,
14717     "kind": "theorem",
14718     "module": "PaperICompletion4.IntrinsicPrimary",
14719     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_2",
14720     "runtime_only": false
14721   },
14722   {
14723     "axioms": [
14724       "propext",
14725       "Classical.choice",
14726       "Quot.sound"
14727     ],
14728     "in_project_namespace": true,
14729     "kind": "theorem",
14730     "module": "KomorebiVerification.TopologicalCompletion",
14731     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.injEq",
14732     "runtime_only": false
14733   },
14734   {
14735     "axioms": [
14736       "propext",
14737       "Classical.choice",
14738       "Quot.sound"
14739     ],
14740     "in_project_namespace": true,
14741     "kind": "theorem",
14742     "module": "PaperICompletion3.PrimarySeedFormula",
14743     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor.eq_1",
14744     "runtime_only": false
14745   },
14746   {
14747     "axioms": [
14748       "propext",
14749       "Classical.choice",
14750       "Quot.sound"
14751     ],
14752     "in_project_namespace": true,
14753     "kind": "definition",
14754     "module": "PaperIRelease.GrammarAlgebra",
14755     "name": "Komorebi.PaperIRelease.GrammarAlgebra.quotient",
14756     "runtime_only": false
14757   },
14758   {
14759     "axioms": [
14760       "propext"
14761     ],
14762     "in_project_namespace": true,
14763     "kind": "theorem",
14764     "module": "PaperIRelease.CategoryExport",
14765     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_1",
14766     "runtime_only": false
14767   },
14768   {
14769     "axioms": [
14770       "propext",
14771       "Classical.choice",
14772       "Quot.sound"
14773     ],
14774     "in_project_namespace": true,
14775     "kind": "theorem",
14776     "module": "KomorebiVerification.TopologicalCompletion",
14777     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.topological_reachability_obstruction",
14778     "runtime_only": false
14779   },
14780   {
14781     "axioms": [
14782       "propext",
14783       "Classical.choice",
14784       "Quot.sound"
14785     ],
14786     "in_project_namespace": true,
14787     "kind": "theorem",
14788     "module": "KomorebiVerification.SeedRankBasics",
14789     "name": "Komorebi.SeedRankBasics.seedRank_le_mk_of_generates",
14790     "runtime_only": false
14791   },
14792   {
14793     "axioms": [
14794       "propext",
14795       "Classical.choice",
14796       "Quot.sound"
14797     ],
14798     "in_project_namespace": true,
14799     "kind": "definition",
14800     "module": "KomorebiVerification.ProjectorCore",
14801     "name": "Komorebi.Foundation.LinearProjectorFamily._sizeOf_1",
14802     "runtime_only": false
14803   },
14804   {
14805     "axioms": [
14806       "propext",
14807       "Classical.choice",
14808       "Quot.sound"
14809     ],
14810     "in_project_namespace": true,
14811     "kind": "definition",
14812     "module": "PaperIRelease.PacketTopologyGeneral",
14813     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM",
14814     "runtime_only": false
14815   },
14816   {
14817     "axioms": [
14818       "propext",
14819       "Classical.choice",
14820       "Quot.sound"
14821     ],
14822     "in_project_namespace": true,
14823     "kind": "definition",
14824     "module": "PaperIRelease.TopologyCategories",
14825     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.noConfusion",
14826     "runtime_only": false
14827   },
14828   {
14829     "axioms": [
14830       "propext",
14831       "Classical.choice",
14832       "Quot.sound"
14833     ],
14834     "in_project_namespace": false,
14835     "kind": "theorem",
14836     "module": "PaperIRelease.TopologyPresentations",
14837     "name": "PaperIRelease.TopologyDenseCompletion.completedFreePresentation._proof_1",
14838     "runtime_only": false
14839   },
14840   {
14841     "axioms": [
14842       "propext"
14843     ],
14844     "in_project_namespace": true,
14845     "kind": "theorem",
14846     "module": "PaperIRelease.CategoryExport",
14847     "name": "Komorebi.PaperIRelease.CategoryExport.additive_equation_transport",
14848     "runtime_only": false
14849   },
14850   {
14851     "axioms": [
14852       "propext",
14853       "Classical.choice",
14854       "Quot.sound"
14855     ],
14856     "in_project_namespace": true,
14857     "kind": "theorem",
14858     "module": "KomorebiVerification.EllipticAlgorithms",
14859     "name": "Komorebi.EllipticCoordinates.P0.eq_1",
14860     "runtime_only": false
14861   },
14862   {
14863     "axioms": [
14864       "propext",
14865       "Classical.choice",
14866       "Quot.sound"
14867     ],
14868     "in_project_namespace": true,
14869     "kind": "definition",
14870     "module": "PaperIRelease.GrammarIdeal",
14871     "name": "Komorebi.PaperIRelease.GrammarAlgebra.presentedToIdeal",
14872     "runtime_only": false
14873   },
14874   {
14875     "axioms": [
14876       "propext",
14877       "Classical.choice",
14878       "Quot.sound"
14879     ],
14880     "in_project_namespace": true,
14881     "kind": "definition",
14882     "module": "KomorebiVerification.ProjectorCore",
14883     "name": "Komorebi.Quantum.logPhase",
14884     "runtime_only": false
14885   },
14886   {
14887     "axioms": [],
14888     "in_project_namespace": true,
14889     "kind": "definition",
14890     "module": "KomorebiVerification.ProjectorCore",
14891     "name": "Komorebi.instDecidableEqClaimKind",
14892     "runtime_only": false
14893   },
14894   {
14895     "axioms": [
14896       "propext",
14897       "Classical.choice",
14898       "Quot.sound"
14899     ],
14900     "in_project_namespace": true,
14901     "kind": "theorem",
14902     "module": "KomorebiVerification.SemisimpleCompletion",
14903     "name": "Komorebi.SemisimpleCompletion.multiplicity_obstruction",
14904     "runtime_only": false
14905   },
14906   {
14907     "axioms": [
14908       "propext",
14909       "Classical.choice",
14910       "Quot.sound"
14911     ],
14912     "in_project_namespace": true,
14913     "kind": "theorem",
14914     "module": "PaperICompletion3.PrimarySeedFormula",
14915     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.operator_seedNumber_isLeast_of_polynomialModule",
14916     "runtime_only": false
14917   },
14918   {
14919     "axioms": [
14920       "propext",
14921       "Classical.choice",
14922       "Quot.sound"
14923     ],
14924     "in_project_namespace": true,
14925     "kind": "theorem",
14926     "module": "PaperIRelease.TensorPackets",
14927     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_6",
14928     "runtime_only": false
14929   },
14930   {
14931     "axioms": [
14932       "propext",
14933       "Quot.sound"
14934     ],
14935     "in_project_namespace": true,
14936     "kind": "theorem",
14937     "module": "PaperIRelease.ScalarExtension",
14938     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_1",
14939     "runtime_only": false
14940   },
14941   {
14942     "axioms": [],
14943     "in_project_namespace": true,
14944     "kind": "constructor",
14945     "module": "KomorebiVerification.ProjectorCore",
14946     "name": "Komorebi.FormalizationStatus.kernelChecked",
14947     "runtime_only": false
14948   },
14949   {
14950     "axioms": [
14951       "propext",
14952       "Classical.choice",
14953       "Quot.sound"
14954     ],
14955     "in_project_namespace": true,
14956     "kind": "theorem",
14957     "module": "KomorebiVerification.TopologicalCompletion",
14958     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_6",
14959     "runtime_only": false
14960   },
14961   {
14962     "axioms": [
14963       "propext",
14964       "Classical.choice",
14965       "Quot.sound"
14966     ],
14967     "in_project_namespace": true,
14968     "kind": "definition",
14969     "module": "PaperIRelease.CoordinateTransport",
14970     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv",
14971     "runtime_only": false
14972   },
14973   {
14974     "axioms": [
14975       "propext",
14976       "Classical.choice",
14977       "Quot.sound"
14978     ],
14979     "in_project_namespace": true,
14980     "kind": "theorem",
14981     "module": "PaperIRelease.GeneralFiniteCompletion",
14982     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_4",
14983     "runtime_only": false
14984   },
14985   {
14986     "axioms": [
14987       "propext",
14988       "Classical.choice",
14989       "Quot.sound"
14990     ],
14991     "in_project_namespace": true,
14992     "kind": "theorem",
14993     "module": "KomorebiVerification.TopologicalCompletion",
14994     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_intertwines",
14995     "runtime_only": false
14996   },
14997   {
14998     "axioms": [
14999       "propext",
15000       "Quot.sound"
15001     ],
15002     "in_project_namespace": true,
15003     "kind": "theorem",
15004     "module": "PaperIRelease.AlgebraPreorder",
15005     "name": "Komorebi.PaperIRelease.strictIdeal_power_mem._proof_1_2",
15006     "runtime_only": false
15007   },
15008   {
15009     "axioms": [
15010       "propext",
15011       "Classical.choice",
15012       "Quot.sound"
15013     ],
15014     "in_project_namespace": true,
15015     "kind": "theorem",
15016     "module": "PaperIRelease.GrammarAlgebra",
15017     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.injEq",
15018     "runtime_only": false
15019   },
15020   {
15021     "axioms": [
15022       "propext",
15023       "Classical.choice",
15024       "Quot.sound"
15025     ],
15026     "in_project_namespace": true,
15027     "kind": "theorem",
15028     "module": "PaperICompletion.CyclicClassification",
15029     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_4",
15030     "runtime_only": false
15031   },
15032   {
15033     "axioms": [
15034       "propext",
15035       "Classical.choice",
15036       "Quot.sound"
15037     ],
15038     "in_project_namespace": false,
15039     "kind": "theorem",
15040     "module": "PaperIRelease.TopologyCountablePackets",
15041     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_3",
15042     "runtime_only": false
15043   },
15044   {
15045     "axioms": [
15046       "propext",
15047       "Classical.choice",
15048       "Quot.sound"
15049     ],
15050     "in_project_namespace": true,
15051     "kind": "definition",
15052     "module": "PaperICompletion4.OperatorIntrinsicFormula",
15053     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsicSeedMaximum.match_1_1",
15054     "runtime_only": false
15055   },
15056   {
15057     "axioms": [
15058       "propext",
15059       "Quot.sound"
15060     ],
15061     "in_project_namespace": true,
15062     "kind": "definition",
15063     "module": "PaperIRelease.GrammarAlgebra",
15064     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertexWord",
15065     "runtime_only": false
15066   },
15067   {
15068     "axioms": [
15069       "propext",
15070       "Classical.choice",
15071       "Quot.sound"
15072     ],
15073     "in_project_namespace": true,
15074     "kind": "theorem",
15075     "module": "PaperIRelease.PolynomialMonic",
15076     "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec_injective",
15077     "runtime_only": false
15078   },
15079   {
15080     "axioms": [
15081       "propext",
15082       "Classical.choice",
15083       "Quot.sound"
15084     ],
15085     "in_project_namespace": true,
15086     "kind": "constructor",
15087     "module": "KomorebiVerification.PacketNaturalityCompletion",
15088     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk",
15089     "runtime_only": false
15090   },
15091   {
15092     "axioms": [
15093       "propext",
15094       "Classical.choice",
15095       "Quot.sound"
15096     ],
15097     "in_project_namespace": true,
15098     "kind": "theorem",
15099     "module": "PaperIRelease.PacketAggregation",
15100     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_4",
15101     "runtime_only": false
15102   },
15103   {
15104     "axioms": [
15105       "propext",
15106       "Classical.choice",
15107       "Quot.sound"
15108     ],
15109     "in_project_namespace": false,
15110     "kind": "theorem",
15111     "module": "PaperIRelease.TopologyDenseCompletion",
15112     "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_apply_mk",
15113     "runtime_only": false
15114   },
15115   {
15116     "axioms": [
15117       "propext",
15118       "Classical.choice",
15119       "Quot.sound"
15120     ],
15121     "in_project_namespace": false,
15122     "kind": "theorem",
15123     "module": "PaperIRelease.TopologyCountablePackets",
15124     "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace.ext_iff",
15125     "runtime_only": false
15126   },
15127   {
15128     "axioms": [
15129       "propext",
15130       "Quot.sound"
15131     ],
15132     "in_project_namespace": true,
15133     "kind": "theorem",
15134     "module": "KomorebiVerification.ProjectorCore",
15135     "name": "Komorebi.Seed.algebraicHull.eq_1",
15136     "runtime_only": false
15137   },
15138   {
15139     "axioms": [
15140       "propext",
15141       "Classical.choice",
15142       "Quot.sound"
15143     ],
15144     "in_project_namespace": true,
15145     "kind": "definition",
15146     "module": "PaperICompletion3.OperatorPrimaryAPI",
15147     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.prime",
15148     "runtime_only": false
15149   },
15150   {
15151     "axioms": [
15152       "propext",
15153       "Classical.choice",
15154       "Quot.sound"
15155     ],
15156     "in_project_namespace": false,
15157     "kind": "theorem",
15158     "module": "PaperIRelease.TopologyCountablePackets",
15159     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv_apply",
15160     "runtime_only": false
15161   },
15162   {
15163     "axioms": [],
15164     "in_project_namespace": true,
15165     "kind": "recursor",
15166     "module": "KomorebiVerification.ProjectorCore",
15167     "name": "Komorebi.Seed.OperatorRelation.rec",
15168     "runtime_only": false
15169   },
15170   {
15171     "axioms": [
15172       "propext",
15173       "Classical.choice",
15174       "Quot.sound"
15175     ],
15176     "in_project_namespace": false,
15177     "kind": "theorem",
15178     "module": "PaperIRelease.TopologyUnconditional",
15179     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedSpace._proof_1",
15180     "runtime_only": false
15181   },
15182   {
15183     "axioms": [
15184       "propext",
15185       "Classical.choice",
15186       "Quot.sound"
15187     ],
15188     "in_project_namespace": true,
15189     "kind": "definition",
15190     "module": "PaperIRelease.GeneralConditionedCoordinates",
15191     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.coordinateOperator",
15192     "runtime_only": false
15193   },
15194   {
15195     "axioms": [
15196       "propext",
15197       "Classical.choice",
15198       "Quot.sound"
15199     ],
15200     "in_project_namespace": true,
15201     "kind": "theorem",
15202     "module": "PaperIRelease.TopologyCategories",
15203     "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_3",
15204     "runtime_only": false
15205   },
15206   {
15207     "axioms": [
15208       "propext",
15209       "Quot.sound"
15210     ],
15211     "in_project_namespace": true,
15212     "kind": "theorem",
15213     "module": "KomorebiVerification.SingleOperatorGraph",
15214     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_12",
15215     "runtime_only": false
15216   },
15217   {
15218     "axioms": [
15219       "propext",
15220       "Classical.choice",
15221       "Quot.sound"
15222     ],
15223     "in_project_namespace": true,
15224     "kind": "theorem",
15225     "module": "PaperIRelease.GrammarTyped",
15226     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_arrow",
15227     "runtime_only": false
15228   },
15229   {
15230     "axioms": [],
15231     "in_project_namespace": true,
15232     "kind": "definition",
15233     "module": "KomorebiVerification.ProjectorCore",
15234     "name": "Komorebi.FormalizationStatus.encodedDefinition.elim",
15235     "runtime_only": false
15236   },
15237   {
15238     "axioms": [
15239       "propext"
15240     ],
15241     "in_project_namespace": true,
15242     "kind": "theorem",
15243     "module": "PaperIRelease.CategoryExport",
15244     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_3",
15245     "runtime_only": false
15246   },
15247   {
15248     "axioms": [
15249       "propext",
15250       "Classical.choice",
15251       "Quot.sound"
15252     ],
15253     "in_project_namespace": true,
15254     "kind": "theorem",
15255     "module": "PaperICompletion8.DivisionBlock",
15256     "name": "Komorebi.PaperICompletion8.DivisionBlock.oneBlock_seedFinrank_eq_ceilDiv",
15257     "runtime_only": false
15258   },
15259   {
15260     "axioms": [
15261       "propext",
15262       "Classical.choice",
15263       "Quot.sound"
15264     ],
15265     "in_project_namespace": false,
15266     "kind": "theorem",
15267     "module": "PaperIRelease.TopologyDenseCompletion",
15268     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_2",
15269     "runtime_only": false
15270   },
15271   {
15272     "axioms": [
15273       "propext",
15274       "Quot.sound"
15275     ],
15276     "in_project_namespace": true,
15277     "kind": "theorem",
15278     "module": "PaperIRelease.PacketDescent",
15279     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv._proof_2",
15280     "runtime_only": false
15281   },
15282   {
15283     "axioms": [],
15284     "in_project_namespace": true,
15285     "kind": "definition",
15286     "module": "KomorebiVerification.ProjectorCore",
15287     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff",
15288     "runtime_only": false
15289   },
15290   {
15291     "axioms": [
15292       "propext",
15293       "Quot.sound"
15294     ],
15295     "in_project_namespace": true,
15296     "kind": "theorem",
15297     "module": "KomorebiVerification.KernelAudit",
15298     "name": "Komorebi.Verification.parityAddress._proof_2",
15299     "runtime_only": false
15300   },
15301   {
15302     "axioms": [
15303       "propext",
15304       "Classical.choice",
15305       "Quot.sound"
15306     ],
15307     "in_project_namespace": true,
15308     "kind": "theorem",
15309     "module": "PaperIRelease.TensorPackets",
15310     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_2",
15311     "runtime_only": false
15312   },
15313   {
15314     "axioms": [
15315       "propext",
15316       "Classical.choice",
15317       "Quot.sound"
15318     ],
15319     "in_project_namespace": true,
15320     "kind": "theorem",
15321     "module": "PaperIRelease.GeneralNormedPackets",
15322     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis._proof_2",
15323     "runtime_only": false
15324   },
15325   {
15326     "axioms": [
15327       "propext",
15328       "Classical.choice",
15329       "Quot.sound"
15330     ],
15331     "in_project_namespace": true,
15332     "kind": "theorem",
15333     "module": "PaperIRelease.AlgebraPreorder",
15334     "name": "Komorebi.PaperIRelease.strictSupportPower_eq_bot",
15335     "runtime_only": false
15336   },
15337   {
15338     "axioms": [
15339       "propext",
15340       "Quot.sound"
15341     ],
15342     "in_project_namespace": true,
15343     "kind": "definition",
15344     "module": "PaperICompletion4.GroupedPrimary",
15345     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr",
15346     "runtime_only": false
15347   },
15348   {
15349     "axioms": [
15350       "propext",
15351       "Classical.choice",
15352       "Quot.sound"
15353     ],
15354     "in_project_namespace": true,
15355     "kind": "theorem",
15356     "module": "PaperICompletion4.IntrinsicPrimary",
15357     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal_ker",
15358     "runtime_only": false
15359   },
15360   {
15361     "axioms": [
15362       "propext",
15363       "Classical.choice",
15364       "Quot.sound"
15365     ],
15366     "in_project_namespace": true,
15367     "kind": "theorem",
15368     "module": "PaperICompletion3.InvariantFactorCount",
15369     "name": "Komorebi.PaperICompletion3.InvariantFactorCount.invariantFactor_operator_seedRanks",
15370     "runtime_only": false
15371   },
15372   {
15373     "axioms": [
15374       "propext",
15375       "Classical.choice",
15376       "Quot.sound"
15377     ],
15378     "in_project_namespace": true,
15379     "kind": "theorem",
15380     "module": "PaperIRelease.GrammarAlgebra",
15381     "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow.eq_1",
15382     "runtime_only": false
15383   },
15384   {
15385     "axioms": [
15386       "propext",
15387       "Classical.choice",
15388       "Quot.sound"
15389     ],
15390     "in_project_namespace": true,
15391     "kind": "definition",
15392     "module": "KomorebiVerification.ProjectorCore",
15393     "name": "Komorebi.Foundation.LinearProjectorFamily.casesOn",
15394     "runtime_only": false
15395   },
15396   {
15397     "axioms": [
15398       "propext",
15399       "Classical.choice",
15400       "Quot.sound"
15401     ],
15402     "in_project_namespace": false,
15403     "kind": "theorem",
15404     "module": "PaperIRelease.TopologyTransport",
15405     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_3",
15406     "runtime_only": false
15407   },
15408   {
15409     "axioms": [
15410       "propext",
15411       "Classical.choice",
15412       "Quot.sound"
15413     ],
15414     "in_project_namespace": true,
15415     "kind": "theorem",
15416     "module": "PaperIRelease.AlgebraTransfer",
15417     "name": "Komorebi.PaperIRelease.activeSources.eq_1",
15418     "runtime_only": false
15419   },
15420   {
15421     "axioms": [],
15422     "in_project_namespace": true,
15423     "kind": "definition",
15424     "module": "KomorebiVerification.ProjectorCore",
15425     "name": "Komorebi.ClaimRecord.source",
15426     "runtime_only": false
15427   },
15428   {
15429     "axioms": [],
15430     "in_project_namespace": true,
15431     "kind": "theorem",
15432     "module": "KomorebiVerification.ProjectorCore",
15433     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_def",
15434     "runtime_only": false
15435   },
15436   {
15437     "axioms": [
15438       "propext",
15439       "Classical.choice",
15440       "Quot.sound"
15441     ],
15442     "in_project_namespace": true,
15443     "kind": "definition",
15444     "module": "PaperICompletion3.OperatorPrimaryAPI",
15445     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk._flat_ctor",
15446     "runtime_only": false
15447   },
15448   {
15449     "axioms": [
15450       "propext",
15451       "Classical.choice",
15452       "Quot.sound"
15453     ],
15454     "in_project_namespace": true,
15455     "kind": "theorem",
15456     "module": "KomorebiVerification.EllipticAlgorithms",
15457     "name": "Komorebi.EllipticCoordinates.discriminant_ne_zero",
15458     "runtime_only": false
15459   },
15460   {
15461     "axioms": [
15462       "propext",
15463       "Classical.choice",
15464       "Quot.sound"
15465     ],
15466     "in_project_namespace": true,
15467     "kind": "theorem",
15468     "module": "PaperIRelease.AlgebraDiagonal",
15469     "name": "Komorebi.PaperIRelease.diagonalProjection._proof_2",
15470     "runtime_only": false
15471   },
15472   {
15473     "axioms": [
15474       "propext",
15475       "Classical.choice",
15476       "Quot.sound"
15477     ],
15478     "in_project_namespace": true,
15479     "kind": "theorem",
15480     "module": "PaperICompletion.CyclicClassification",
15481     "name": "Komorebi.PaperICompletion.CyclicClassification.minpoly_eq_charpoly_of_cyclic",
15482     "runtime_only": false
15483   },
15484   {
15485     "axioms": [
15486       "propext",
15487       "Classical.choice",
15488       "Quot.sound"
15489     ],
15490     "in_project_namespace": true,
15491     "kind": "theorem",
15492     "module": "PaperIRelease.GrammarEquivalence",
15493     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ext_iff",
15494     "runtime_only": false
15495   },
15496   {
15497     "axioms": [],
15498     "in_project_namespace": true,
15499     "kind": "definition",
15500     "module": "KomorebiVerification.SemisimpleCompletion",
15501     "name": "Komorebi.SemisimpleCompletion.BlockModule",
15502     "runtime_only": false
15503   },
15504   {
15505     "axioms": [
15506       "propext",
15507       "Classical.choice",
15508       "Quot.sound"
15509     ],
15510     "in_project_namespace": true,
15511     "kind": "definition",
15512     "module": "KomorebiVerification.EllipticAlgorithms",
15513     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter",
15514     "runtime_only": false
15515   },
15516   {
15517     "axioms": [
15518       "propext",
15519       "Classical.choice",
15520       "Quot.sound"
15521     ],
15522     "in_project_namespace": true,
15523     "kind": "theorem",
15524     "module": "PaperICompletion4.OperatorIntrinsicFormula",
15525     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_of_span_eq",
15526     "runtime_only": false
15527   },
15528   {
15529     "axioms": [
15530       "propext",
15531       "Quot.sound"
15532     ],
15533     "in_project_namespace": true,
15534     "kind": "theorem",
15535     "module": "KomorebiVerification.PacketNaturalityCompletion",
15536     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule.eq_1",
15537     "runtime_only": false
15538   },
15539   {
15540     "axioms": [
15541       "propext",
15542       "Classical.choice",
15543       "Quot.sound"
15544     ],
15545     "in_project_namespace": true,
15546     "kind": "definition",
15547     "module": "KomorebiVerification.ProjectorCore",
15548     "name": "Komorebi.Foundation.LinearProjectorFamily.analyze",
15549     "runtime_only": false
15550   },
15551   {
15552     "axioms": [
15553       "propext",
15554       "Classical.choice",
15555       "Quot.sound"
15556     ],
15557     "in_project_namespace": true,
15558     "kind": "theorem",
15559     "module": "PaperIRelease.PacketBoundaryTests",
15560     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_submodule_bounded_equiv_mk",
15561     "runtime_only": false
15562   },
15563   {
15564     "axioms": [],
15565     "in_project_namespace": true,
15566     "kind": "definition",
15567     "module": "KomorebiVerification.ProjectorCore",
15568     "name": "Komorebi.Algebra.IsUpperTriangular",
15569     "runtime_only": false
15570   },
15571   {
15572     "axioms": [
15573       "propext",
15574       "Classical.choice",
15575       "Quot.sound"
15576     ],
15577     "in_project_namespace": true,
15578     "kind": "theorem",
15579     "module": "PaperICompletion7.ModuleTop",
15580     "name": "Komorebi.PaperICompletion7.ModuleTop.image_generates_iff",
15581     "runtime_only": false
15582   },
15583   {
15584     "axioms": [
15585       "propext",
15586       "Classical.choice",
15587       "Quot.sound"
15588     ],
15589     "in_project_namespace": true,
15590     "kind": "theorem",
15591     "module": "KomorebiVerification.PaperITransport",
15592     "name": "Komorebi.Foundation.transferBlock_natural",
15593     "runtime_only": false
15594   },
15595   {
15596     "axioms": [
15597       "propext",
15598       "Classical.choice",
15599       "Quot.sound"
15600     ],
15601     "in_project_namespace": true,
15602     "kind": "theorem",
15603     "module": "PaperIRelease.TensorPackets",
15604     "name": "Komorebi.PaperIRelease.dualPackets._proof_3",
15605     "runtime_only": false
15606   },
15607   {
15608     "axioms": [
15609       "propext",
15610       "Classical.choice",
15611       "Quot.sound"
15612     ],
15613     "in_project_namespace": false,
15614     "kind": "theorem",
15615     "module": "PaperIRelease.TopologyDenseCompletion",
15616     "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_dense",
15617     "runtime_only": false
15618   },
15619   {
15620     "axioms": [
15621       "propext",
15622       "Classical.choice",
15623       "Quot.sound"
15624     ],
15625     "in_project_namespace": true,
15626     "kind": "theorem",
15627     "module": "KomorebiVerification.ExactCoordinates",
15628     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis_rangeAnalysis",
15629     "runtime_only": false
15630   },
15631   {
15632     "axioms": [
15633       "propext",
15634       "Classical.choice",
15635       "Quot.sound"
15636     ],
15637     "in_project_namespace": true,
15638     "kind": "definition",
15639     "module": "KomorebiVerification.SeedRankBasics",
15640     "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv",
15641     "runtime_only": false
15642   },
15643   {
15644     "axioms": [
15645       "propext",
15646       "Classical.choice",
15647       "Quot.sound"
15648     ],
15649     "in_project_namespace": false,
15650     "kind": "definition",
15651     "module": "PaperIRelease.TopologyUnconditional",
15652     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_3",
15653     "runtime_only": false
15654   },
15655   {
15656     "axioms": [
15657       "propext",
15658       "Quot.sound"
15659     ],
15660     "in_project_namespace": true,
15661     "kind": "theorem",
15662     "module": "PaperIRelease.GrammarModules",
15663     "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_1",
15664     "runtime_only": false
15665   },
15666   {
15667     "axioms": [
15668       "propext",
15669       "Classical.choice",
15670       "Quot.sound"
15671     ],
15672     "in_project_namespace": true,
15673     "kind": "theorem",
15674     "module": "PaperIRelease.GrammarEquivalence",
15675     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.sizeOf_spec",
15676     "runtime_only": false
15677   },
15678   {
15679     "axioms": [
15680       "propext",
15681       "Classical.choice",
15682       "Quot.sound"
15683     ],
15684     "in_project_namespace": true,
15685     "kind": "inductive",
15686     "module": "KomorebiVerification.TopologicalCompletion",
15687     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation",
15688     "runtime_only": false
15689   },
15690   {
15691     "axioms": [
15692       "propext",
15693       "Classical.choice",
15694       "Quot.sound"
15695     ],
15696     "in_project_namespace": true,
15697     "kind": "theorem",
15698     "module": "KomorebiVerification.SingleOperatorGraph",
15699     "name": "Komorebi.SingleOperatorGraph.seedNumber_one_isLeast_of_cyclic",
15700     "runtime_only": false
15701   },
15702   {
15703     "axioms": [
15704       "propext",
15705       "Quot.sound"
15706     ],
15707     "in_project_namespace": true,
15708     "kind": "theorem",
15709     "module": "PaperIRelease.PacketCorners",
15710     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_2",
15711     "runtime_only": false
15712   },
15713   {
15714     "axioms": [
15715       "propext",
15716       "Classical.choice",
15717       "Quot.sound"
15718     ],
15719     "in_project_namespace": true,
15720     "kind": "theorem",
15721     "module": "PaperIRelease.GeneralNormedPackets",
15722     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis._proof_1",
15723     "runtime_only": false
15724   },
15725   {
15726     "axioms": [],
15727     "in_project_namespace": true,
15728     "kind": "theorem",
15729     "module": "KomorebiVerification.ProjectorCore",
15730     "name": "Komorebi.FiniteDifference.forwardDiff.eq_1",
15731     "runtime_only": false
15732   },
15733   {
15734     "axioms": [
15735       "propext",
15736       "Classical.choice",
15737       "Quot.sound"
15738     ],
15739     "in_project_namespace": true,
15740     "kind": "theorem",
15741     "module": "PaperIRelease.GrammarEquivalence",
15742     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_8",
15743     "runtime_only": false
15744   },
15745   {
15746     "axioms": [],
15747     "in_project_namespace": true,
15748     "kind": "theorem",
15749     "module": "KomorebiVerification.ProjectorCore",
15750     "name": "Komorebi.FormalizationStatus.numericalOnly.sizeOf_spec",
15751     "runtime_only": false
15752   },
15753   {
15754     "axioms": [
15755       "propext",
15756       "Classical.choice",
15757       "Quot.sound"
15758     ],
15759     "in_project_namespace": true,
15760     "kind": "definition",
15761     "module": "PaperIRelease.TopologyCategories",
15762     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.recOn",
15763     "runtime_only": false
15764   },
15765   {
15766     "axioms": [
15767       "propext",
15768       "Quot.sound"
15769     ],
15770     "in_project_namespace": true,
15771     "kind": "theorem",
15772     "module": "PaperIRelease.GrammarPaths",
15773     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._proof_1",
15774     "runtime_only": false
15775   },
15776   {
15777     "axioms": [
15778       "propext",
15779       "Classical.choice",
15780       "Quot.sound"
15781     ],
15782     "in_project_namespace": true,
15783     "kind": "definition",
15784     "module": "KomorebiVerification.SemisimpleCompletion",
15785     "name": "Komorebi.SemisimpleCompletion.multiplicityBlockModuleAction",
15786     "runtime_only": false
15787   },
15788   {
15789     "axioms": [
15790       "propext",
15791       "Quot.sound"
15792     ],
15793     "in_project_namespace": true,
15794     "kind": "theorem",
15795     "module": "PaperIRelease.GrammarModules",
15796     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_5",
15797     "runtime_only": false
15798   },
15799   {
15800     "axioms": [
15801       "propext",
15802       "Classical.choice",
15803       "Quot.sound"
15804     ],
15805     "in_project_namespace": false,
15806     "kind": "theorem",
15807     "module": "PaperIRelease.TopologyUnconditionalBridge",
15808     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_2",
15809     "runtime_only": false
15810   },
15811   {
15812     "axioms": [
15813       "propext",
15814       "Classical.choice",
15815       "Quot.sound"
15816     ],
15817     "in_project_namespace": true,
15818     "kind": "theorem",
15819     "module": "PaperIRelease.TopologyCategories",
15820     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.map_closedHull",
15821     "runtime_only": false
15822   },
15823   {
15824     "axioms": [
15825       "propext",
15826       "Classical.choice",
15827       "Quot.sound"
15828     ],
15829     "in_project_namespace": true,
15830     "kind": "definition",
15831     "module": "PaperICompletion.ConditionedCoordinates",
15832     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator",
15833     "runtime_only": false
15834   },
15835   {
15836     "axioms": [
15837       "propext",
15838       "Classical.choice",
15839       "Quot.sound"
15840     ],
15841     "in_project_namespace": true,
15842     "kind": "theorem",
15843     "module": "KomorebiVerification.ExactCoordinates",
15844     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates._proof_2",
15845     "runtime_only": false
15846   },
15847   {
15848     "axioms": [
15849       "propext",
15850       "Classical.choice",
15851       "Quot.sound"
15852     ],
15853     "in_project_namespace": true,
15854     "kind": "definition",
15855     "module": "PaperIRelease.PacketSourceLower",
15856     "name": "Komorebi.PaperIRelease.localNonzeroSeeds",
15857     "runtime_only": false
15858   },
15859   {
15860     "axioms": [
15861       "propext",
15862       "Classical.choice",
15863       "Quot.sound"
15864     ],
15865     "in_project_namespace": false,
15866     "kind": "definition",
15867     "module": "PaperIRelease.TopologyUnconditional",
15868     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets._sizeOf_inst",
15869     "runtime_only": false
15870   },
15871   {
15872     "axioms": [
15873       "propext",
15874       "Classical.choice",
15875       "Quot.sound"
15876     ],
15877     "in_project_namespace": true,
15878     "kind": "theorem",
15879     "module": "KomorebiVerification.PacketNaturalityCompletion",
15880     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock_supported",
15881     "runtime_only": false
15882   },
15883   {
15884     "axioms": [
15885       "propext",
15886       "Classical.choice",
15887       "Quot.sound"
15888     ],
15889     "in_project_namespace": true,
15890     "kind": "theorem",
15891     "module": "KomorebiVerification.SingleOperatorGraph",
15892     "name": "Komorebi.SingleOperatorGraph.restrictScalars_span_operatorAlgebra_eq_span_orbit",
15893     "runtime_only": false
15894   },
15895   {
15896     "axioms": [
15897       "propext",
15898       "Quot.sound"
15899     ],
15900     "in_project_namespace": true,
15901     "kind": "theorem",
15902     "module": "KomorebiVerification.SingleOperatorGraph",
15903     "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_1",
15904     "runtime_only": false
15905   },
15906   {
15907     "axioms": [
15908       "propext",
15909       "Classical.choice",
15910       "Quot.sound"
15911     ],
15912     "in_project_namespace": true,
15913     "kind": "theorem",
15914     "module": "PaperICompletion8.SemisimpleFormula",
15915     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.split_originalRing_top_seedRank",
15916     "runtime_only": false
15917   },
15918   {
15919     "axioms": [
15920       "propext",
15921       "Classical.choice",
15922       "Quot.sound"
15923     ],
15924     "in_project_namespace": true,
15925     "kind": "theorem",
15926     "module": "PaperIRelease.PacketTopology",
15927     "name": "Komorebi.Foundation.LinearProjectorFamily.projectToPacketQuotient._proof_1",
15928     "runtime_only": false
15929   },
15930   {
15931     "axioms": [
15932       "propext",
15933       "Classical.choice",
15934       "Quot.sound"
15935     ],
15936     "in_project_namespace": true,
15937     "kind": "theorem",
15938     "module": "KomorebiVerification.PacketNaturalityCompletion",
15939     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.packet_natural_apply",
15940     "runtime_only": false
15941   },
15942   {
15943     "axioms": [
15944       "propext",
15945       "Classical.choice",
15946       "Quot.sound"
15947     ],
15948     "in_project_namespace": true,
15949     "kind": "definition",
15950     "module": "KomorebiVerification.EllipticAlgorithms",
15951     "name": "Komorebi.EllipticCoordinates.curveWeight",
15952     "runtime_only": false
15953   },
15954   {
15955     "axioms": [
15956       "propext",
15957       "Quot.sound"
15958     ],
15959     "in_project_namespace": true,
15960     "kind": "theorem",
15961     "module": "PaperIRelease.GrammarModules",
15962     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_2",
15963     "runtime_only": false
15964   },
15965   {
15966     "axioms": [],
15967     "in_project_namespace": true,
15968     "kind": "definition",
15969     "module": "KomorebiVerification.ProjectorCore",
15970     "name": "Komorebi.FormalizationStatus._sizeOf_inst",
15971     "runtime_only": false
15972   },
15973   {
15974     "axioms": [
15975       "propext",
15976       "Classical.choice",
15977       "Quot.sound"
15978     ],
15979     "in_project_namespace": true,
15980     "kind": "definition",
15981     "module": "KomorebiVerification.ProjectorCore",
15982     "name": "Komorebi.Quantum.finiteAmplitude",
15983     "runtime_only": false
15984   },
15985   {
15986     "axioms": [
15987       "propext",
15988       "Classical.choice",
15989       "Quot.sound"
15990     ],
15991     "in_project_namespace": true,
15992     "kind": "theorem",
15993     "module": "PaperICompletion4.ResidueQuotient",
15994     "name": "Komorebi.PaperICompletion4.ResidueQuotient.factor_eq_zero_iff_smul",
15995     "runtime_only": false
15996   },
15997   {
15998     "axioms": [
15999       "propext",
16000       "Quot.sound"
16001     ],
16002     "in_project_namespace": true,
16003     "kind": "theorem",
16004     "module": "PaperIRelease.GrammarAlgebra",
16005     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.injEq",
16006     "runtime_only": false
16007   },
16008   {
16009     "axioms": [
16010       "propext",
16011       "Classical.choice",
16012       "Quot.sound"
16013     ],
16014     "in_project_namespace": true,
16015     "kind": "theorem",
16016     "module": "PaperIRelease.PacketLocalRank",
16017     "name": "Komorebi.PaperIRelease.local_proj_zero_iff",
16018     "runtime_only": false
16019   },
16020   {
16021     "axioms": [
16022       "propext",
16023       "Classical.choice",
16024       "Quot.sound"
16025     ],
16026     "in_project_namespace": true,
16027     "kind": "theorem",
16028     "module": "PaperIRelease.TopologyCategories",
16029     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.sizeOf_spec",
16030     "runtime_only": false
16031   },
16032   {
16033     "axioms": [
16034       "propext",
16035       "Classical.choice",
16036       "Quot.sound"
16037     ],
16038     "in_project_namespace": true,
16039     "kind": "theorem",
16040     "module": "PaperIRelease.PacketAggregation",
16041     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_2",
16042     "runtime_only": false
16043   },
16044   {
16045     "axioms": [
16046       "propext",
16047       "Classical.choice",
16048       "Quot.sound"
16049     ],
16050     "in_project_namespace": true,
16051     "kind": "theorem",
16052     "module": "PaperIRelease.AlgebraClassGrouping",
16053     "name": "Komorebi.PaperIRelease.preorderDiagonalHom_eq_zero_iff",
16054     "runtime_only": false
16055   },
16056   {
16057     "axioms": [
16058       "propext",
16059       "Quot.sound"
16060     ],
16061     "in_project_namespace": true,
16062     "kind": "theorem",
16063     "module": "KomorebiVerification.ResidueProjectors",
16064     "name": "Komorebi.Residue.residueProj_apply",
16065     "runtime_only": false
16066   },
16067   {
16068     "axioms": [
16069       "propext",
16070       "Classical.choice",
16071       "Quot.sound"
16072     ],
16073     "in_project_namespace": true,
16074     "kind": "definition",
16075     "module": "PaperIRelease.AlgebraClassGrouping",
16076     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv",
16077     "runtime_only": false
16078   },
16079   {
16080     "axioms": [
16081       "propext",
16082       "Quot.sound"
16083     ],
16084     "in_project_namespace": true,
16085     "kind": "theorem",
16086     "module": "PaperIRelease.AlgebraQuotient",
16087     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_3",
16088     "runtime_only": false
16089   },
16090   {
16091     "axioms": [
16092       "propext",
16093       "Classical.choice",
16094       "Quot.sound"
16095     ],
16096     "in_project_namespace": true,
16097     "kind": "theorem",
16098     "module": "KomorebiVerification.TopologicalCompletion",
16099     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv._proof_1",
16100     "runtime_only": false
16101   },
16102   {
16103     "axioms": [],
16104     "in_project_namespace": true,
16105     "kind": "definition",
16106     "module": "KomorebiVerification.ProjectorCore",
16107     "name": "Komorebi.ClaimKind._sizeOf_inst",
16108     "runtime_only": false
16109   },
16110   {
16111     "axioms": [
16112       "propext",
16113       "Classical.choice",
16114       "Quot.sound"
16115     ],
16116     "in_project_namespace": true,
16117     "kind": "theorem",
16118     "module": "PaperIRelease.PacketTopology",
16119     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseAmbient._proof_1",
16120     "runtime_only": false
16121   },
16122   {
16123     "axioms": [
16124       "propext",
16125       "Quot.sound"
16126     ],
16127     "in_project_namespace": true,
16128     "kind": "definition",
16129     "module": "PaperIRelease.GrammarModules",
16130     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject._sizeOf_inst",
16131     "runtime_only": false
16132   },
16133   {
16134     "axioms": [
16135       "propext",
16136       "Classical.choice",
16137       "Quot.sound"
16138     ],
16139     "in_project_namespace": true,
16140     "kind": "theorem",
16141     "module": "PaperIRelease.GrammarAlgebra",
16142     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_2",
16143     "runtime_only": false
16144   },
16145   {
16146     "axioms": [
16147       "propext",
16148       "Classical.choice",
16149       "Quot.sound"
16150     ],
16151     "in_project_namespace": true,
16152     "kind": "theorem",
16153     "module": "KomorebiVerification.EllipticAlgorithms",
16154     "name": "Komorebi.FiniteAlgorithms.orbitHull_algorithm_terminates_and_correct",
16155     "runtime_only": false
16156   },
16157   {
16158     "axioms": [
16159       "propext",
16160       "Quot.sound"
16161     ],
16162     "in_project_namespace": true,
16163     "kind": "definition",
16164     "module": "PaperIRelease.GrammarTyped",
16165     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.noConfusionType",
16166     "runtime_only": false
16167   },
16168   {
16169     "axioms": [],
16170     "in_project_namespace": true,
16171     "kind": "definition",
16172     "module": "KomorebiVerification.ProjectorCore",
16173     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._f",
16174     "runtime_only": false
16175   },
16176   {
16177     "axioms": [
16178       "propext",
16179       "Classical.choice",
16180       "Quot.sound"
16181     ],
16182     "in_project_namespace": true,
16183     "kind": "definition",
16184     "module": "KomorebiVerification.ProjectorCore",
16185     "name": "Komorebi.Foundation.transferBlock",
16186     "runtime_only": false
16187   },
16188   {
16189     "axioms": [
16190       "propext",
16191       "Classical.choice",
16192       "Quot.sound"
16193     ],
16194     "in_project_namespace": true,
16195     "kind": "theorem",
16196     "module": "PaperIRelease.GrammarAlgebra",
16197     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors._proof_2",
16198     "runtime_only": false
16199   },
16200   {
16201     "axioms": [
16202       "propext",
16203       "Classical.choice",
16204       "Quot.sound"
16205     ],
16206     "in_project_namespace": true,
16207     "kind": "theorem",
16208     "module": "PaperIRelease.BoundedStar",
16209     "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_1",
16210     "runtime_only": false
16211   },
16212   {
16213     "axioms": [
16214       "propext",
16215       "Classical.choice",
16216       "Quot.sound"
16217     ],
16218     "in_project_namespace": true,
16219     "kind": "definition",
16220     "module": "PaperIRelease.PacketTopology",
16221     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseCLM",
16222     "runtime_only": false
16223   },
16224   {
16225     "axioms": [
16226       "propext",
16227       "Classical.choice",
16228       "Quot.sound"
16229     ],
16230     "in_project_namespace": true,
16231     "kind": "theorem",
16232     "module": "PaperIRelease.PacketSourceLower",
16233     "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_3",
16234     "runtime_only": false
16235   },
16236   {
16237     "axioms": [
16238       "propext",
16239       "Classical.choice",
16240       "Quot.sound"
16241     ],
16242     "in_project_namespace": true,
16243     "kind": "theorem",
16244     "module": "KomorebiVerification.PacketNaturalityCompletion",
16245     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.full_transfer_edge_zero_pattern_correspondence",
16246     "runtime_only": false
16247   },
16248   {
16249     "axioms": [
16250       "propext",
16251       "Classical.choice",
16252       "Quot.sound"
16253     ],
16254     "in_project_namespace": true,
16255     "kind": "theorem",
16256     "module": "PaperIRelease.PacketDescent",
16257     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_3",
16258     "runtime_only": false
16259   },
16260   {
16261     "axioms": [
16262       "propext",
16263       "Classical.choice",
16264       "Quot.sound"
16265     ],
16266     "in_project_namespace": false,
16267     "kind": "theorem",
16268     "module": "PaperIRelease.TopologyCountablePackets",
16269     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_2",
16270     "runtime_only": false
16271   },
16272   {
16273     "axioms": [
16274       "propext",
16275       "Classical.choice",
16276       "Quot.sound"
16277     ],
16278     "in_project_namespace": false,
16279     "kind": "theorem",
16280     "module": "PaperIRelease.TopologyDenseCompletion",
16281     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._simp_1",
16282     "runtime_only": false
16283   },
16284   {
16285     "axioms": [
16286       "propext",
16287       "Quot.sound"
16288     ],
16289     "in_project_namespace": true,
16290     "kind": "theorem",
16291     "module": "PaperIRelease.TensorPackets",
16292     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_5",
16293     "runtime_only": false
16294   },
16295   {
16296     "axioms": [
16297       "propext",
16298       "Classical.choice",
16299       "Quot.sound"
16300     ],
16301     "in_project_namespace": true,
16302     "kind": "theorem",
16303     "module": "PaperICompletion5.CyclicGeometricCriterion",
16304     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.spectralSeedMaximum_attained",
16305     "runtime_only": false
16306   },
16307   {
16308     "axioms": [],
16309     "in_project_namespace": true,
16310     "kind": "theorem",
16311     "module": "PaperIRelease.CategoryExport",
16312     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.sizeOf_spec",
16313     "runtime_only": false
16314   },
16315   {
16316     "axioms": [
16317       "propext",
16318       "Classical.choice",
16319       "Quot.sound"
16320     ],
16321     "in_project_namespace": true,
16322     "kind": "theorem",
16323     "module": "PaperIRelease.PacketTopologyGeneral",
16324     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorNormedHom._proof_2",
16325     "runtime_only": false
16326   },
16327   {
16328     "axioms": [
16329       "propext",
16330       "Classical.choice",
16331       "Quot.sound"
16332     ],
16333     "in_project_namespace": true,
16334     "kind": "theorem",
16335     "module": "KomorebiVerification.SeedRankBasics",
16336     "name": "Komorebi.SeedRankBasics.seedRank.eq_1",
16337     "runtime_only": false
16338   },
16339   {
16340     "axioms": [
16341       "propext",
16342       "Classical.choice",
16343       "Quot.sound"
16344     ],
16345     "in_project_namespace": false,
16346     "kind": "theorem",
16347     "module": "PaperIRelease.TopologySeedRank",
16348     "name": "PaperIRelease.TopologyTransport.seedRank_equiv",
16349     "runtime_only": false
16350   },
16351   {
16352     "axioms": [
16353       "propext",
16354       "Classical.choice",
16355       "Quot.sound"
16356     ],
16357     "in_project_namespace": true,
16358     "kind": "theorem",
16359     "module": "KomorebiVerification.PacketNaturalityCompletion",
16360     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock.eq_1",
16361     "runtime_only": false
16362   },
16363   {
16364     "axioms": [
16365       "propext",
16366       "Quot.sound"
16367     ],
16368     "in_project_namespace": true,
16369     "kind": "theorem",
16370     "module": "PaperIRelease.SeedOperations",
16371     "name": "Komorebi.PaperIRelease.SeedOperations.mem_vectorAnnihilator",
16372     "runtime_only": false
16373   },
16374   {
16375     "axioms": [
16376       "propext",
16377       "Classical.choice",
16378       "Quot.sound"
16379     ],
16380     "in_project_namespace": true,
16381     "kind": "theorem",
16382     "module": "PaperICompletion6.OneInvariantFactor",
16383     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.factor_eq_minpoly",
16384     "runtime_only": false
16385   },
16386   {
16387     "axioms": [
16388       "propext",
16389       "Classical.choice",
16390       "Quot.sound"
16391     ],
16392     "in_project_namespace": true,
16393     "kind": "definition",
16394     "module": "PaperIRelease.PacketExactSequence",
16395     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient",
16396     "runtime_only": false
16397   },
16398   {
16399     "axioms": [],
16400     "in_project_namespace": true,
16401     "kind": "theorem",
16402     "module": "PaperICompletion4.IntrinsicPrimary",
16403     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_1",
16404     "runtime_only": false
16405   },
16406   {
16407     "axioms": [
16408       "propext",
16409       "Classical.choice",
16410       "Quot.sound"
16411     ],
16412     "in_project_namespace": true,
16413     "kind": "theorem",
16414     "module": "KomorebiVerification.ExactCoordinates",
16415     "name": "Komorebi.Foundation.LinearProjectorFamily.proj_packet_eq_zero",
16416     "runtime_only": false
16417   },
16418   {
16419     "axioms": [
16420       "propext"
16421     ],
16422     "in_project_namespace": true,
16423     "kind": "theorem",
16424     "module": "KomorebiVerification.TopologicalCompletion",
16425     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula._simp_1_2",
16426     "runtime_only": false
16427   },
16428   {
16429     "axioms": [
16430       "propext",
16431       "Classical.choice",
16432       "Quot.sound"
16433     ],
16434     "in_project_namespace": true,
16435     "kind": "definition",
16436     "module": "PaperIRelease.PolynomialModule",
16437     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv",
16438     "runtime_only": false
16439   },
16440   {
16441     "axioms": [
16442       "propext",
16443       "Classical.choice",
16444       "Quot.sound"
16445     ],
16446     "in_project_namespace": true,
16447     "kind": "definition",
16448     "module": "PaperIRelease.TopologyCategories",
16449     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.ctorIdx",
16450     "runtime_only": false
16451   },
16452   {
16453     "axioms": [
16454       "propext",
16455       "Classical.choice",
16456       "Quot.sound"
16457     ],
16458     "in_project_namespace": false,
16459     "kind": "definition",
16460     "module": "PaperIRelease.TopologySemilinearRank",
16461     "name": "PaperIRelease.TopologySemilinearRank.moduleSeedRank",
16462     "runtime_only": false
16463   },
16464   {
16465     "axioms": [
16466       "propext",
16467       "Classical.choice",
16468       "Quot.sound"
16469     ],
16470     "in_project_namespace": true,
16471     "kind": "theorem",
16472     "module": "KomorebiVerification.EllipticAlgorithms",
16473     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_Mx",
16474     "runtime_only": false
16475   },
16476   {
16477     "axioms": [
16478       "propext",
16479       "Classical.choice",
16480       "Quot.sound"
16481     ],
16482     "in_project_namespace": true,
16483     "kind": "definition",
16484     "module": "KomorebiVerification.PacketNaturalityCompletion",
16485     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.casesOn",
16486     "runtime_only": false
16487   },
16488   {
16489     "axioms": [
16490       "propext",
16491       "Classical.choice",
16492       "Quot.sound"
16493     ],
16494     "in_project_namespace": false,
16495     "kind": "theorem",
16496     "module": "PaperIRelease.TopologyUnconditional",
16497     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_dist_le",
16498     "runtime_only": false
16499   },
16500   {
16501     "axioms": [
16502       "propext",
16503       "Classical.choice",
16504       "Quot.sound"
16505     ],
16506     "in_project_namespace": true,
16507     "kind": "theorem",
16508     "module": "PaperIRelease.CategoryPackets",
16509     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.inj",
16510     "runtime_only": false
16511   },
16512   {
16513     "axioms": [
16514       "propext",
16515       "Classical.choice",
16516       "Quot.sound"
16517     ],
16518     "in_project_namespace": true,
16519     "kind": "definition",
16520     "module": "KomorebiVerification.PacketNaturalityCompletion",
16521     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlockAlgebra",
16522     "runtime_only": false
16523   },
16524   {
16525     "axioms": [],
16526     "in_project_namespace": true,
16527     "kind": "definition",
16528     "module": "KomorebiVerification.ProjectorCore",
16529     "name": "Komorebi.Seed.OperatorRelation._sizeOf_inst",
16530     "runtime_only": false
16531   },
16532   {
16533     "axioms": [
16534       "propext",
16535       "Quot.sound"
16536     ],
16537     "in_project_namespace": true,
16538     "kind": "theorem",
16539     "module": "PaperICompletion4.GroupedPrimary",
16540     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_11",
16541     "runtime_only": false
16542   },
16543   {
16544     "axioms": [
16545       "propext",
16546       "Classical.choice",
16547       "Quot.sound"
16548     ],
16549     "in_project_namespace": false,
16550     "kind": "theorem",
16551     "module": "PaperIRelease.TopologyCountablePackets",
16552     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues_bddAbove",
16553     "runtime_only": false
16554   },
16555   {
16556     "axioms": [
16557       "propext",
16558       "Classical.choice",
16559       "Quot.sound"
16560     ],
16561     "in_project_namespace": true,
16562     "kind": "theorem",
16563     "module": "KomorebiVerification.SingleOperatorGraph",
16564     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv",
16565     "runtime_only": false
16566   },
16567   {
16568     "axioms": [
16569       "propext",
16570       "Quot.sound"
16571     ],
16572     "in_project_namespace": true,
16573     "kind": "definition",
16574     "module": "PaperIRelease.GrammarTyped",
16575     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.casesOn",
16576     "runtime_only": false
16577   },
16578   {
16579     "axioms": [
16580       "propext",
16581       "Classical.choice",
16582       "Quot.sound"
16583     ],
16584     "in_project_namespace": true,
16585     "kind": "theorem",
16586     "module": "KomorebiVerification.TopologicalCompletion",
16587     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis.eq_1",
16588     "runtime_only": false
16589   },
16590   {
16591     "axioms": [
16592       "propext",
16593       "Quot.sound"
16594     ],
16595     "in_project_namespace": true,
16596     "kind": "definition",
16597     "module": "PaperIRelease.GrammarModules",
16598     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.noConfusion",
16599     "runtime_only": false
16600   },
16601   {
16602     "axioms": [
16603       "propext",
16604       "Classical.choice",
16605       "Quot.sound"
16606     ],
16607     "in_project_namespace": true,
16608     "kind": "definition",
16609     "module": "KomorebiVerification.ProjectorCore",
16610     "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize",
16611     "runtime_only": false
16612   },
16613   {
16614     "axioms": [
16615       "propext",
16616       "Classical.choice",
16617       "Quot.sound"
16618     ],
16619     "in_project_namespace": true,
16620     "kind": "definition",
16621     "module": "PaperIRelease.GrammarEquivalence",
16622     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso",
16623     "runtime_only": false
16624   },
16625   {
16626     "axioms": [
16627       "propext",
16628       "Classical.choice",
16629       "Quot.sound"
16630     ],
16631     "in_project_namespace": false,
16632     "kind": "theorem",
16633     "module": "PaperIRelease.TopologyCountablePackets",
16634     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis._proof_1",
16635     "runtime_only": false
16636   },
16637   {
16638     "axioms": [
16639       "propext",
16640       "Classical.choice",
16641       "Quot.sound"
16642     ],
16643     "in_project_namespace": true,
16644     "kind": "theorem",
16645     "module": "KomorebiVerification.PacketNaturalityCompletion",
16646     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOps.eq_1",
16647     "runtime_only": false
16648   },
16649   {
16650     "axioms": [
16651       "propext",
16652       "Classical.choice",
16653       "Quot.sound"
16654     ],
16655     "in_project_namespace": false,
16656     "kind": "theorem",
16657     "module": "PaperIRelease.TopologyDenseCompletion",
16658     "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_3",
16659     "runtime_only": false
16660   },
16661   {
16662     "axioms": [
16663       "propext",
16664       "Classical.choice",
16665       "Quot.sound"
16666     ],
16667     "in_project_namespace": true,
16668     "kind": "theorem",
16669     "module": "PaperICompletion8.DivisionProduct",
16670     "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv_isLeast_product_generatorCount",
16671     "runtime_only": false
16672   },
16673   {
16674     "axioms": [
16675       "propext",
16676       "Classical.choice",
16677       "Quot.sound"
16678     ],
16679     "in_project_namespace": true,
16680     "kind": "definition",
16681     "module": "KomorebiVerification.SeedRankBasics",
16682     "name": "Komorebi.SeedRankBasics.seedFinrank",
16683     "runtime_only": false
16684   },
16685   {
16686     "axioms": [
16687       "propext",
16688       "Classical.choice",
16689       "Quot.sound"
16690     ],
16691     "in_project_namespace": true,
16692     "kind": "theorem",
16693     "module": "PaperIRelease.PacketBoundaryTests",
16694     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_submodule_packet_exact",
16695     "runtime_only": false
16696   },
16697   {
16698     "axioms": [
16699       "propext",
16700       "Quot.sound"
16701     ],
16702     "in_project_namespace": true,
16703     "kind": "definition",
16704     "module": "KomorebiVerification.PacketNaturalityCompletion",
16705     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2082",
16706     "runtime_only": false
16707   },
16708   {
16709     "axioms": [
16710       "propext",
16711       "Classical.choice",
16712       "Quot.sound"
16713     ],
16714     "in_project_namespace": true,
16715     "kind": "definition",
16716     "module": "PaperIRelease.PacketAggregation",
16717     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis",
16718     "runtime_only": false
16719   },
16720   {
16721     "axioms": [],
16722     "in_project_namespace": true,
16723     "kind": "theorem",
16724     "module": "PaperIRelease.CategoryExport",
16725     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.inj",
16726     "runtime_only": false
16727   },
16728   {
16729     "axioms": [
16730       "propext",
16731       "Classical.choice",
16732       "Quot.sound"
16733     ],
16734     "in_project_namespace": false,
16735     "kind": "theorem",
16736     "module": "PaperIRelease.TopologyUnconditionalBridge",
16737     "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_1",
16738     "runtime_only": false
16739   },
16740   {
16741     "axioms": [
16742       "propext",
16743       "Classical.choice",
16744       "Quot.sound"
16745     ],
16746     "in_project_namespace": true,
16747     "kind": "theorem",
16748     "module": "PaperICompletion.CyclicClassification",
16749     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_6",
16750     "runtime_only": false
16751   },
16752   {
16753     "axioms": [
16754       "propext",
16755       "Classical.choice",
16756       "Quot.sound"
16757     ],
16758     "in_project_namespace": true,
16759     "kind": "theorem",
16760     "module": "PaperIRelease.GeneralFiniteCompletion",
16761     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_3",
16762     "runtime_only": false
16763   },
16764   {
16765     "axioms": [
16766       "propext",
16767       "Quot.sound"
16768     ],
16769     "in_project_namespace": true,
16770     "kind": "theorem",
16771     "module": "PaperIRelease.PolynomialModule",
16772     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_4",
16773     "runtime_only": false
16774   },
16775   {
16776     "axioms": [
16777       "propext",
16778       "Classical.choice",
16779       "Quot.sound"
16780     ],
16781     "in_project_namespace": true,
16782     "kind": "theorem",
16783     "module": "PaperIRelease.GrammarEquivalence",
16784     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.natural",
16785     "runtime_only": false
16786   },
16787   {
16788     "axioms": [
16789       "propext",
16790       "Classical.choice",
16791       "Quot.sound"
16792     ],
16793     "in_project_namespace": true,
16794     "kind": "theorem",
16795     "module": "KomorebiVerification.TopologicalCompletion",
16796     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis_apply_coe",
16797     "runtime_only": false
16798   },
16799   {
16800     "axioms": [
16801       "propext",
16802       "Classical.choice",
16803       "Quot.sound"
16804     ],
16805     "in_project_namespace": false,
16806     "kind": "theorem",
16807     "module": "PaperIRelease.TopologyDenseCompletion",
16808     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv.congr_simp",
16809     "runtime_only": false
16810   },
16811   {
16812     "axioms": [
16813       "propext",
16814       "Classical.choice",
16815       "Quot.sound"
16816     ],
16817     "in_project_namespace": true,
16818     "kind": "definition",
16819     "module": "PaperIRelease.CategoryPackets",
16820     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.noConfusion",
16821     "runtime_only": false
16822   },
16823   {
16824     "axioms": [
16825       "propext",
16826       "Classical.choice",
16827       "Quot.sound"
16828     ],
16829     "in_project_namespace": true,
16830     "kind": "theorem",
16831     "module": "PaperICompletion5.GeometricSeedFormula",
16832     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedRank_eq_geometricSeedMaximum",
16833     "runtime_only": false
16834   },
16835   {
16836     "axioms": [
16837       "propext",
16838       "Classical.choice",
16839       "Quot.sound"
16840     ],
16841     "in_project_namespace": true,
16842     "kind": "definition",
16843     "module": "KomorebiVerification.TopologicalCompletion",
16844     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.recOn",
16845     "runtime_only": false
16846   },
16847   {
16848     "axioms": [
16849       "propext",
16850       "Classical.choice",
16851       "Quot.sound"
16852     ],
16853     "in_project_namespace": true,
16854     "kind": "theorem",
16855     "module": "KomorebiVerification.SeedRankBasics",
16856     "name": "Komorebi.SeedRankBasics.seedRank_eq_zero_iff",
16857     "runtime_only": false
16858   },
16859   {
16860     "axioms": [
16861       "propext",
16862       "Classical.choice",
16863       "Quot.sound"
16864     ],
16865     "in_project_namespace": true,
16866     "kind": "theorem",
16867     "module": "PaperICompletion7.ModuleTop",
16868     "name": "Komorebi.PaperICompletion7.ModuleTop.seedFinrank_eq_idealTop",
16869     "runtime_only": false
16870   },
16871   {
16872     "axioms": [
16873       "propext",
16874       "Classical.choice",
16875       "Quot.sound"
16876     ],
16877     "in_project_namespace": true,
16878     "kind": "theorem",
16879     "module": "PaperIRelease.GrammarEquivalence",
16880     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_14",
16881     "runtime_only": false
16882   },
16883   {
16884     "axioms": [
16885       "propext",
16886       "Classical.choice",
16887       "Quot.sound"
16888     ],
16889     "in_project_namespace": true,
16890     "kind": "theorem",
16891     "module": "PaperIRelease.GrammarTyped",
16892     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_apply",
16893     "runtime_only": false
16894   },
16895   {
16896     "axioms": [
16897       "propext",
16898       "Classical.choice",
16899       "Quot.sound"
16900     ],
16901     "in_project_namespace": false,
16902     "kind": "theorem",
16903     "module": "ReleaseBoundary",
16904     "name": "PaperIBlock08Tests.regular_columns_literal",
16905     "runtime_only": false
16906   },
16907   {
16908     "axioms": [],
16909     "in_project_namespace": true,
16910     "kind": "definition",
16911     "module": "KomorebiVerification.ProjectorCore",
16912     "name": "Komorebi.Seed.OperatorRelation.noConfusionType",
16913     "runtime_only": false
16914   },
16915   {
16916     "axioms": [
16917       "propext",
16918       "Classical.choice",
16919       "Quot.sound"
16920     ],
16921     "in_project_namespace": true,
16922     "kind": "theorem",
16923     "module": "PaperIRelease.BoundedStar",
16924     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_1",
16925     "runtime_only": false
16926   },
16927   {
16928     "axioms": [
16929       "propext"
16930     ],
16931     "in_project_namespace": true,
16932     "kind": "theorem",
16933     "module": "KomorebiVerification.SingleOperatorGraph",
16934     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_5",
16935     "runtime_only": false
16936   },
16937   {
16938     "axioms": [],
16939     "in_project_namespace": true,
16940     "kind": "definition",
16941     "module": "KomorebiVerification.ProjectorCore",
16942     "name": "Komorebi.Seed.OperatorRelation.mk._flat_ctor",
16943     "runtime_only": false
16944   },
16945   {
16946     "axioms": [
16947       "propext",
16948       "Quot.sound"
16949     ],
16950     "in_project_namespace": true,
16951     "kind": "recursor",
16952     "module": "PaperIRelease.GrammarAlgebra",
16953     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.rec",
16954     "runtime_only": false
16955   },
16956   {
16957     "axioms": [
16958       "propext",
16959       "Classical.choice",
16960       "Quot.sound"
16961     ],
16962     "in_project_namespace": false,
16963     "kind": "definition",
16964     "module": "PaperIRelease.TopologyUnconditionalBridge",
16965     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceIsometry",
16966     "runtime_only": false
16967   },
16968   {
16969     "axioms": [],
16970     "in_project_namespace": true,
16971     "kind": "constructor",
16972     "module": "KomorebiVerification.ProjectorCore",
16973     "name": "Komorebi.FormalizationStatus.numericalOnly",
16974     "runtime_only": false
16975   },
16976   {
16977     "axioms": [
16978       "propext",
16979       "Classical.choice",
16980       "Quot.sound"
16981     ],
16982     "in_project_namespace": false,
16983     "kind": "definition",
16984     "module": "PaperIRelease.TopologyCountablePackets",
16985     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv",
16986     "runtime_only": false
16987   },
16988   {
16989     "axioms": [],
16990     "in_project_namespace": true,
16991     "kind": "theorem",
16992     "module": "KomorebiVerification.ProjectorCore",
16993     "name": "Komorebi.ClaimKind.ofNat_ctorIdx",
16994     "runtime_only": false
16995   },
16996   {
16997     "axioms": [
16998       "propext",
16999       "Classical.choice",
17000       "Quot.sound"
17001     ],
17002     "in_project_namespace": true,
17003     "kind": "theorem",
17004     "module": "KomorebiVerification.SemisimpleCompletion",
17005     "name": "Komorebi.SemisimpleCompletion.exists_splitProduct_generators_iff_coordinate_bounds",
17006     "runtime_only": false
17007   },
17008   {
17009     "axioms": [],
17010     "in_project_namespace": false,
17011     "kind": "theorem",
17012     "module": "PaperIRelease.GrammarPaths",
17013     "name": "_private.PaperIRelease.GrammarPaths.0.PSigma.casesOn._arg_pusher",
17014     "runtime_only": false
17015   },
17016   {
17017     "axioms": [
17018       "propext",
17019       "Classical.choice",
17020       "Quot.sound"
17021     ],
17022     "in_project_namespace": true,
17023     "kind": "theorem",
17024     "module": "PaperICompletion4.ResidueQuotient",
17025     "name": "Komorebi.PaperICompletion4.ResidueQuotient.smul_surjective_of_coprime",
17026     "runtime_only": false
17027   },
17028   {
17029     "axioms": [
17030       "propext",
17031       "Classical.choice",
17032       "Quot.sound"
17033     ],
17034     "in_project_namespace": true,
17035     "kind": "theorem",
17036     "module": "KomorebiVerification.PacketNaturalityCompletion",
17037     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.identity_blocks_supported_iff_reflexive",
17038     "runtime_only": false
17039   },
17040   {
17041     "axioms": [
17042       "propext",
17043       "Classical.choice",
17044       "Quot.sound"
17045     ],
17046     "in_project_namespace": true,
17047     "kind": "theorem",
17048     "module": "KomorebiVerification.SingleOperatorGraph",
17049     "name": "Komorebi.SingleOperatorGraph.FamilyGenerates.eq_1",
17050     "runtime_only": false
17051   },
17052   {
17053     "axioms": [
17054       "propext",
17055       "Classical.choice",
17056       "Quot.sound"
17057     ],
17058     "in_project_namespace": true,
17059     "kind": "theorem",
17060     "module": "PaperIRelease.PacketPureRank",
17061     "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_sum_corner",
17062     "runtime_only": false
17063   },
17064   {
17065     "axioms": [
17066       "propext",
17067       "Quot.sound"
17068     ],
17069     "in_project_namespace": true,
17070     "kind": "definition",
17071     "module": "PaperIRelease.GrammarModules",
17072     "name": "Komorebi.PaperIRelease.GrammarModules.ofModule",
17073     "runtime_only": false
17074   },
17075   {
17076     "axioms": [
17077       "propext",
17078       "Classical.choice",
17079       "Quot.sound"
17080     ],
17081     "in_project_namespace": true,
17082     "kind": "theorem",
17083     "module": "KomorebiVerification.SemisimpleCompletion",
17084     "name": "Komorebi.SemisimpleCompletion.block_smul_eq_mul",
17085     "runtime_only": false
17086   },
17087   {
17088     "axioms": [
17089       "propext",
17090       "Classical.choice",
17091       "Quot.sound"
17092     ],
17093     "in_project_namespace": true,
17094     "kind": "theorem",
17095     "module": "KomorebiVerification.PacketNaturalityCompletion",
17096     "name": "Komorebi.PacketNaturalityCompletion.Reachability.source_reachable",
17097     "runtime_only": false
17098   },
17099   {
17100     "axioms": [
17101       "propext",
17102       "Classical.choice",
17103       "Quot.sound"
17104     ],
17105     "in_project_namespace": false,
17106     "kind": "theorem",
17107     "module": "PaperIRelease.TopologySemilinearRank",
17108     "name": "PaperIRelease.TopologySemilinearRank.rank_attained",
17109     "runtime_only": false
17110   },
17111   {
17112     "axioms": [
17113       "propext",
17114       "Classical.choice",
17115       "Quot.sound"
17116     ],
17117     "in_project_namespace": true,
17118     "kind": "theorem",
17119     "module": "PaperIRelease.BoundedStar",
17120     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_5",
17121     "runtime_only": false
17122   },
17123   {
17124     "axioms": [
17125       "propext",
17126       "Classical.choice",
17127       "Quot.sound"
17128     ],
17129     "in_project_namespace": true,
17130     "kind": "theorem",
17131     "module": "KomorebiVerification.PacketNaturalityCompletion",
17132     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks.eq_1",
17133     "runtime_only": false
17134   },
17135   {
17136     "axioms": [
17137       "propext",
17138       "Classical.choice",
17139       "Quot.sound"
17140     ],
17141     "in_project_namespace": true,
17142     "kind": "definition",
17143     "module": "KomorebiVerification.PacketNaturalityCompletion",
17144     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk._flat_ctor",
17145     "runtime_only": false
17146   },
17147   {
17148     "axioms": [
17149       "propext",
17150       "Classical.choice",
17151       "Quot.sound"
17152     ],
17153     "in_project_namespace": true,
17154     "kind": "theorem",
17155     "module": "PaperIRelease.BoundedStar",
17156     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_3",
17157     "runtime_only": false
17158   },
17159   {
17160     "axioms": [
17161       "propext",
17162       "Classical.choice",
17163       "Quot.sound"
17164     ],
17165     "in_project_namespace": true,
17166     "kind": "definition",
17167     "module": "PaperICompletion3.PrimarySeedFormula",
17168     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap",
17169     "runtime_only": false
17170   },
17171   {
17172     "axioms": [
17173       "propext",
17174       "Classical.choice",
17175       "Quot.sound"
17176     ],
17177     "in_project_namespace": true,
17178     "kind": "theorem",
17179     "module": "KomorebiVerification.EllipticAlgorithms",
17180     "name": "Komorebi.FiniteAlgorithms.mem_graphSpectrum_iff._simp_1",
17181     "runtime_only": false
17182   },
17183   {
17184     "axioms": [
17185       "propext",
17186       "Classical.choice",
17187       "Quot.sound"
17188     ],
17189     "in_project_namespace": true,
17190     "kind": "theorem",
17191     "module": "PaperIRelease.CategoryPackets",
17192     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ext_iff",
17193     "runtime_only": false
17194   },
17195   {
17196     "axioms": [
17197       "propext",
17198       "Classical.choice",
17199       "Quot.sound"
17200     ],
17201     "in_project_namespace": true,
17202     "kind": "definition",
17203     "module": "PaperIRelease.AlgebraClassGrouping",
17204     "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv",
17205     "runtime_only": false
17206   },
17207   {
17208     "axioms": [
17209       "propext",
17210       "Classical.choice",
17211       "Quot.sound"
17212     ],
17213     "in_project_namespace": true,
17214     "kind": "theorem",
17215     "module": "PaperIRelease.CategoryBoundaries",
17216     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_1",
17217     "runtime_only": false
17218   },
17219   {
17220     "axioms": [],
17221     "in_project_namespace": true,
17222     "kind": "definition",
17223     "module": "KomorebiVerification.ProjectorCore",
17224     "name": "Komorebi.ClaimRecord.targetNamespace._default",
17225     "runtime_only": false
17226   },
17227   {
17228     "axioms": [
17229       "propext",
17230       "Classical.choice",
17231       "Quot.sound"
17232     ],
17233     "in_project_namespace": true,
17234     "kind": "theorem",
17235     "module": "PaperICompletion8.SemisimpleFormula",
17236     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.radicalTop_seedFinrank_of_decompositions",
17237     "runtime_only": false
17238   },
17239   {
17240     "axioms": [],
17241     "in_project_namespace": true,
17242     "kind": "constructor",
17243     "module": "KomorebiVerification.ProjectorCore",
17244     "name": "Komorebi.Seed.OperatorExpr.id",
17245     "runtime_only": false
17246   },
17247   {
17248     "axioms": [
17249       "propext",
17250       "Classical.choice",
17251       "Quot.sound"
17252     ],
17253     "in_project_namespace": true,
17254     "kind": "theorem",
17255     "module": "PaperIRelease.PacketPureBoundaryTests",
17256     "name": "Komorebi.PaperIRelease.PureBoundaryTests.zero_module_rank",
17257     "runtime_only": false
17258   },
17259   {
17260     "axioms": [
17261       "propext",
17262       "Classical.choice",
17263       "Quot.sound"
17264     ],
17265     "in_project_namespace": true,
17266     "kind": "inductive",
17267     "module": "PaperICompletion3.OperatorPrimaryAPI",
17268     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation",
17269     "runtime_only": false
17270   },
17271   {
17272     "axioms": [
17273       "propext",
17274       "Classical.choice",
17275       "Quot.sound"
17276     ],
17277     "in_project_namespace": true,
17278     "kind": "theorem",
17279     "module": "PaperIRelease.AlgebraClassGrouping",
17280     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_9",
17281     "runtime_only": false
17282   },
17283   {
17284     "axioms": [
17285       "propext",
17286       "Classical.choice",
17287       "Quot.sound"
17288     ],
17289     "in_project_namespace": true,
17290     "kind": "theorem",
17291     "module": "PaperIRelease.AlgebraClassGrouping",
17292     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_8",
17293     "runtime_only": false
17294   },
17295   {
17296     "axioms": [
17297       "propext"
17298     ],
17299     "in_project_namespace": true,
17300     "kind": "theorem",
17301     "module": "PaperIRelease.GrammarPaths",
17302     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.injEq",
17303     "runtime_only": false
17304   },
17305   {
17306     "axioms": [
17307       "propext",
17308       "Classical.choice",
17309       "Quot.sound"
17310     ],
17311     "in_project_namespace": true,
17312     "kind": "definition",
17313     "module": "PaperIRelease.TopologyCategories",
17314     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.casesOn",
17315     "runtime_only": false
17316   },
17317   {
17318     "axioms": [
17319       "propext",
17320       "Quot.sound"
17321     ],
17322     "in_project_namespace": true,
17323     "kind": "theorem",
17324     "module": "PaperICompletion4.ResidueQuotient",
17325     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_3",
17326     "runtime_only": false
17327   },
17328   {
17329     "axioms": [
17330       "propext",
17331       "Quot.sound"
17332     ],
17333     "in_project_namespace": true,
17334     "kind": "theorem",
17335     "module": "KomorebiVerification.PathGraphKrylov",
17336     "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_3",
17337     "runtime_only": false
17338   },
17339   {
17340     "axioms": [
17341       "propext",
17342       "Classical.choice",
17343       "Quot.sound"
17344     ],
17345     "in_project_namespace": true,
17346     "kind": "theorem",
17347     "module": "KomorebiVerification.SingleOperatorGraph",
17348     "name": "Komorebi.SingleOperatorGraph.seedNumber_zero_isLeast_of_subsingleton",
17349     "runtime_only": false
17350   },
17351   {
17352     "axioms": [
17353       "propext",
17354       "Classical.choice",
17355       "Quot.sound"
17356     ],
17357     "in_project_namespace": true,
17358     "kind": "theorem",
17359     "module": "KomorebiVerification.SingleOperatorGraph",
17360     "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_apply",
17361     "runtime_only": false
17362   },
17363   {
17364     "axioms": [
17365       "propext"
17366     ],
17367     "in_project_namespace": true,
17368     "kind": "theorem",
17369     "module": "PaperIRelease.CategoryExport",
17370     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_2",
17371     "runtime_only": false
17372   },
17373   {
17374     "axioms": [],
17375     "in_project_namespace": false,
17376     "kind": "theorem",
17377     "module": "PaperIRelease.GrammarPaths",
17378     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1._arg_pusher",
17379     "runtime_only": false
17380   },
17381   {
17382     "axioms": [
17383       "propext",
17384       "Classical.choice",
17385       "Quot.sound"
17386     ],
17387     "in_project_namespace": true,
17388     "kind": "theorem",
17389     "module": "PaperIRelease.PacketTopology",
17390     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_3",
17391     "runtime_only": false
17392   },
17393   {
17394     "axioms": [],
17395     "in_project_namespace": false,
17396     "kind": "theorem",
17397     "module": "PaperIRelease.CategoryExport",
17398     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_1",
17399     "runtime_only": false
17400   },
17401   {
17402     "axioms": [
17403       "propext",
17404       "Classical.choice",
17405       "Quot.sound"
17406     ],
17407     "in_project_namespace": true,
17408     "kind": "definition",
17409     "module": "PaperIRelease.CategoryPackets",
17410     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.module",
17411     "runtime_only": false
17412   },
17413   {
17414     "axioms": [],
17415     "in_project_namespace": false,
17416     "kind": "theorem",
17417     "module": "KomorebiVerification.EllipticAlgorithms",
17418     "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.eq_2",
17419     "runtime_only": false
17420   },
17421   {
17422     "axioms": [
17423       "propext",
17424       "Classical.choice",
17425       "Quot.sound"
17426     ],
17427     "in_project_namespace": true,
17428     "kind": "theorem",
17429     "module": "PaperIRelease.PacketPureBoundaryTests",
17430     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_2",
17431     "runtime_only": false
17432   },
17433   {
17434     "axioms": [
17435       "propext",
17436       "Quot.sound"
17437     ],
17438     "in_project_namespace": true,
17439     "kind": "theorem",
17440     "module": "KomorebiVerification.PacketNaturalityCompletion",
17441     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlocks._proof_1",
17442     "runtime_only": false
17443   },
17444   {
17445     "axioms": [
17446       "propext",
17447       "Classical.choice",
17448       "Quot.sound"
17449     ],
17450     "in_project_namespace": true,
17451     "kind": "theorem",
17452     "module": "PaperICompletion.CyclicClassification",
17453     "name": "Komorebi.PaperICompletion.CyclicClassification.operatorAlgebra_seedRank_eq_one_iff_minpoly_eq_charpoly",
17454     "runtime_only": false
17455   },
17456   {
17457     "axioms": [
17458       "propext",
17459       "Classical.choice",
17460       "Quot.sound"
17461     ],
17462     "in_project_namespace": true,
17463     "kind": "theorem",
17464     "module": "PaperIRelease.PacketExactSequence",
17465     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient._proof_2",
17466     "runtime_only": false
17467   },
17468   {
17469     "axioms": [],
17470     "in_project_namespace": true,
17471     "kind": "definition",
17472     "module": "PaperIRelease.GrammarPaths",
17473     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.noConfusion",
17474     "runtime_only": false
17475   },
17476   {
17477     "axioms": [
17478       "propext",
17479       "Quot.sound"
17480     ],
17481     "in_project_namespace": true,
17482     "kind": "theorem",
17483     "module": "PaperIRelease.PacketAggregation",
17484     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeDirectSumEquiv._proof_1",
17485     "runtime_only": false
17486   },
17487   {
17488     "axioms": [
17489       "propext",
17490       "Classical.choice",
17491       "Quot.sound"
17492     ],
17493     "in_project_namespace": true,
17494     "kind": "definition",
17495     "module": "KomorebiVerification.PacketNaturalityCompletion",
17496     "name": "Komorebi.PacketNaturalityCompletion.Reachability.ReachableFrom",
17497     "runtime_only": false
17498   },
17499   {
17500     "axioms": [
17501       "propext",
17502       "Classical.choice",
17503       "Quot.sound"
17504     ],
17505     "in_project_namespace": true,
17506     "kind": "theorem",
17507     "module": "PaperIRelease.GeneralNormedPackets",
17508     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.annihilate",
17509     "runtime_only": false
17510   },
17511   {
17512     "axioms": [
17513       "propext",
17514       "Classical.choice",
17515       "Quot.sound"
17516     ],
17517     "in_project_namespace": true,
17518     "kind": "theorem",
17519     "module": "KomorebiVerification.Basic",
17520     "name": "KomorebiVerification.binomialSquare",
17521     "runtime_only": false
17522   },
17523   {
17524     "axioms": [],
17525     "in_project_namespace": true,
17526     "kind": "definition",
17527     "module": "PaperICompletion.SpectralCertificates",
17528     "name": "Komorebi.PaperICompletion.SpectralCertificates.EigenLabels",
17529     "runtime_only": false
17530   },
17531   {
17532     "axioms": [
17533       "propext",
17534       "Classical.choice",
17535       "Quot.sound"
17536     ],
17537     "in_project_namespace": true,
17538     "kind": "theorem",
17539     "module": "PaperIRelease.PacketTopology",
17540     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM._proof_2",
17541     "runtime_only": false
17542   },
17543   {
17544     "axioms": [
17545       "propext",
17546       "Classical.choice",
17547       "Quot.sound"
17548     ],
17549     "in_project_namespace": true,
17550     "kind": "theorem",
17551     "module": "KomorebiVerification.TopologicalCompletion",
17552     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_zero",
17553     "runtime_only": false
17554   },
17555   {
17556     "axioms": [
17557       "propext",
17558       "Classical.choice",
17559       "Quot.sound"
17560     ],
17561     "in_project_namespace": true,
17562     "kind": "theorem",
17563     "module": "PaperIRelease.TopologyCategories",
17564     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.inj",
17565     "runtime_only": false
17566   },
17567   {
17568     "axioms": [
17569       "propext",
17570       "Classical.choice",
17571       "Quot.sound"
17572     ],
17573     "in_project_namespace": false,
17574     "kind": "theorem",
17575     "module": "PaperIRelease.TopologySemilinearRank",
17576     "name": "PaperIRelease.TopologySemilinearRank.moduleSeedRank_eq_operatorSeedRank",
17577     "runtime_only": false
17578   },
17579   {
17580     "axioms": [
17581       "propext",
17582       "Classical.choice",
17583       "Quot.sound"
17584     ],
17585     "in_project_namespace": true,
17586     "kind": "theorem",
17587     "module": "PaperICompletion3.PrimarySeedFormula",
17588     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residue_finrank_le_card_of_generates",
17589     "runtime_only": false
17590   },
17591   {
17592     "axioms": [
17593       "propext",
17594       "Classical.choice",
17595       "Quot.sound"
17596     ],
17597     "in_project_namespace": true,
17598     "kind": "theorem",
17599     "module": "PaperIRelease.PacketDescent",
17600     "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_3",
17601     "runtime_only": false
17602   },
17603   {
17604     "axioms": [
17605       "propext",
17606       "Classical.choice",
17607       "Quot.sound"
17608     ],
17609     "in_project_namespace": true,
17610     "kind": "definition",
17611     "module": "KomorebiVerification.PacketNaturalityCompletion",
17612     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraZeroAt",
17613     "runtime_only": false
17614   },
17615   {
17616     "axioms": [
17617       "propext",
17618       "Quot.sound"
17619     ],
17620     "in_project_namespace": true,
17621     "kind": "definition",
17622     "module": "KomorebiVerification.PacketNaturalityCompletion",
17623     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083",
17624     "runtime_only": false
17625   },
17626   {
17627     "axioms": [
17628       "propext",
17629       "Quot.sound"
17630     ],
17631     "in_project_namespace": true,
17632     "kind": "theorem",
17633     "module": "PaperICompletion4.GroupedPrimary",
17634     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_7",
17635     "runtime_only": false
17636   },
17637   {
17638     "axioms": [
17639       "propext",
17640       "Classical.choice",
17641       "Quot.sound"
17642     ],
17643     "in_project_namespace": true,
17644     "kind": "theorem",
17645     "module": "PaperIRelease.GrammarAlgebra",
17646     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.inj",
17647     "runtime_only": false
17648   },
17649   {
17650     "axioms": [
17651       "propext",
17652       "Classical.choice",
17653       "Quot.sound"
17654     ],
17655     "in_project_namespace": true,
17656     "kind": "definition",
17657     "module": "PaperICompletion3.OperatorPrimaryAPI",
17658     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation._sizeOf_1",
17659     "runtime_only": false
17660   },
17661   {
17662     "axioms": [
17663       "propext",
17664       "Classical.choice",
17665       "Quot.sound"
17666     ],
17667     "in_project_namespace": false,
17668     "kind": "theorem",
17669     "module": "PaperIRelease.TopologyFiniteCompletion",
17670     "name": "PaperIRelease.TopologyFiniteCompletion.extended_packet_range",
17671     "runtime_only": false
17672   },
17673   {
17674     "axioms": [
17675       "propext",
17676       "Quot.sound"
17677     ],
17678     "in_project_namespace": true,
17679     "kind": "theorem",
17680     "module": "PaperIRelease.PacketBoundaryTests",
17681     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_1",
17682     "runtime_only": false
17683   },
17684   {
17685     "axioms": [
17686       "propext",
17687       "Quot.sound"
17688     ],
17689     "in_project_namespace": true,
17690     "kind": "theorem",
17691     "module": "KomorebiVerification.PacketNaturalityCompletion",
17692     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.image_generates_of_surjective_intertwining",
17693     "runtime_only": false
17694   },
17695   {
17696     "axioms": [
17697       "propext",
17698       "Classical.choice",
17699       "Quot.sound"
17700     ],
17701     "in_project_namespace": true,
17702     "kind": "theorem",
17703     "module": "PaperIRelease.PolynomialMonic",
17704     "name": "Komorebi.PaperIRelease.PolynomialModule.finitely_many_monic_primary_components",
17705     "runtime_only": false
17706   },
17707   {
17708     "axioms": [
17709       "propext",
17710       "Classical.choice",
17711       "Quot.sound"
17712     ],
17713     "in_project_namespace": true,
17714     "kind": "theorem",
17715     "module": "KomorebiVerification.PathGraphKrylov",
17716     "name": "Komorebi.PathGraphKrylov.walkMatrix_diagonal",
17717     "runtime_only": false
17718   },
17719   {
17720     "axioms": [
17721       "propext",
17722       "Classical.choice",
17723       "Quot.sound"
17724     ],
17725     "in_project_namespace": true,
17726     "kind": "theorem",
17727     "module": "PaperIRelease.GrammarPaths",
17728     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_1",
17729     "runtime_only": false
17730   },
17731   {
17732     "axioms": [
17733       "propext",
17734       "Classical.choice",
17735       "Quot.sound"
17736     ],
17737     "in_project_namespace": true,
17738     "kind": "theorem",
17739     "module": "KomorebiVerification.EllipticAlgorithms",
17740     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_symm_apply",
17741     "runtime_only": false
17742   },
17743   {
17744     "axioms": [
17745       "propext",
17746       "Classical.choice",
17747       "Quot.sound"
17748     ],
17749     "in_project_namespace": true,
17750     "kind": "theorem",
17751     "module": "PaperIRelease.PacketAggregation",
17752     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis_analysis",
17753     "runtime_only": false
17754   },
17755   {
17756     "axioms": [
17757       "propext",
17758       "Quot.sound"
17759     ],
17760     "in_project_namespace": true,
17761     "kind": "inductive",
17762     "module": "PaperIRelease.GrammarModules",
17763     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject",
17764     "runtime_only": false
17765   },
17766   {
17767     "axioms": [
17768       "propext",
17769       "Classical.choice",
17770       "Quot.sound"
17771     ],
17772     "in_project_namespace": true,
17773     "kind": "theorem",
17774     "module": "KomorebiVerification.SingleOperatorGraph",
17775     "name": "Komorebi.SingleOperatorGraph.not_seedNumberLE_zero",
17776     "runtime_only": false
17777   },
17778   {
17779     "axioms": [],
17780     "in_project_namespace": true,
17781     "kind": "definition",
17782     "module": "PaperICompletion8.RegularMultiplicity",
17783     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.Simple",
17784     "runtime_only": false
17785   },
17786   {
17787     "axioms": [
17788       "propext",
17789       "Quot.sound"
17790     ],
17791     "in_project_namespace": true,
17792     "kind": "theorem",
17793     "module": "PaperIRelease.PacketBoundaryTests",
17794     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_2",
17795     "runtime_only": false
17796   },
17797   {
17798     "axioms": [
17799       "propext",
17800       "Classical.choice",
17801       "Quot.sound"
17802     ],
17803     "in_project_namespace": true,
17804     "kind": "theorem",
17805     "module": "KomorebiVerification.SeedRankBasics",
17806     "name": "Komorebi.SeedRankBasics.seedRank_le_of_surjective",
17807     "runtime_only": false
17808   },
17809   {
17810     "axioms": [
17811       "propext",
17812       "Classical.choice",
17813       "Quot.sound"
17814     ],
17815     "in_project_namespace": true,
17816     "kind": "theorem",
17817     "module": "PaperIRelease.PacketDescent",
17818     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_2",
17819     "runtime_only": false
17820   },
17821   {
17822     "axioms": [],
17823     "in_project_namespace": false,
17824     "kind": "theorem",
17825     "module": "PaperIRelease.CategoryExport",
17826     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_6",
17827     "runtime_only": false
17828   },
17829   {
17830     "axioms": [
17831       "propext",
17832       "Classical.choice",
17833       "Quot.sound"
17834     ],
17835     "in_project_namespace": true,
17836     "kind": "definition",
17837     "module": "PaperIRelease.TopologyCategories",
17838     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject._sizeOf_1",
17839     "runtime_only": false
17840   },
17841   {
17842     "axioms": [
17843       "propext",
17844       "Classical.choice",
17845       "Quot.sound"
17846     ],
17847     "in_project_namespace": true,
17848     "kind": "constructor",
17849     "module": "PaperIRelease.GrammarAlgebra",
17850     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk",
17851     "runtime_only": false
17852   },
17853   {
17854     "axioms": [
17855       "propext",
17856       "Classical.choice",
17857       "Quot.sound"
17858     ],
17859     "in_project_namespace": true,
17860     "kind": "definition",
17861     "module": "PaperICompletion.CyclicClassification",
17862     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit",
17863     "runtime_only": false
17864   },
17865   {
17866     "axioms": [
17867       "propext",
17868       "Classical.choice",
17869       "Quot.sound"
17870     ],
17871     "in_project_namespace": true,
17872     "kind": "theorem",
17873     "module": "PaperIRelease.PacketTopology",
17874     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM._proof_2",
17875     "runtime_only": false
17876   },
17877   {
17878     "axioms": [
17879       "propext",
17880       "Classical.choice",
17881       "Quot.sound"
17882     ],
17883     "in_project_namespace": true,
17884     "kind": "theorem",
17885     "module": "PaperICompletion7.ModuleTop",
17886     "name": "Komorebi.PaperICompletion7.ModuleTop.seedFinrank_eq_radicalTop",
17887     "runtime_only": false
17888   },
17889   {
17890     "axioms": [
17891       "propext",
17892       "Classical.choice",
17893       "Quot.sound"
17894     ],
17895     "in_project_namespace": true,
17896     "kind": "theorem",
17897     "module": "PaperIRelease.PacketDescent",
17898     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_proj_apply",
17899     "runtime_only": false
17900   },
17901   {
17902     "axioms": [],
17903     "in_project_namespace": true,
17904     "kind": "definition",
17905     "module": "KomorebiVerification.ProjectorCore",
17906     "name": "Komorebi.Seed.OperatorExpr.eval._unsafe_rec",
17907     "runtime_only": true
17908   },
17909   {
17910     "axioms": [
17911       "propext",
17912       "Classical.choice",
17913       "Quot.sound"
17914     ],
17915     "in_project_namespace": true,
17916     "kind": "theorem",
17917     "module": "KomorebiVerification.TopologicalCompletion",
17918     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_unique",
17919     "runtime_only": false
17920   },
17921   {
17922     "axioms": [],
17923     "in_project_namespace": true,
17924     "kind": "recursor",
17925     "module": "KomorebiVerification.ProjectorCore",
17926     "name": "Komorebi.Seed.OperatorExpr.rec",
17927     "runtime_only": false
17928   },
17929   {
17930     "axioms": [
17931       "propext",
17932       "Quot.sound"
17933     ],
17934     "in_project_namespace": true,
17935     "kind": "theorem",
17936     "module": "PaperIRelease.PacketDescent",
17937     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_1",
17938     "runtime_only": false
17939   },
17940   {
17941     "axioms": [
17942       "propext",
17943       "Classical.choice",
17944       "Quot.sound"
17945     ],
17946     "in_project_namespace": true,
17947     "kind": "theorem",
17948     "module": "PaperIRelease.BoundedStar",
17949     "name": "Komorebi.PaperIRelease.BoundedSupport.exists_nonzero_packet",
17950     "runtime_only": false
17951   },
17952   {
17953     "axioms": [],
17954     "in_project_namespace": true,
17955     "kind": "definition",
17956     "module": "KomorebiVerification.ProjectorCore",
17957     "name": "Komorebi.Seed.OperatorRelation.noConfusion",
17958     "runtime_only": false
17959   },
17960   {
17961     "axioms": [
17962       "propext",
17963       "Classical.choice",
17964       "Quot.sound"
17965     ],
17966     "in_project_namespace": true,
17967     "kind": "theorem",
17968     "module": "KomorebiVerification.EllipticAlgorithms",
17969     "name": "Komorebi.EllipticCoordinates.P0_P1_orthogonal",
17970     "runtime_only": false
17971   },
17972   {
17973     "axioms": [],
17974     "in_project_namespace": true,
17975     "kind": "definition",
17976     "module": "KomorebiVerification.ProjectorCore",
17977     "name": "Komorebi.FiniteDifference.iteratedDiff.match_1",
17978     "runtime_only": false
17979   },
17980   {
17981     "axioms": [
17982       "propext",
17983       "Classical.choice",
17984       "Quot.sound"
17985     ],
17986     "in_project_namespace": false,
17987     "kind": "definition",
17988     "module": "PaperIRelease.TopologyUnconditional",
17989     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.ctorIdx",
17990     "runtime_only": false
17991   },
17992   {
17993     "axioms": [
17994       "propext",
17995       "Classical.choice",
17996       "Quot.sound"
17997     ],
17998     "in_project_namespace": true,
17999     "kind": "theorem",
18000     "module": "PaperIRelease.GrammarEquivalence",
18001     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.vertex_natural",
18002     "runtime_only": false
18003   },
18004   {
18005     "axioms": [],
18006     "in_project_namespace": true,
18007     "kind": "definition",
18008     "module": "PaperIRelease.CategoryExport",
18009     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn.go",
18010     "runtime_only": false
18011   },
18012   {
18013     "axioms": [
18014       "propext",
18015       "Classical.choice",
18016       "Quot.sound"
18017     ],
18018     "in_project_namespace": true,
18019     "kind": "definition",
18020     "module": "PaperICompletion3.PrimarySeedFormula",
18021     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.maxMultiplicity",
18022     "runtime_only": false
18023   },
18024   {
18025     "axioms": [
18026       "propext",
18027       "Classical.choice",
18028       "Quot.sound"
18029     ],
18030     "in_project_namespace": false,
18031     "kind": "definition",
18032     "module": "PaperIRelease.TopologyCountablePackets",
18033     "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm",
18034     "runtime_only": false
18035   },
18036   {
18037     "axioms": [
18038       "propext",
18039       "Classical.choice",
18040       "Quot.sound"
18041     ],
18042     "in_project_namespace": true,
18043     "kind": "theorem",
18044     "module": "KomorebiVerification.PacketNaturalityCompletion",
18045     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.orbit_mem_hull",
18046     "runtime_only": false
18047   },
18048   {
18049     "axioms": [
18050       "propext",
18051       "Classical.choice",
18052       "Quot.sound"
18053     ],
18054     "in_project_namespace": true,
18055     "kind": "definition",
18056     "module": "PaperIRelease.AlgebraQuotient",
18057     "name": "Komorebi.PaperIRelease.diagonalClassHom",
18058     "runtime_only": false
18059   },
18060   {
18061     "axioms": [
18062       "propext",
18063       "Classical.choice",
18064       "Quot.sound"
18065     ],
18066     "in_project_namespace": true,
18067     "kind": "theorem",
18068     "module": "PaperIRelease.GrammarPaths",
18069     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unary.eq_def",
18070     "runtime_only": false
18071   },
18072   {
18073     "axioms": [
18074       "propext",
18075       "Classical.choice",
18076       "Quot.sound"
18077     ],
18078     "in_project_namespace": true,
18079     "kind": "theorem",
18080     "module": "PaperICompletion.CyclicClassification",
18081     "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_exists_surjective",
18082     "runtime_only": false
18083   },
18084   {
18085     "axioms": [
18086       "propext",
18087       "Classical.choice",
18088       "Quot.sound"
18089     ],
18090     "in_project_namespace": true,
18091     "kind": "theorem",
18092     "module": "PaperICompletion.CyclicClassification",
18093     "name": "Komorebi.PaperICompletion.CyclicClassification.minpoly_degree_eq_finrank_of_cyclic",
18094     "runtime_only": false
18095   },
18096   {
18097     "axioms": [
18098       "propext",
18099       "Classical.choice",
18100       "Quot.sound"
18101     ],
18102     "in_project_namespace": true,
18103     "kind": "definition",
18104     "module": "PaperIRelease.TensorPackets",
18105     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv",
18106     "runtime_only": false
18107   },
18108   {
18109     "axioms": [
18110       "propext",
18111       "Classical.choice",
18112       "Quot.sound"
18113     ],
18114     "in_project_namespace": false,
18115     "kind": "theorem",
18116     "module": "PaperIRelease.TopologyCountablePackets",
18117     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_22",
18118     "runtime_only": false
18119   },
18120   {
18121     "axioms": [
18122       "propext",
18123       "Quot.sound"
18124     ],
18125     "in_project_namespace": true,
18126     "kind": "definition",
18127     "module": "PaperIRelease.GraphPropagation",
18128     "name": "Komorebi.PaperIRelease.AlgebraInvariant",
18129     "runtime_only": false
18130   },
18131   {
18132     "axioms": [
18133       "propext",
18134       "Quot.sound"
18135     ],
18136     "in_project_namespace": true,
18137     "kind": "theorem",
18138     "module": "KomorebiVerification.PacketNaturalityCompletion",
18139     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet._proof_2",
18140     "runtime_only": false
18141   },
18142   {
18143     "axioms": [],
18144     "in_project_namespace": false,
18145     "kind": "theorem",
18146     "module": "PaperIRelease.GrammarPaths",
18147     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.eq_1",
18148     "runtime_only": false
18149   },
18150   {
18151     "axioms": [
18152       "propext",
18153       "Quot.sound"
18154     ],
18155     "in_project_namespace": true,
18156     "kind": "theorem",
18157     "module": "KomorebiVerification.PathGraphKrylov",
18158     "name": "Komorebi.PathGraphKrylov.krylov_diagonal",
18159     "runtime_only": false
18160   },
18161   {
18162     "axioms": [
18163       "propext",
18164       "Classical.choice",
18165       "Quot.sound"
18166     ],
18167     "in_project_namespace": false,
18168     "kind": "definition",
18169     "module": "PaperIRelease.TopologyUnconditional",
18170     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_8",
18171     "runtime_only": false
18172   },
18173   {
18174     "axioms": [
18175       "propext"
18176     ],
18177     "in_project_namespace": true,
18178     "kind": "theorem",
18179     "module": "KomorebiVerification.ProjectorCore",
18180     "name": "Komorebi.Seed.OperatorRelation.mk.injEq",
18181     "runtime_only": false
18182   },
18183   {
18184     "axioms": [
18185       "propext",
18186       "Classical.choice",
18187       "Quot.sound"
18188     ],
18189     "in_project_namespace": true,
18190     "kind": "definition",
18191     "module": "KomorebiVerification.SeedRankBasics",
18192     "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv",
18193     "runtime_only": false
18194   },
18195   {
18196     "axioms": [
18197       "propext"
18198     ],
18199     "in_project_namespace": true,
18200     "kind": "definition",
18201     "module": "PaperIRelease.CategoryExport",
18202     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._sunfold",
18203     "runtime_only": false
18204   },
18205   {
18206     "axioms": [
18207       "propext",
18208       "Classical.choice",
18209       "Quot.sound"
18210     ],
18211     "in_project_namespace": true,
18212     "kind": "theorem",
18213     "module": "KomorebiVerification.PacketNaturalityCompletion",
18214     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetInclusion.eq_1",
18215     "runtime_only": false
18216   },
18217   {
18218     "axioms": [],
18219     "in_project_namespace": false,
18220     "kind": "definition",
18221     "module": "ReleaseBoundary",
18222     "name": "PaperIBlock08Tests.mults",
18223     "runtime_only": false
18224   },
18225   {
18226     "axioms": [
18227       "propext",
18228       "Classical.choice",
18229       "Quot.sound"
18230     ],
18231     "in_project_namespace": false,
18232     "kind": "theorem",
18233     "module": "KomorebiVerification.SeedRankOperations",
18234     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.seedRank_prod_le_left_of_le",
18235     "runtime_only": false
18236   },
18237   {
18238     "axioms": [],
18239     "in_project_namespace": true,
18240     "kind": "definition",
18241     "module": "KomorebiVerification.ProjectorCore",
18242     "name": "Komorebi.Seed.OperatorExpr.comp.noConfusion",
18243     "runtime_only": false
18244   },
18245   {
18246     "axioms": [
18247       "propext"
18248     ],
18249     "in_project_namespace": true,
18250     "kind": "theorem",
18251     "module": "KomorebiVerification.ProjectorCore",
18252     "name": "Komorebi.Algebra.IsLowerTriangular.add",
18253     "runtime_only": false
18254   },
18255   {
18256     "axioms": [
18257       "propext",
18258       "Classical.choice",
18259       "Quot.sound"
18260     ],
18261     "in_project_namespace": true,
18262     "kind": "definition",
18263     "module": "KomorebiVerification.PacketNaturalityCompletion",
18264     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR",
18265     "runtime_only": false
18266   },
18267   {
18268     "axioms": [
18269       "propext",
18270       "Quot.sound"
18271     ],
18272     "in_project_namespace": true,
18273     "kind": "theorem",
18274     "module": "PaperICompletion4.GroupedPrimary",
18275     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_5",
18276     "runtime_only": false
18277   },
18278   {
18279     "axioms": [
18280       "propext",
18281       "Classical.choice",
18282       "Quot.sound"
18283     ],
18284     "in_project_namespace": true,
18285     "kind": "theorem",
18286     "module": "PaperIRelease.PacketPureBoundaryTests",
18287     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infinite_single_source_formula",
18288     "runtime_only": false
18289   },
18290   {
18291     "axioms": [
18292       "propext"
18293     ],
18294     "in_project_namespace": true,
18295     "kind": "theorem",
18296     "module": "PaperICompletion4.IntrinsicPrimary",
18297     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.mem_primarySubmodule",
18298     "runtime_only": false
18299   },
18300   {
18301     "axioms": [
18302       "propext",
18303       "Classical.choice",
18304       "Quot.sound"
18305     ],
18306     "in_project_namespace": true,
18307     "kind": "definition",
18308     "module": "PaperIRelease.AlgebraPreorder",
18309     "name": "Komorebi.PaperIRelease.strictSupportIdeal",
18310     "runtime_only": false
18311   },
18312   {
18313     "axioms": [],
18314     "in_project_namespace": true,
18315     "kind": "definition",
18316     "module": "KomorebiVerification.ProjectorCore",
18317     "name": "Komorebi.FormalizationStatus.ofNat",
18318     "runtime_only": false
18319   },
18320   {
18321     "axioms": [],
18322     "in_project_namespace": true,
18323     "kind": "definition",
18324     "module": "KomorebiVerification.ProjectorCore",
18325     "name": "Komorebi.ClaimKind.lemmaClaim.elim",
18326     "runtime_only": false
18327   },
18328   {
18329     "axioms": [
18330       "propext",
18331       "Classical.choice",
18332       "Quot.sound"
18333     ],
18334     "in_project_namespace": true,
18335     "kind": "theorem",
18336     "module": "KomorebiVerification.ProjectorCore",
18337     "name": "Komorebi.Foundation.LinearProjectorFamily.mk.injEq",
18338     "runtime_only": false
18339   },
18340   {
18341     "axioms": [
18342       "propext",
18343       "Classical.choice",
18344       "Quot.sound"
18345     ],
18346     "in_project_namespace": true,
18347     "kind": "theorem",
18348     "module": "PaperICompletion4.ResidueQuotient",
18349     "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff._simp_1_1",
18350     "runtime_only": false
18351   },
18352   {
18353     "axioms": [
18354       "propext",
18355       "Classical.choice",
18356       "Quot.sound"
18357     ],
18358     "in_project_namespace": true,
18359     "kind": "theorem",
18360     "module": "KomorebiVerification.PacketNaturalityCompletion",
18361     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_synthesizeBlocks",
18362     "runtime_only": false
18363   },
18364   {
18365     "axioms": [
18366       "propext",
18367       "Quot.sound"
18368     ],
18369     "in_project_namespace": true,
18370     "kind": "theorem",
18371     "module": "KomorebiVerification.PathGraphKrylov",
18372     "name": "Komorebi.PathGraphKrylov.rightStep.eq_1",
18373     "runtime_only": false
18374   },
18375   {
18376     "axioms": [
18377       "propext",
18378       "Quot.sound"
18379     ],
18380     "in_project_namespace": true,
18381     "kind": "definition",
18382     "module": "KomorebiVerification.SeedRankOperations",
18383     "name": "Komorebi.SeedRankOperations.tensorRightModuleInstance",
18384     "runtime_only": false
18385   },
18386   {
18387     "axioms": [
18388       "propext",
18389       "Classical.choice",
18390       "Quot.sound"
18391     ],
18392     "in_project_namespace": true,
18393     "kind": "theorem",
18394     "module": "KomorebiVerification.EllipticAlgorithms",
18395     "name": "Komorebi.FiniteAlgorithms.seeds_subset_orbitHull",
18396     "runtime_only": false
18397   },
18398   {
18399     "axioms": [],
18400     "in_project_namespace": true,
18401     "kind": "definition",
18402     "module": "PaperICompletion8.RegularMultiplicity",
18403     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.MultiplicityModule",
18404     "runtime_only": false
18405   },
18406   {
18407     "axioms": [],
18408     "in_project_namespace": true,
18409     "kind": "theorem",
18410     "module": "KomorebiVerification.ProjectorCore",
18411     "name": "Komorebi.ClaimKind.conjecture.sizeOf_spec",
18412     "runtime_only": false
18413   },
18414   {
18415     "axioms": [
18416       "propext",
18417       "Classical.choice",
18418       "Quot.sound"
18419     ],
18420     "in_project_namespace": true,
18421     "kind": "definition",
18422     "module": "PaperIRelease.PolynomialMonic",
18423     "name": "Komorebi.PaperIRelease.PolynomialModule.MonicIrreducibles",
18424     "runtime_only": false
18425   },
18426   {
18427     "axioms": [],
18428     "in_project_namespace": true,
18429     "kind": "theorem",
18430     "module": "KomorebiVerification.ProjectorCore",
18431     "name": "Komorebi.ClaimRecord.mk.sizeOf_spec",
18432     "runtime_only": false
18433   },
18434   {
18435     "axioms": [],
18436     "in_project_namespace": true,
18437     "kind": "definition",
18438     "module": "PaperIRelease.AlgebraPreorder",
18439     "name": "Komorebi.PaperIRelease.StrictPath._f",
18440     "runtime_only": false
18441   },
18442   {
18443     "axioms": [
18444       "propext",
18445       "Classical.choice",
18446       "Quot.sound"
18447     ],
18448     "in_project_namespace": true,
18449     "kind": "definition",
18450     "module": "PaperIRelease.GrammarAlgebra",
18451     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex",
18452     "runtime_only": false
18453   },
18454   {
18455     "axioms": [
18456       "propext",
18457       "Classical.choice",
18458       "Quot.sound"
18459     ],
18460     "in_project_namespace": true,
18461     "kind": "theorem",
18462     "module": "KomorebiVerification.ExactCoordinates",
18463     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates_apply",
18464     "runtime_only": false
18465   },
18466   {
18467     "axioms": [
18468       "propext",
18469       "Classical.choice",
18470       "Quot.sound"
18471     ],
18472     "in_project_namespace": true,
18473     "kind": "definition",
18474     "module": "PaperIRelease.CategoryPackets",
18475     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.fintype",
18476     "runtime_only": false
18477   },
18478   {
18479     "axioms": [
18480       "propext",
18481       "Classical.choice",
18482       "Quot.sound"
18483     ],
18484     "in_project_namespace": true,
18485     "kind": "theorem",
18486     "module": "PaperICompletion7.Nakayama",
18487     "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_jacobson_smul",
18488     "runtime_only": false
18489   },
18490   {
18491     "axioms": [
18492       "propext",
18493       "Classical.choice",
18494       "Quot.sound"
18495     ],
18496     "in_project_namespace": true,
18497     "kind": "theorem",
18498     "module": "PaperIRelease.PacketTopology",
18499     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM._proof_2",
18500     "runtime_only": false
18501   },
18502   {
18503     "axioms": [
18504       "propext",
18505       "Classical.choice",
18506       "Quot.sound"
18507     ],
18508     "in_project_namespace": false,
18509     "kind": "theorem",
18510     "module": "PaperIRelease.TopologyCountablePackets",
18511     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues.eq_1",
18512     "runtime_only": false
18513   },
18514   {
18515     "axioms": [
18516       "propext",
18517       "Classical.choice",
18518       "Quot.sound"
18519     ],
18520     "in_project_namespace": true,
18521     "kind": "theorem",
18522     "module": "KomorebiVerification.EllipticAlgorithms",
18523     "name": "Komorebi.EllipticCoordinates.Mx_pow_apply",
18524     "runtime_only": false
18525   },
18526   {
18527     "axioms": [
18528       "propext",
18529       "Classical.choice",
18530       "Quot.sound"
18531     ],
18532     "in_project_namespace": true,
18533     "kind": "theorem",
18534     "module": "PaperIRelease.GrammarEquivalence",
18535     "name": "Komorebi.PaperIRelease.GrammarAlgebra.total_liftActionHom",
18536     "runtime_only": false
18537   },
18538   {
18539     "axioms": [
18540       "propext",
18541       "Classical.choice",
18542       "Quot.sound"
18543     ],
18544     "in_project_namespace": true,
18545     "kind": "definition",
18546     "module": "PaperIRelease.PacketExactSequence",
18547     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion",
18548     "runtime_only": false
18549   },
18550   {
18551     "axioms": [
18552       "propext",
18553       "Classical.choice",
18554       "Quot.sound"
18555     ],
18556     "in_project_namespace": true,
18557     "kind": "theorem",
18558     "module": "PaperIRelease.GeneralConditionedCoordinates",
18559     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.equivalent_norm_conditioned_coordinates",
18560     "runtime_only": false
18561   },
18562   {
18563     "axioms": [],
18564     "in_project_namespace": true,
18565     "kind": "inductive",
18566     "module": "KomorebiVerification.ProjectorCore",
18567     "name": "Komorebi.Seed.OperatorRelation",
18568     "runtime_only": false
18569   },
18570   {
18571     "axioms": [
18572       "propext",
18573       "Classical.choice",
18574       "Quot.sound"
18575     ],
18576     "in_project_namespace": true,
18577     "kind": "definition",
18578     "module": "PaperIRelease.TopologyCategories",
18579     "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull",
18580     "runtime_only": false
18581   },
18582   {
18583     "axioms": [],
18584     "in_project_namespace": true,
18585     "kind": "theorem",
18586     "module": "KomorebiVerification.ProjectorCore",
18587     "name": "Komorebi.ClaimKind.numericalCertificate.sizeOf_spec",
18588     "runtime_only": false
18589   },
18590   {
18591     "axioms": [
18592       "propext",
18593       "Classical.choice",
18594       "Quot.sound"
18595     ],
18596     "in_project_namespace": true,
18597     "kind": "definition",
18598     "module": "KomorebiVerification.PacketNaturalityCompletion",
18599     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._f",
18600     "runtime_only": false
18601   },
18602   {
18603     "axioms": [
18604       "propext",
18605       "Classical.choice",
18606       "Quot.sound"
18607     ],
18608     "in_project_namespace": false,
18609     "kind": "theorem",
18610     "module": "PaperIRelease.TopologyUnconditional",
18611     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_le_norm",
18612     "runtime_only": false
18613   },
18614   {
18615     "axioms": [
18616       "propext",
18617       "Classical.choice",
18618       "Quot.sound"
18619     ],
18620     "in_project_namespace": true,
18621     "kind": "theorem",
18622     "module": "PaperICompletion4.OperatorIntrinsicFormula",
18623     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_card_of_component_decomposition",
18624     "runtime_only": false
18625   },
18626   {
18627     "axioms": [
18628       "propext",
18629       "Classical.choice",
18630       "Quot.sound"
18631     ],
18632     "in_project_namespace": false,
18633     "kind": "theorem",
18634     "module": "PaperIRelease.TopologyDenseCompletion",
18635     "name": "PaperIRelease.TopologyDenseCompletion.transported_isUniformInducing",
18636     "runtime_only": false
18637   },
18638   {
18639     "axioms": [
18640       "propext",
18641       "Classical.choice",
18642       "Quot.sound"
18643     ],
18644     "in_project_namespace": true,
18645     "kind": "definition",
18646     "module": "KomorebiVerification.TopologicalCompletion",
18647     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.noConfusion",
18648     "runtime_only": false
18649   },
18650   {
18651     "axioms": [
18652       "propext",
18653       "Classical.choice",
18654       "Quot.sound"
18655     ],
18656     "in_project_namespace": true,
18657     "kind": "definition",
18658     "module": "PaperICompletion.SpectralCertificates",
18659     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenLabelsFintype",
18660     "runtime_only": false
18661   },
18662   {
18663     "axioms": [
18664       "propext",
18665       "Classical.choice",
18666       "Quot.sound"
18667     ],
18668     "in_project_namespace": true,
18669     "kind": "constructor",
18670     "module": "PaperIRelease.GrammarAlgebra",
18671     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.arrow_corner",
18672     "runtime_only": false
18673   },
18674   {
18675     "axioms": [
18676       "propext",
18677       "Classical.choice",
18678       "Quot.sound"
18679     ],
18680     "in_project_namespace": false,
18681     "kind": "theorem",
18682     "module": "PaperIRelease.TopologyCountablePackets",
18683     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packet_neg_val",
18684     "runtime_only": false
18685   },
18686   {
18687     "axioms": [
18688       "propext",
18689       "Quot.sound"
18690     ],
18691     "in_project_namespace": true,
18692     "kind": "theorem",
18693     "module": "KomorebiVerification.PacketNaturalityCompletion",
18694     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv._proof_1",
18695     "runtime_only": false
18696   },
18697   {
18698     "axioms": [
18699       "propext",
18700       "Quot.sound"
18701     ],
18702     "in_project_namespace": true,
18703     "kind": "theorem",
18704     "module": "KomorebiVerification.ProjectorCore",
18705     "name": "Komorebi.Seed.hull_le",
18706     "runtime_only": false
18707   },
18708   {
18709     "axioms": [
18710       "propext",
18711       "Classical.choice",
18712       "Quot.sound"
18713     ],
18714     "in_project_namespace": false,
18715     "kind": "theorem",
18716     "module": "PaperIRelease.TopologyUnconditional",
18717     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_smul_val",
18718     "runtime_only": false
18719   },
18720   {
18721     "axioms": [
18722       "propext",
18723       "Classical.choice",
18724       "Quot.sound"
18725     ],
18726     "in_project_namespace": true,
18727     "kind": "theorem",
18728     "module": "KomorebiVerification.ProjectorCore",
18729     "name": "Komorebi.Foundation.LinearProjectorFamily.orthogonal",
18730     "runtime_only": false
18731   },
18732   {
18733     "axioms": [
18734       "propext",
18735       "Classical.choice",
18736       "Quot.sound"
18737     ],
18738     "in_project_namespace": true,
18739     "kind": "theorem",
18740     "module": "PaperIRelease.AlgebraClassGrouping",
18741     "name": "Komorebi.PaperIRelease.classPacketFamily.eq_1",
18742     "runtime_only": false
18743   },
18744   {
18745     "axioms": [
18746       "propext",
18747       "Classical.choice",
18748       "Quot.sound"
18749     ],
18750     "in_project_namespace": true,
18751     "kind": "definition",
18752     "module": "PaperIRelease.GrammarTyped",
18753     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.splitData",
18754     "runtime_only": false
18755   },
18756   {
18757     "axioms": [
18758       "propext",
18759       "Classical.choice",
18760       "Quot.sound"
18761     ],
18762     "in_project_namespace": true,
18763     "kind": "theorem",
18764     "module": "PaperIRelease.GrammarAlgebra",
18765     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_3",
18766     "runtime_only": false
18767   },
18768   {
18769     "axioms": [
18770       "propext",
18771       "Classical.choice",
18772       "Quot.sound"
18773     ],
18774     "in_project_namespace": true,
18775     "kind": "theorem",
18776     "module": "PaperICompletion8.SemisimpleFormula",
18777     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.finiteAlgebra_radicalQuotient_isSemisimple",
18778     "runtime_only": false
18779   },
18780   {
18781     "axioms": [
18782       "propext",
18783       "Classical.choice",
18784       "Quot.sound"
18785     ],
18786     "in_project_namespace": true,
18787     "kind": "definition",
18788     "module": "PaperIRelease.GrammarAlgebra",
18789     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates",
18790     "runtime_only": false
18791   },
18792   {
18793     "axioms": [
18794       "propext",
18795       "Classical.choice",
18796       "Quot.sound"
18797     ],
18798     "in_project_namespace": false,
18799     "kind": "definition",
18800     "module": "PaperIRelease.TopologyCountablePackets",
18801     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.noConfusion",
18802     "runtime_only": false
18803   },
18804   {
18805     "axioms": [
18806       "propext"
18807     ],
18808     "in_project_namespace": true,
18809     "kind": "theorem",
18810     "module": "KomorebiVerification.ProjectorCore",
18811     "name": "Komorebi.FiniteDifference.iteratedDiff_two",
18812     "runtime_only": false
18813   },
18814   {
18815     "axioms": [
18816       "propext",
18817       "Quot.sound"
18818     ],
18819     "in_project_namespace": true,
18820     "kind": "theorem",
18821     "module": "PaperIRelease.CoordinateTransport",
18822     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_2",
18823     "runtime_only": false
18824   },
18825   {
18826     "axioms": [
18827       "propext",
18828       "Classical.choice",
18829       "Quot.sound"
18830     ],
18831     "in_project_namespace": true,
18832     "kind": "theorem",
18833     "module": "PaperIRelease.GraphSourceBoundary",
18834     "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_source_boundary",
18835     "runtime_only": false
18836   },
18837   {
18838     "axioms": [
18839       "propext",
18840       "Classical.choice",
18841       "Quot.sound"
18842     ],
18843     "in_project_namespace": true,
18844     "kind": "theorem",
18845     "module": "PaperIRelease.GrammarEquivalence",
18846     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_full",
18847     "runtime_only": false
18848   },
18849   {
18850     "axioms": [],
18851     "in_project_namespace": true,
18852     "kind": "definition",
18853     "module": "KomorebiVerification.ProjectorCore",
18854     "name": "Komorebi.ClaimRecord.noConfusionType",
18855     "runtime_only": false
18856   },
18857   {
18858     "axioms": [
18859       "propext",
18860       "Classical.choice",
18861       "Quot.sound"
18862     ],
18863     "in_project_namespace": true,
18864     "kind": "definition",
18865     "module": "PaperIRelease.CategoryPackets",
18866     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.ctorIdx",
18867     "runtime_only": false
18868   },
18869   {
18870     "axioms": [
18871       "propext",
18872       "Classical.choice",
18873       "Quot.sound"
18874     ],
18875     "in_project_namespace": true,
18876     "kind": "definition",
18877     "module": "PaperIRelease.PacketUniversal",
18878     "name": "Komorebi.PaperIRelease.PacketUniversal.packetProjection",
18879     "runtime_only": false
18880   },
18881   {
18882     "axioms": [],
18883     "in_project_namespace": true,
18884     "kind": "definition",
18885     "module": "PaperIRelease.CategoryExport",
18886     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.noConfusion",
18887     "runtime_only": false
18888   },
18889   {
18890     "axioms": [
18891       "propext",
18892       "Quot.sound"
18893     ],
18894     "in_project_namespace": true,
18895     "kind": "theorem",
18896     "module": "PaperICompletion8.DivisionRows",
18897     "name": "Komorebi.PaperICompletion8.DivisionRows.RowsSpan.eq_1",
18898     "runtime_only": false
18899   },
18900   {
18901     "axioms": [
18902       "propext",
18903       "Classical.choice",
18904       "Quot.sound"
18905     ],
18906     "in_project_namespace": true,
18907     "kind": "definition",
18908     "module": "PaperIRelease.PolynomialMonic",
18909     "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec",
18910     "runtime_only": false
18911   },
18912   {
18913     "axioms": [
18914       "propext",
18915       "Classical.choice",
18916       "Quot.sound"
18917     ],
18918     "in_project_namespace": true,
18919     "kind": "theorem",
18920     "module": "PaperIRelease.GrammarAlgebra",
18921     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.respects",
18922     "runtime_only": false
18923   },
18924   {
18925     "axioms": [
18926       "propext",
18927       "Classical.choice",
18928       "Quot.sound"
18929     ],
18930     "in_project_namespace": true,
18931     "kind": "theorem",
18932     "module": "PaperIRelease.AlgebraSupport",
18933     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_5",
18934     "runtime_only": false
18935   },
18936   {
18937     "axioms": [],
18938     "in_project_namespace": true,
18939     "kind": "definition",
18940     "module": "KomorebiVerification.ProjectorCore",
18941     "name": "Komorebi.Seed.instReprOperatorExpr.repr._f",
18942     "runtime_only": false
18943   },
18944   {
18945     "axioms": [
18946       "propext",
18947       "Classical.choice",
18948       "Quot.sound"
18949     ],
18950     "in_project_namespace": false,
18951     "kind": "theorem",
18952     "module": "PaperIRelease.TopologyTransport",
18953     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_2",
18954     "runtime_only": false
18955   },
18956   {
18957     "axioms": [],
18958     "in_project_namespace": true,
18959     "kind": "definition",
18960     "module": "PaperIRelease.CategoryExport",
18961     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.elim",
18962     "runtime_only": false
18963   },
18964   {
18965     "axioms": [
18966       "propext",
18967       "Classical.choice",
18968       "Quot.sound"
18969     ],
18970     "in_project_namespace": true,
18971     "kind": "theorem",
18972     "module": "KomorebiVerification.SingleOperatorGraph",
18973     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity",
18974     "runtime_only": false
18975   },
18976   {
18977     "axioms": [
18978       "propext",
18979       "Classical.choice",
18980       "Quot.sound"
18981     ],
18982     "in_project_namespace": true,
18983     "kind": "definition",
18984     "module": "KomorebiVerification.SingleOperatorGraph",
18985     "name": "Komorebi.SingleOperatorGraph.evalVector",
18986     "runtime_only": false
18987   },
18988   {
18989     "axioms": [
18990       "propext",
18991       "Classical.choice",
18992       "Quot.sound"
18993     ],
18994     "in_project_namespace": true,
18995     "kind": "theorem",
18996     "module": "PaperICompletion3.OperatorPrimaryAPI",
18997     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_iff_minpoly_eq_charpoly",
18998     "runtime_only": false
18999   },
19000   {
19001     "axioms": [],
19002     "in_project_namespace": false,
19003     "kind": "theorem",
19004     "module": "PaperIRelease.AlgebraClassGrouping",
19005     "name": "_private.PaperIRelease.AlgebraClassGrouping.0.Komorebi.PaperIRelease.strictPath_map",
19006     "runtime_only": false
19007   },
19008   {
19009     "axioms": [
19010       "propext",
19011       "Classical.choice",
19012       "Quot.sound"
19013     ],
19014     "in_project_namespace": false,
19015     "kind": "definition",
19016     "module": "PaperIRelease.TopologyUnconditional",
19017     "name": "PaperIRelease.TopologyUnconditional.Coefficients",
19018     "runtime_only": false
19019   },
19020   {
19021     "axioms": [
19022       "propext",
19023       "Classical.choice",
19024       "Quot.sound"
19025     ],
19026     "in_project_namespace": true,
19027     "kind": "definition",
19028     "module": "KomorebiVerification.EllipticAlgorithms",
19029     "name": "Komorebi.EllipticCoordinates.NormalForm",
19030     "runtime_only": false
19031   },
19032   {
19033     "axioms": [
19034       "propext",
19035       "Classical.choice",
19036       "Quot.sound"
19037     ],
19038     "in_project_namespace": true,
19039     "kind": "theorem",
19040     "module": "KomorebiVerification.PathGraphKrylov",
19041     "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_3",
19042     "runtime_only": false
19043   },
19044   {
19045     "axioms": [
19046       "propext",
19047       "Classical.choice",
19048       "Quot.sound"
19049     ],
19050     "in_project_namespace": true,
19051     "kind": "theorem",
19052     "module": "KomorebiVerification.PacketNaturalityCompletion",
19053     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB.eq_1",
19054     "runtime_only": false
19055   },
19056   {
19057     "axioms": [
19058       "propext",
19059       "Quot.sound"
19060     ],
19061     "in_project_namespace": true,
19062     "kind": "theorem",
19063     "module": "KomorebiVerification.PacketNaturalityCompletion",
19064     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.missingSeed.eq_1",
19065     "runtime_only": false
19066   },
19067   {
19068     "axioms": [
19069       "propext",
19070       "Classical.choice",
19071       "Quot.sound"
19072     ],
19073     "in_project_namespace": false,
19074     "kind": "definition",
19075     "module": "PaperIRelease.TopologyCountablePackets",
19076     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNorm",
19077     "runtime_only": false
19078   },
19079   {
19080     "axioms": [
19081       "propext",
19082       "Classical.choice",
19083       "Quot.sound"
19084     ],
19085     "in_project_namespace": true,
19086     "kind": "definition",
19087     "module": "KomorebiVerification.PacketNaturalityCompletion",
19088     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._sunfold",
19089     "runtime_only": false
19090   },
19091   {
19092     "axioms": [
19093       "propext",
19094       "Quot.sound"
19095     ],
19096     "in_project_namespace": true,
19097     "kind": "theorem",
19098     "module": "PaperIRelease.CoordinateTransport",
19099     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_1",
19100     "runtime_only": false
19101   },
19102   {
19103     "axioms": [
19104       "propext",
19105       "Quot.sound"
19106     ],
19107     "in_project_namespace": true,
19108     "kind": "theorem",
19109     "module": "PaperICompletion5.LinearPrimaryEigenspace",
19110     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_1",
19111     "runtime_only": false
19112   },
19113   {
19114     "axioms": [],
19115     "in_project_namespace": true,
19116     "kind": "constructor",
19117     "module": "KomorebiVerification.ProjectorCore",
19118     "name": "Komorebi.FormalizationStatus.externalInput",
19119     "runtime_only": false
19120   },
19121   {
19122     "axioms": [
19123       "propext",
19124       "Classical.choice",
19125       "Quot.sound"
19126     ],
19127     "in_project_namespace": true,
19128     "kind": "theorem",
19129     "module": "PaperIRelease.PacketPureBoundaryTests",
19130     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_1",
19131     "runtime_only": false
19132   },
19133   {
19134     "axioms": [
19135       "propext",
19136       "Classical.choice",
19137       "Quot.sound"
19138     ],
19139     "in_project_namespace": false,
19140     "kind": "theorem",
19141     "module": "PaperIRelease.TopologyCountablePackets",
19142     "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound._proof_2",
19143     "runtime_only": false
19144   },
19145   {
19146     "axioms": [
19147       "propext",
19148       "Classical.choice",
19149       "Quot.sound"
19150     ],
19151     "in_project_namespace": false,
19152     "kind": "theorem",
19153     "module": "PaperIRelease.TopologyUnconditional",
19154     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_18",
19155     "runtime_only": false
19156   },
19157   {
19158     "axioms": [
19159       "propext",
19160       "Quot.sound"
19161     ],
19162     "in_project_namespace": true,
19163     "kind": "theorem",
19164     "module": "KomorebiVerification.SeedRankBasics",
19165     "name": "Komorebi.SeedRankBasics.Generates.eq_1",
19166     "runtime_only": false
19167   },
19168   {
19169     "axioms": [],
19170     "in_project_namespace": true,
19171     "kind": "constructor",
19172     "module": "KomorebiVerification.ProjectorCore",
19173     "name": "Komorebi.ClaimKind.propositionClaim",
19174     "runtime_only": false
19175   },
19176   {
19177     "axioms": [
19178       "propext",
19179       "Quot.sound"
19180     ],
19181     "in_project_namespace": true,
19182     "kind": "theorem",
19183     "module": "PaperIRelease.GrammarModules",
19184     "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_2",
19185     "runtime_only": false
19186   },
19187   {
19188     "axioms": [
19189       "propext",
19190       "Quot.sound"
19191     ],
19192     "in_project_namespace": true,
19193     "kind": "theorem",
19194     "module": "PaperICompletion4.ResidueQuotient",
19195     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_2",
19196     "runtime_only": false
19197   },
19198   {
19199     "axioms": [
19200       "propext",
19201       "Quot.sound"
19202     ],
19203     "in_project_namespace": true,
19204     "kind": "theorem",
19205     "module": "PaperIRelease.PacketCorners",
19206     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_1",
19207     "runtime_only": false
19208   },
19209   {
19210     "axioms": [
19211       "propext",
19212       "Quot.sound"
19213     ],
19214     "in_project_namespace": true,
19215     "kind": "theorem",
19216     "module": "PaperICompletion4.GroupedPrimary",
19217     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_10",
19218     "runtime_only": false
19219   },
19220   {
19221     "axioms": [
19222       "propext",
19223       "Classical.choice",
19224       "Quot.sound"
19225     ],
19226     "in_project_namespace": true,
19227     "kind": "theorem",
19228     "module": "KomorebiVerification.PaperIBlockCompletion",
19229     "name": "Komorebi.Foundation.end_comp_eq_sum_transferBlock_comps",
19230     "runtime_only": false
19231   },
19232   {
19233     "axioms": [
19234       "propext",
19235       "Classical.choice",
19236       "Quot.sound"
19237     ],
19238     "in_project_namespace": true,
19239     "kind": "theorem",
19240     "module": "KomorebiVerification.EllipticAlgorithms",
19241     "name": "Komorebi.EllipticCoordinates.My_pow_apply",
19242     "runtime_only": false
19243   },
19244   {
19245     "axioms": [
19246       "propext",
19247       "Classical.choice",
19248       "Quot.sound"
19249     ],
19250     "in_project_namespace": true,
19251     "kind": "theorem",
19252     "module": "PaperIRelease.PacketCorners",
19253     "name": "Komorebi.PaperIRelease.cornerCompression._proof_2",
19254     "runtime_only": false
19255   },
19256   {
19257     "axioms": [],
19258     "in_project_namespace": true,
19259     "kind": "theorem",
19260     "module": "KomorebiVerification.ProjectorCore",
19261     "name": "Komorebi.FormalizationStatus.externalInput.sizeOf_spec",
19262     "runtime_only": false
19263   },
19264   {
19265     "axioms": [
19266       "propext",
19267       "Classical.choice",
19268       "Quot.sound"
19269     ],
19270     "in_project_namespace": true,
19271     "kind": "theorem",
19272     "module": "KomorebiVerification.PacketNaturalityCompletion",
19273     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_3",
19274     "runtime_only": false
19275   },
19276   {
19277     "axioms": [
19278       "propext",
19279       "Classical.choice",
19280       "Quot.sound"
19281     ],
19282     "in_project_namespace": true,
19283     "kind": "theorem",
19284     "module": "PaperIRelease.PacketCorners",
19285     "name": "Komorebi.PaperIRelease.idempotent_range_fixed",
19286     "runtime_only": false
19287   },
19288   {
19289     "axioms": [
19290       "propext",
19291       "Classical.choice",
19292       "Quot.sound"
19293     ],
19294     "in_project_namespace": true,
19295     "kind": "theorem",
19296     "module": "KomorebiVerification.PacketNaturalityCompletion",
19297     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_seedRank_eq_of_bijective",
19298     "runtime_only": false
19299   },
19300   {
19301     "axioms": [
19302       "propext",
19303       "Classical.choice",
19304       "Quot.sound"
19305     ],
19306     "in_project_namespace": true,
19307     "kind": "theorem",
19308     "module": "PaperICompletion3.PrimarySeedFormula",
19309     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds.eq_1",
19310     "runtime_only": false
19311   },
19312   {
19313     "axioms": [
19314       "propext",
19315       "Classical.choice",
19316       "Quot.sound"
19317     ],
19318     "in_project_namespace": true,
19319     "kind": "definition",
19320     "module": "PaperIRelease.GrammarAlgebra",
19321     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex",
19322     "runtime_only": false
19323   },
19324   {
19325     "axioms": [
19326       "propext",
19327       "Classical.choice",
19328       "Quot.sound"
19329     ],
19330     "in_project_namespace": true,
19331     "kind": "definition",
19332     "module": "KomorebiVerification.ProjectorCore",
19333     "name": "Komorebi.Foundation.LinearProjectorFamily.mk._flat_ctor",
19334     "runtime_only": false
19335   },
19336   {
19337     "axioms": [
19338       "propext",
19339       "Classical.choice",
19340       "Quot.sound"
19341     ],
19342     "in_project_namespace": true,
19343     "kind": "theorem",
19344     "module": "PaperIRelease.TopologyCategories",
19345     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.packet_continuous",
19346     "runtime_only": false
19347   },
19348   {
19349     "axioms": [],
19350     "in_project_namespace": true,
19351     "kind": "definition",
19352     "module": "PaperIRelease.GrammarPaths",
19353     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath._sizeOf_1",
19354     "runtime_only": false
19355   },
19356   {
19357     "axioms": [
19358       "propext",
19359       "Classical.choice",
19360       "Quot.sound"
19361     ],
19362     "in_project_namespace": true,
19363     "kind": "definition",
19364     "module": "PaperICompletion3.PrimarySeedFormula",
19365     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv",
19366     "runtime_only": false
19367   },
19368   {
19369     "axioms": [
19370       "propext",
19371       "Classical.choice",
19372       "Quot.sound"
19373     ],
19374     "in_project_namespace": true,
19375     "kind": "theorem",
19376     "module": "PaperICompletion5.LinearPrimaryEigenspace",
19377     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_1",
19378     "runtime_only": false
19379   },
19380   {
19381     "axioms": [
19382       "propext",
19383       "Classical.choice",
19384       "Quot.sound"
19385     ],
19386     "in_project_namespace": true,
19387     "kind": "theorem",
19388     "module": "PaperIRelease.AlgebraSupport",
19389     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_3",
19390     "runtime_only": false
19391   },
19392   {
19393     "axioms": [
19394       "propext",
19395       "Classical.choice",
19396       "Quot.sound"
19397     ],
19398     "in_project_namespace": true,
19399     "kind": "theorem",
19400     "module": "PaperICompletion5.CyclicGeometricCriterion",
19401     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.minpoly_eq_charpoly_iff_all_spectral_multiplicities_one",
19402     "runtime_only": false
19403   },
19404   {
19405     "axioms": [
19406       "propext",
19407       "Classical.choice",
19408       "Quot.sound"
19409     ],
19410     "in_project_namespace": true,
19411     "kind": "theorem",
19412     "module": "PaperIRelease.PacketDescent",
19413     "name": "Komorebi.Foundation.LinearProjectorFamily.transferBlock_descends",
19414     "runtime_only": false
19415   },
19416   {
19417     "axioms": [
19418       "propext",
19419       "Quot.sound"
19420     ],
19421     "in_project_namespace": false,
19422     "kind": "definition",
19423     "module": "PaperIRelease.TopologyTransport",
19424     "name": "PaperIRelease.TopologyTransport.operatorHull",
19425     "runtime_only": false
19426   },
19427   {
19428     "axioms": [],
19429     "in_project_namespace": true,
19430     "kind": "theorem",
19431     "module": "KomorebiVerification.ProjectorCore",
19432     "name": "Komorebi.Quantum.diagonalApply.eq_1",
19433     "runtime_only": false
19434   },
19435   {
19436     "axioms": [
19437       "propext",
19438       "Quot.sound"
19439     ],
19440     "in_project_namespace": true,
19441     "kind": "theorem",
19442     "module": "KomorebiVerification.KernelAudit",
19443     "name": "Komorebi.Verification.parityAddress._proof_1",
19444     "runtime_only": false
19445   },
19446   {
19447     "axioms": [
19448       "propext",
19449       "Classical.choice",
19450       "Quot.sound"
19451     ],
19452     "in_project_namespace": true,
19453     "kind": "theorem",
19454     "module": "PaperICompletion.SpectralCertificates",
19455     "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedNumber_isLeast._proof_1_1",
19456     "runtime_only": false
19457   },
19458   {
19459     "axioms": [
19460       "propext",
19461       "Classical.choice",
19462       "Quot.sound"
19463     ],
19464     "in_project_namespace": true,
19465     "kind": "theorem",
19466     "module": "PaperIRelease.GrammarTyped",
19467     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrow_corner",
19468     "runtime_only": false
19469   },
19470   {
19471     "axioms": [],
19472     "in_project_namespace": true,
19473     "kind": "theorem",
19474     "module": "PaperIRelease.CategoryExport",
19475     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.inj",
19476     "runtime_only": false
19477   },
19478   {
19479     "axioms": [
19480       "propext",
19481       "Classical.choice",
19482       "Quot.sound"
19483     ],
19484     "in_project_namespace": true,
19485     "kind": "definition",
19486     "module": "PaperIRelease.TopologyCategories",
19487     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject._sizeOf_inst",
19488     "runtime_only": false
19489   },
19490   {
19491     "axioms": [
19492       "propext"
19493     ],
19494     "in_project_namespace": true,
19495     "kind": "theorem",
19496     "module": "KomorebiVerification.ProjectorCore",
19497     "name": "Komorebi.FiniteDifference.iteratedDiff_three",
19498     "runtime_only": false
19499   },
19500   {
19501     "axioms": [
19502       "propext",
19503       "Classical.choice",
19504       "Quot.sound"
19505     ],
19506     "in_project_namespace": true,
19507     "kind": "theorem",
19508     "module": "PaperICompletion6.PrimaryCyclicCriterion",
19509     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_polynomialModule_cyclic",
19510     "runtime_only": false
19511   },
19512   {
19513     "axioms": [
19514       "propext",
19515       "Classical.choice",
19516       "Quot.sound"
19517     ],
19518     "in_project_namespace": true,
19519     "kind": "definition",
19520     "module": "PaperICompletion4.ResidueQuotient",
19521     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryProductQuotientEquiv",
19522     "runtime_only": false
19523   },
19524   {
19525     "axioms": [
19526       "propext",
19527       "Quot.sound"
19528     ],
19529     "in_project_namespace": true,
19530     "kind": "theorem",
19531     "module": "PaperICompletion3.PrimarySeedFormula",
19532     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv._proof_1",
19533     "runtime_only": false
19534   },
19535   {
19536     "axioms": [
19537       "propext",
19538       "Classical.choice",
19539       "Quot.sound"
19540     ],
19541     "in_project_namespace": true,
19542     "kind": "theorem",
19543     "module": "KomorebiVerification.SemisimpleCompletion",
19544     "name": "Komorebi.SemisimpleCompletion.splitProduct_seedRank_eq_maxCeilDiv",
19545     "runtime_only": false
19546   },
19547   {
19548     "axioms": [
19549       "propext",
19550       "Classical.choice",
19551       "Quot.sound"
19552     ],
19553     "in_project_namespace": true,
19554     "kind": "theorem",
19555     "module": "KomorebiVerification.SeedRankOperations",
19556     "name": "Komorebi.SeedRankOperations.seedRank_eq_of_bijective_semilinear",
19557     "runtime_only": false
19558   },
19559   {
19560     "axioms": [
19561       "propext",
19562       "Classical.choice",
19563       "Quot.sound"
19564     ],
19565     "in_project_namespace": true,
19566     "kind": "definition",
19567     "module": "PaperIRelease.PacketSourceLower",
19568     "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding",
19569     "runtime_only": false
19570   },
19571   {
19572     "axioms": [
19573       "propext",
19574       "Classical.choice",
19575       "Quot.sound"
19576     ],
19577     "in_project_namespace": true,
19578     "kind": "theorem",
19579     "module": "KomorebiVerification.EllipticAlgorithms",
19580     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_4",
19581     "runtime_only": false
19582   },
19583   {
19584     "axioms": [
19585       "propext",
19586       "Classical.choice",
19587       "Quot.sound"
19588     ],
19589     "in_project_namespace": false,
19590     "kind": "definition",
19591     "module": "PaperIRelease.TopologyUnconditional",
19592     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedSpace",
19593     "runtime_only": false
19594   },
19595   {
19596     "axioms": [
19597       "propext",
19598       "Quot.sound"
19599     ],
19600     "in_project_namespace": false,
19601     "kind": "theorem",
19602     "module": "KomorebiVerification.SeedRankOperations",
19603     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_1",
19604     "runtime_only": false
19605   },
19606   {
19607     "axioms": [
19608       "propext",
19609       "Classical.choice",
19610       "Quot.sound"
19611     ],
19612     "in_project_namespace": true,
19613     "kind": "definition",
19614     "module": "PaperIRelease.CategoryPackets",
19615     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.casesOn",
19616     "runtime_only": false
19617   },
19618   {
19619     "axioms": [
19620       "propext",
19621       "Classical.choice",
19622       "Quot.sound"
19623     ],
19624     "in_project_namespace": true,
19625     "kind": "theorem",
19626     "module": "KomorebiVerification.PacketNaturalityCompletion",
19627     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_apply_coe",
19628     "runtime_only": false
19629   },
19630   {
19631     "axioms": [
19632       "propext",
19633       "Classical.choice",
19634       "Quot.sound"
19635     ],
19636     "in_project_namespace": true,
19637     "kind": "theorem",
19638     "module": "PaperICompletion8.RegularMultiplicity",
19639     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv._proof_1",
19640     "runtime_only": false
19641   },
19642   {
19643     "axioms": [
19644       "propext"
19645     ],
19646     "in_project_namespace": true,
19647     "kind": "theorem",
19648     "module": "PaperIRelease.CategoryExport",
19649     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.injEq",
19650     "runtime_only": false
19651   },
19652   {
19653     "axioms": [
19654       "propext",
19655       "Classical.choice",
19656       "Quot.sound"
19657     ],
19658     "in_project_namespace": true,
19659     "kind": "theorem",
19660     "module": "PaperIRelease.GraphReachability",
19661     "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra._proof_2",
19662     "runtime_only": false
19663   },
19664   {
19665     "axioms": [
19666       "propext",
19667       "Classical.choice",
19668       "Quot.sound"
19669     ],
19670     "in_project_namespace": true,
19671     "kind": "theorem",
19672     "module": "PaperICompletion6.OneInvariantFactor",
19673     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_5",
19674     "runtime_only": false
19675   },
19676   {
19677     "axioms": [],
19678     "in_project_namespace": true,
19679     "kind": "theorem",
19680     "module": "KomorebiVerification.ProjectorCore",
19681     "name": "Komorebi.ClaimKind.propositionClaim.sizeOf_spec",
19682     "runtime_only": false
19683   },
19684   {
19685     "axioms": [
19686       "propext",
19687       "Classical.choice",
19688       "Quot.sound"
19689     ],
19690     "in_project_namespace": true,
19691     "kind": "definition",
19692     "module": "PaperICompletion3.OperatorPrimaryAPI",
19693     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation._sizeOf_inst",
19694     "runtime_only": false
19695   },
19696   {
19697     "axioms": [
19698       "propext",
19699       "Classical.choice",
19700       "Quot.sound"
19701     ],
19702     "in_project_namespace": true,
19703     "kind": "theorem",
19704     "module": "PaperICompletion5.CyclicGeometricCriterion",
19705     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_all_spectral_multiplicities_one",
19706     "runtime_only": false
19707   },
19708   {
19709     "axioms": [
19710       "propext",
19711       "Classical.choice",
19712       "Quot.sound"
19713     ],
19714     "in_project_namespace": true,
19715     "kind": "theorem",
19716     "module": "KomorebiVerification.SingleOperatorGraph",
19717     "name": "Komorebi.SingleOperatorGraph.path_endpoint_seedNumber_isLeast_one",
19718     "runtime_only": false
19719   },
19720   {
19721     "axioms": [
19722       "propext",
19723       "Classical.choice",
19724       "Quot.sound"
19725     ],
19726     "in_project_namespace": true,
19727     "kind": "definition",
19728     "module": "PaperIRelease.CategoryPackets",
19729     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.recOn",
19730     "runtime_only": false
19731   },
19732   {
19733     "axioms": [
19734       "propext",
19735       "Classical.choice",
19736       "Quot.sound"
19737     ],
19738     "in_project_namespace": false,
19739     "kind": "inductive",
19740     "module": "PaperIRelease.TopologyCountablePackets",
19741     "name": "PaperIRelease.TopologyCountablePackets.Projectors",
19742     "runtime_only": false
19743   },
19744   {
19745     "axioms": [
19746       "propext",
19747       "Classical.choice",
19748       "Quot.sound"
19749     ],
19750     "in_project_namespace": true,
19751     "kind": "theorem",
19752     "module": "PaperIRelease.GraphPropagation",
19753     "name": "Komorebi.PaperIRelease.submodule_eq_top_of_sources",
19754     "runtime_only": false
19755   },
19756   {
19757     "axioms": [
19758       "propext",
19759       "Classical.choice",
19760       "Quot.sound"
19761     ],
19762     "in_project_namespace": true,
19763     "kind": "theorem",
19764     "module": "KomorebiVerification.ExactCoordinates",
19765     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates_symm_apply",
19766     "runtime_only": false
19767   },
19768   {
19769     "axioms": [
19770       "propext",
19771       "Quot.sound"
19772     ],
19773     "in_project_namespace": true,
19774     "kind": "theorem",
19775     "module": "PaperIRelease.AlgebraQuotient",
19776     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_2",
19777     "runtime_only": false
19778   },
19779   {
19780     "axioms": [
19781       "propext",
19782       "Quot.sound"
19783     ],
19784     "in_project_namespace": true,
19785     "kind": "theorem",
19786     "module": "PaperIRelease.GraphPropagation",
19787     "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_2",
19788     "runtime_only": false
19789   },
19790   {
19791     "axioms": [
19792       "propext",
19793       "Quot.sound"
19794     ],
19795     "in_project_namespace": true,
19796     "kind": "definition",
19797     "module": "KomorebiVerification.EllipticAlgorithms",
19798     "name": "Komorebi.FiniteAlgorithms.orbitHull",
19799     "runtime_only": false
19800   },
19801   {
19802     "axioms": [
19803       "propext",
19804       "Classical.choice",
19805       "Quot.sound"
19806     ],
19807     "in_project_namespace": true,
19808     "kind": "theorem",
19809     "module": "KomorebiVerification.SemisimpleCompletion",
19810     "name": "Komorebi.SemisimpleCompletion.multiplicity_seedRank_formula",
19811     "runtime_only": false
19812   },
19813   {
19814     "axioms": [
19815       "propext",
19816       "Quot.sound"
19817     ],
19818     "in_project_namespace": true,
19819     "kind": "theorem",
19820     "module": "PaperIRelease.PolynomialModule",
19821     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_1",
19822     "runtime_only": false
19823   },
19824   {
19825     "axioms": [
19826       "propext",
19827       "Classical.choice",
19828       "Quot.sound"
19829     ],
19830     "in_project_namespace": true,
19831     "kind": "theorem",
19832     "module": "KomorebiVerification.ExactCoordinates",
19833     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis._proof_1",
19834     "runtime_only": false
19835   },
19836   {
19837     "axioms": [
19838       "propext",
19839       "Classical.choice",
19840       "Quot.sound"
19841     ],
19842     "in_project_namespace": false,
19843     "kind": "theorem",
19844     "module": "PaperIRelease.TopologyCountablePackets",
19845     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packet_norm_eq",
19846     "runtime_only": false
19847   },
19848   {
19849     "axioms": [],
19850     "in_project_namespace": true,
19851     "kind": "definition",
19852     "module": "KomorebiVerification.ProjectorCore",
19853     "name": "Komorebi.Packet.fibreProj",
19854     "runtime_only": false
19855   },
19856   {
19857     "axioms": [
19858       "propext",
19859       "Classical.choice",
19860       "Quot.sound"
19861     ],
19862     "in_project_namespace": true,
19863     "kind": "definition",
19864     "module": "PaperIRelease.TopologyCategories",
19865     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.noConfusion",
19866     "runtime_only": false
19867   },
19868   {
19869     "axioms": [
19870       "propext",
19871       "Classical.choice",
19872       "Quot.sound"
19873     ],
19874     "in_project_namespace": true,
19875     "kind": "theorem",
19876     "module": "PaperICompletion6.OneInvariantFactor",
19877     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.toMatrix_quotientCompanionBasis",
19878     "runtime_only": false
19879   },
19880   {
19881     "axioms": [
19882       "propext",
19883       "Classical.choice",
19884       "Quot.sound"
19885     ],
19886     "in_project_namespace": true,
19887     "kind": "theorem",
19888     "module": "PaperIRelease.PacketBoundaryTests",
19889     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.restriction_to_zero_is_zero",
19890     "runtime_only": false
19891   },
19892   {
19893     "axioms": [
19894       "propext",
19895       "Classical.choice",
19896       "Quot.sound"
19897     ],
19898     "in_project_namespace": true,
19899     "kind": "theorem",
19900     "module": "PaperIRelease.BoundedStar",
19901     "name": "Komorebi.PaperIRelease.BoundedSupport.block_rankOne",
19902     "runtime_only": false
19903   },
19904   {
19905     "axioms": [
19906       "propext",
19907       "Classical.choice",
19908       "Quot.sound"
19909     ],
19910     "in_project_namespace": true,
19911     "kind": "definition",
19912     "module": "PaperIRelease.GraphReachability",
19913     "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra",
19914     "runtime_only": false
19915   },
19916   {
19917     "axioms": [
19918       "propext",
19919       "Classical.choice",
19920       "Quot.sound"
19921     ],
19922     "in_project_namespace": true,
19923     "kind": "theorem",
19924     "module": "PaperIRelease.GraphSourceBoundary",
19925     "name": "Komorebi.PaperIRelease.FiniteDigraph.empty_graph_source_boundary",
19926     "runtime_only": false
19927   },
19928   {
19929     "axioms": [
19930       "propext",
19931       "Quot.sound"
19932     ],
19933     "in_project_namespace": true,
19934     "kind": "theorem",
19935     "module": "PaperICompletion5.CyclicGeometricCriterion",
19936     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_4",
19937     "runtime_only": false
19938   },
19939   {
19940     "axioms": [
19941       "propext",
19942       "Classical.choice",
19943       "Quot.sound"
19944     ],
19945     "in_project_namespace": true,
19946     "kind": "theorem",
19947     "module": "PaperIRelease.GrammarAlgebra",
19948     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_5",
19949     "runtime_only": false
19950   },
19951   {
19952     "axioms": [
19953       "propext",
19954       "Classical.choice",
19955       "Quot.sound"
19956     ],
19957     "in_project_namespace": true,
19958     "kind": "theorem",
19959     "module": "PaperIRelease.CategoryPackets",
19960     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.comp._proof_1",
19961     "runtime_only": false
19962   },
19963   {
19964     "axioms": [
19965       "propext",
19966       "Quot.sound"
19967     ],
19968     "in_project_namespace": true,
19969     "kind": "definition",
19970     "module": "PaperIRelease.GrammarModules",
19971     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory",
19972     "runtime_only": false
19973   },
19974   {
19975     "axioms": [
19976       "propext",
19977       "Quot.sound"
19978     ],
19979     "in_project_namespace": true,
19980     "kind": "definition",
19981     "module": "KomorebiVerification.PacketNaturalityCompletion",
19982     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2081",
19983     "runtime_only": false
19984   },
19985   {
19986     "axioms": [
19987       "propext",
19988       "Quot.sound"
19989     ],
19990     "in_project_namespace": true,
19991     "kind": "theorem",
19992     "module": "PaperIRelease.AlgebraClassGrouping",
19993     "name": "Komorebi.PaperIRelease.classSupport_iff._simp_1_3",
19994     "runtime_only": false
19995   },
19996   {
19997     "axioms": [
19998       "propext",
19999       "Classical.choice",
20000       "Quot.sound"
20001     ],
20002     "in_project_namespace": true,
20003     "kind": "definition",
20004     "module": "KomorebiVerification.TopologicalCompletion",
20005     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta",
20006     "runtime_only": false
20007   },
20008   {
20009     "axioms": [
20010       "propext",
20011       "Classical.choice",
20012       "Quot.sound"
20013     ],
20014     "in_project_namespace": true,
20015     "kind": "theorem",
20016     "module": "PaperIRelease.CoordinateTransport",
20017     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_6",
20018     "runtime_only": false
20019   },
20020   {
20021     "axioms": [
20022       "propext",
20023       "Quot.sound"
20024     ],
20025     "in_project_namespace": true,
20026     "kind": "theorem",
20027     "module": "KomorebiVerification.SingleOperatorGraph",
20028     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_1",
20029     "runtime_only": false
20030   },
20031   {
20032     "axioms": [
20033       "propext",
20034       "Classical.choice",
20035       "Quot.sound"
20036     ],
20037     "in_project_namespace": true,
20038     "kind": "theorem",
20039     "module": "PaperIRelease.BoundedStar",
20040     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_6",
20041     "runtime_only": false
20042   },
20043   {
20044     "axioms": [
20045       "propext",
20046       "Classical.choice",
20047       "Quot.sound"
20048     ],
20049     "in_project_namespace": true,
20050     "kind": "constructor",
20051     "module": "PaperIRelease.TopologyCategories",
20052     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk",
20053     "runtime_only": false
20054   },
20055   {
20056     "axioms": [
20057       "propext",
20058       "Quot.sound"
20059     ],
20060     "in_project_namespace": true,
20061     "kind": "theorem",
20062     "module": "PaperIRelease.GrammarModules",
20063     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_3",
20064     "runtime_only": false
20065   },
20066   {
20067     "axioms": [
20068       "propext",
20069       "Classical.choice",
20070       "Quot.sound"
20071     ],
20072     "in_project_namespace": true,
20073     "kind": "theorem",
20074     "module": "PaperICompletion3.PrimarySeedFormula",
20075     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor._proof_2",
20076     "runtime_only": false
20077   },
20078   {
20079     "axioms": [
20080       "propext",
20081       "Classical.choice",
20082       "Quot.sound"
20083     ],
20084     "in_project_namespace": false,
20085     "kind": "definition",
20086     "module": "PaperIRelease.TopologyCountablePackets",
20087     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences",
20088     "runtime_only": false
20089   },
20090   {
20091     "axioms": [
20092       "propext",
20093       "Quot.sound"
20094     ],
20095     "in_project_namespace": true,
20096     "kind": "theorem",
20097     "module": "KomorebiVerification.ProjectorCore",
20098     "name": "Komorebi.Seed.seed_subset_hull._simp_1",
20099     "runtime_only": false
20100   },
20101   {
20102     "axioms": [
20103       "propext",
20104       "Classical.choice",
20105       "Quot.sound"
20106     ],
20107     "in_project_namespace": true,
20108     "kind": "theorem",
20109     "module": "PaperIRelease.AlgebraClassGrouping",
20110     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily.eq_1",
20111     "runtime_only": false
20112   },
20113   {
20114     "axioms": [
20115       "propext",
20116       "Classical.choice",
20117       "Quot.sound"
20118     ],
20119     "in_project_namespace": true,
20120     "kind": "definition",
20121     "module": "PaperIRelease.GrammarEquivalence",
20122     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.recOn",
20123     "runtime_only": false
20124   },
20125   {
20126     "axioms": [
20127       "propext",
20128       "Classical.choice",
20129       "Quot.sound"
20130     ],
20131     "in_project_namespace": true,
20132     "kind": "definition",
20133     "module": "PaperIRelease.GrammarTyped",
20134     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse",
20135     "runtime_only": false
20136   },
20137   {
20138     "axioms": [
20139       "propext",
20140       "Classical.choice",
20141       "Quot.sound"
20142     ],
20143     "in_project_namespace": false,
20144     "kind": "theorem",
20145     "module": "PaperIRelease.TopologyCountablePackets",
20146     "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_zero",
20147     "runtime_only": false
20148   },
20149   {
20150     "axioms": [
20151       "propext",
20152       "Classical.choice",
20153       "Quot.sound"
20154     ],
20155     "in_project_namespace": true,
20156     "kind": "theorem",
20157     "module": "PaperICompletion8.RegularMultiplicity",
20158     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicityDirectSumEquiv._proof_1",
20159     "runtime_only": false
20160   },
20161   {
20162     "axioms": [
20163       "propext",
20164       "Classical.choice",
20165       "Quot.sound"
20166     ],
20167     "in_project_namespace": true,
20168     "kind": "theorem",
20169     "module": "KomorebiVerification.PacketNaturalityCompletion",
20170     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB_comp_arrowA",
20171     "runtime_only": false
20172   },
20173   {
20174     "axioms": [
20175       "propext",
20176       "Classical.choice",
20177       "Quot.sound"
20178     ],
20179     "in_project_namespace": true,
20180     "kind": "theorem",
20181     "module": "PaperIRelease.GraphPropagation",
20182     "name": "Komorebi.PaperIRelease.transferBlock_preserves_invariant",
20183     "runtime_only": false
20184   },
20185   {
20186     "axioms": [
20187       "propext",
20188       "Classical.choice",
20189       "Quot.sound"
20190     ],
20191     "in_project_namespace": true,
20192     "kind": "theorem",
20193     "module": "KomorebiVerification.SeedRankBasics",
20194     "name": "Komorebi.SeedRankBasics.exists_generating_set_card_eq_seedRank",
20195     "runtime_only": false
20196   },
20197   {
20198     "axioms": [
20199       "propext",
20200       "Quot.sound"
20201     ],
20202     "in_project_namespace": true,
20203     "kind": "theorem",
20204     "module": "PaperIRelease.GrammarAlgebra",
20205     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.inj",
20206     "runtime_only": false
20207   },
20208   {
20209     "axioms": [
20210       "propext",
20211       "Classical.choice",
20212       "Quot.sound"
20213     ],
20214     "in_project_namespace": false,
20215     "kind": "theorem",
20216     "module": "PaperIRelease.TopologyUnconditionalBridge",
20217     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_10",
20218     "runtime_only": false
20219   },
20220   {
20221     "axioms": [
20222       "propext",
20223       "Classical.choice",
20224       "Quot.sound"
20225     ],
20226     "in_project_namespace": true,
20227     "kind": "theorem",
20228     "module": "PaperIRelease.GrammarTyped",
20229     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_3",
20230     "runtime_only": false
20231   },
20232   {
20233     "axioms": [
20234       "propext",
20235       "Classical.choice",
20236       "Quot.sound"
20237     ],
20238     "in_project_namespace": true,
20239     "kind": "definition",
20240     "module": "PaperIRelease.GrammarAlgebra",
20241     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.noConfusionType",
20242     "runtime_only": false
20243   },
20244   {
20245     "axioms": [
20246       "propext",
20247       "Classical.choice",
20248       "Quot.sound"
20249     ],
20250     "in_project_namespace": true,
20251     "kind": "theorem",
20252     "module": "PaperIRelease.GeneralPacketBounds",
20253     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_isBounded",
20254     "runtime_only": false
20255   },
20256   {
20257     "axioms": [
20258       "propext",
20259       "Classical.choice",
20260       "Quot.sound"
20261     ],
20262     "in_project_namespace": true,
20263     "kind": "theorem",
20264     "module": "PaperIRelease.PacketExactSequence",
20265     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_2",
20266     "runtime_only": false
20267   },
20268   {
20269     "axioms": [
20270       "propext",
20271       "Classical.choice",
20272       "Quot.sound"
20273     ],
20274     "in_project_namespace": true,
20275     "kind": "theorem",
20276     "module": "KomorebiVerification.SemisimpleCompletion",
20277     "name": "Komorebi.SemisimpleCompletion.seedFinrank_eq_of_exists_fin_family_iff",
20278     "runtime_only": false
20279   },
20280   {
20281     "axioms": [
20282       "propext",
20283       "Classical.choice",
20284       "Quot.sound"
20285     ],
20286     "in_project_namespace": false,
20287     "kind": "theorem",
20288     "module": "PaperIRelease.TopologyFiniteCompletion",
20289     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_1",
20290     "runtime_only": false
20291   },
20292   {
20293     "axioms": [
20294       "propext",
20295       "Quot.sound"
20296     ],
20297     "in_project_namespace": true,
20298     "kind": "theorem",
20299     "module": "KomorebiVerification.PacketNaturalityCompletion",
20300     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_2",
20301     "runtime_only": false
20302   },
20303   {
20304     "axioms": [
20305       "propext",
20306       "Classical.choice",
20307       "Quot.sound"
20308     ],
20309     "in_project_namespace": true,
20310     "kind": "definition",
20311     "module": "PaperIRelease.PacketTopologyGeneral",
20312     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM",
20313     "runtime_only": false
20314   },
20315   {
20316     "axioms": [
20317       "propext",
20318       "Classical.choice",
20319       "Quot.sound"
20320     ],
20321     "in_project_namespace": true,
20322     "kind": "theorem",
20323     "module": "PaperIRelease.GraphSourceCount",
20324     "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_5",
20325     "runtime_only": false
20326   },
20327   {
20328     "axioms": [
20329       "propext",
20330       "Classical.choice",
20331       "Quot.sound"
20332     ],
20333     "in_project_namespace": true,
20334     "kind": "theorem",
20335     "module": "PaperIRelease.GraphSourceCount",
20336     "name": "Komorebi.PaperIRelease.generating_set_meets_source",
20337     "runtime_only": false
20338   },
20339   {
20340     "axioms": [
20341       "propext",
20342       "Classical.choice",
20343       "Quot.sound"
20344     ],
20345     "in_project_namespace": true,
20346     "kind": "theorem",
20347     "module": "KomorebiVerification.PacketNaturalityCompletion",
20348     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_natural_general",
20349     "runtime_only": false
20350   },
20351   {
20352     "axioms": [
20353       "propext",
20354       "Classical.choice",
20355       "Quot.sound"
20356     ],
20357     "in_project_namespace": true,
20358     "kind": "theorem",
20359     "module": "PaperIRelease.GeneralConditionedCoordinates",
20360     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packet_conditioned_coordinate_bounds",
20361     "runtime_only": false
20362   },
20363   {
20364     "axioms": [],
20365     "in_project_namespace": true,
20366     "kind": "theorem",
20367     "module": "KomorebiVerification.ProjectorCore",
20368     "name": "Komorebi.Seed.OperatorExpr.eval_id",
20369     "runtime_only": false
20370   },
20371   {
20372     "axioms": [
20373       "propext",
20374       "Classical.choice",
20375       "Quot.sound"
20376     ],
20377     "in_project_namespace": true,
20378     "kind": "theorem",
20379     "module": "KomorebiVerification.EllipticAlgorithms",
20380     "name": "Komorebi.FiniteAlgorithms.le_orbitClosureStep",
20381     "runtime_only": false
20382   },
20383   {
20384     "axioms": [
20385       "propext",
20386       "Classical.choice",
20387       "Quot.sound"
20388     ],
20389     "in_project_namespace": true,
20390     "kind": "theorem",
20391     "module": "PaperICompletion7.LocalResidue",
20392     "name": "Komorebi.PaperICompletion7.LocalResidue.seedFinrank_eq_residue_finrank",
20393     "runtime_only": false
20394   },
20395   {
20396     "axioms": [
20397       "propext",
20398       "Quot.sound"
20399     ],
20400     "in_project_namespace": true,
20401     "kind": "theorem",
20402     "module": "PaperICompletion4.OperatorIntrinsicFormula",
20403     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_2",
20404     "runtime_only": false
20405   },
20406   {
20407     "axioms": [
20408       "propext",
20409       "Classical.choice",
20410       "Quot.sound"
20411     ],
20412     "in_project_namespace": false,
20413     "kind": "theorem",
20414     "module": "PaperIRelease.TopologyCountablePackets",
20415     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_5",
20416     "runtime_only": false
20417   },
20418   {
20419     "axioms": [
20420       "propext",
20421       "Classical.choice",
20422       "Quot.sound"
20423     ],
20424     "in_project_namespace": true,
20425     "kind": "theorem",
20426     "module": "PaperIRelease.CoordinateTransport",
20427     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_4",
20428     "runtime_only": false
20429   },
20430   {
20431     "axioms": [
20432       "propext",
20433       "Classical.choice",
20434       "Quot.sound"
20435     ],
20436     "in_project_namespace": true,
20437     "kind": "theorem",
20438     "module": "PaperICompletion.ConditionedCoordinates",
20439     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator.eq_1",
20440     "runtime_only": false
20441   },
20442   {
20443     "axioms": [],
20444     "in_project_namespace": true,
20445     "kind": "theorem",
20446     "module": "KomorebiVerification.ProjectorCore",
20447     "name": "Komorebi.ClaimKind.boundary.sizeOf_spec",
20448     "runtime_only": false
20449   },
20450   {
20451     "axioms": [],
20452     "in_project_namespace": true,
20453     "kind": "definition",
20454     "module": "KomorebiVerification.PacketNaturalityCompletion",
20455     "name": "Komorebi.PacketNaturalityCompletion.Reachability.OperatorWord",
20456     "runtime_only": false
20457   },
20458   {
20459     "axioms": [
20460       "propext"
20461     ],
20462     "in_project_namespace": true,
20463     "kind": "theorem",
20464     "module": "KomorebiVerification.ProjectorCore",
20465     "name": "Komorebi.Algebra.MatrixSupported.neg",
20466     "runtime_only": false
20467   },
20468   {
20469     "axioms": [
20470       "propext",
20471       "Classical.choice",
20472       "Quot.sound"
20473     ],
20474     "in_project_namespace": true,
20475     "kind": "theorem",
20476     "module": "PaperICompletion6.OneInvariantFactor",
20477     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.hasCyclicVector_iff_oneInvariantFactor",
20478     "runtime_only": false
20479   },
20480   {
20481     "axioms": [
20482       "propext",
20483       "Classical.choice",
20484       "Quot.sound"
20485     ],
20486     "in_project_namespace": true,
20487     "kind": "definition",
20488     "module": "PaperIRelease.TopologyCategories",
20489     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk._flat_ctor",
20490     "runtime_only": false
20491   },
20492   {
20493     "axioms": [
20494       "propext",
20495       "Classical.choice",
20496       "Quot.sound"
20497     ],
20498     "in_project_namespace": true,
20499     "kind": "theorem",
20500     "module": "PaperIRelease.PacketAggregation",
20501     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_3",
20502     "runtime_only": false
20503   },
20504   {
20505     "axioms": [],
20506     "in_project_namespace": true,
20507     "kind": "definition",
20508     "module": "KomorebiVerification.ProjectorCore",
20509     "name": "Komorebi.FormalizationStatus.ctorElimType",
20510     "runtime_only": false
20511   },
20512   {
20513     "axioms": [],
20514     "in_project_namespace": true,
20515     "kind": "definition",
20516     "module": "KomorebiVerification.ResidueProjectors",
20517     "name": "Komorebi.Residue.fineAddress",
20518     "runtime_only": false
20519   },
20520   {
20521     "axioms": [
20522       "propext",
20523       "Classical.choice",
20524       "Quot.sound"
20525     ],
20526     "in_project_namespace": true,
20527     "kind": "theorem",
20528     "module": "PaperIRelease.PacketDescent",
20529     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_6",
20530     "runtime_only": false
20531   },
20532   {
20533     "axioms": [
20534       "propext",
20535       "Classical.choice",
20536       "Quot.sound"
20537     ],
20538     "in_project_namespace": true,
20539     "kind": "theorem",
20540     "module": "PaperIRelease.TopologyCategories",
20541     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.hausdorff",
20542     "runtime_only": false
20543   },
20544   {
20545     "axioms": [
20546       "propext",
20547       "Classical.choice",
20548       "Quot.sound"
20549     ],
20550     "in_project_namespace": false,
20551     "kind": "theorem",
20552     "module": "PaperIRelease.TopologyUnconditionalBridge",
20553     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_8",
20554     "runtime_only": false
20555   },
20556   {
20557     "axioms": [
20558       "propext",
20559       "Classical.choice",
20560       "Quot.sound"
20561     ],
20562     "in_project_namespace": true,
20563     "kind": "theorem",
20564     "module": "KomorebiVerification.SemisimpleCompletion",
20565     "name": "Komorebi.SemisimpleCompletion.leftGenerates_iff_familyGenerates",
20566     "runtime_only": false
20567   },
20568   {
20569     "axioms": [
20570       "propext",
20571       "Classical.choice",
20572       "Quot.sound"
20573     ],
20574     "in_project_namespace": false,
20575     "kind": "theorem",
20576     "module": "PaperIRelease.TopologySeedRank",
20577     "name": "PaperIRelease.TopologyTransport.generates_univ",
20578     "runtime_only": false
20579   },
20580   {
20581     "axioms": [
20582       "propext",
20583       "Quot.sound"
20584     ],
20585     "in_project_namespace": true,
20586     "kind": "definition",
20587     "module": "KomorebiVerification.SeedRankOperations",
20588     "name": "Komorebi.SeedRankOperations.productModule",
20589     "runtime_only": false
20590   },
20591   {
20592     "axioms": [
20593       "propext",
20594       "Classical.choice",
20595       "Quot.sound"
20596     ],
20597     "in_project_namespace": false,
20598     "kind": "theorem",
20599     "module": "PaperIRelease.TopologyFiniteCompletion",
20600     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_4",
20601     "runtime_only": false
20602   },
20603   {
20604     "axioms": [
20605       "propext",
20606       "Classical.choice",
20607       "Quot.sound"
20608     ],
20609     "in_project_namespace": false,
20610     "kind": "theorem",
20611     "module": "PaperIRelease.TopologyCountablePackets",
20612     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_18",
20613     "runtime_only": false
20614   },
20615   {
20616     "axioms": [
20617       "propext",
20618       "Classical.choice",
20619       "Quot.sound"
20620     ],
20621     "in_project_namespace": false,
20622     "kind": "theorem",
20623     "module": "PaperIRelease.TopologyUnconditional",
20624     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_7",
20625     "runtime_only": false
20626   },
20627   {
20628     "axioms": [
20629       "propext",
20630       "Classical.choice",
20631       "Quot.sound"
20632     ],
20633     "in_project_namespace": true,
20634     "kind": "theorem",
20635     "module": "PaperIRelease.GraphPropagation",
20636     "name": "Komorebi.PaperIRelease.projector_mem_generatedAlgebra",
20637     "runtime_only": false
20638   },
20639   {
20640     "axioms": [
20641       "propext",
20642       "Quot.sound"
20643     ],
20644     "in_project_namespace": true,
20645     "kind": "theorem",
20646     "module": "KomorebiVerification.SeedRankOperations",
20647     "name": "Komorebi.SeedRankOperations.tensorActionsCommuteInstalled",
20648     "runtime_only": false
20649   },
20650   {
20651     "axioms": [
20652       "propext",
20653       "Classical.choice",
20654       "Quot.sound"
20655     ],
20656     "in_project_namespace": false,
20657     "kind": "definition",
20658     "module": "PaperIRelease.TopologyCountablePackets",
20659     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_16",
20660     "runtime_only": false
20661   },
20662   {
20663     "axioms": [
20664       "propext"
20665     ],
20666     "in_project_namespace": true,
20667     "kind": "theorem",
20668     "module": "PaperIRelease.CategoryExport",
20669     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_6",
20670     "runtime_only": false
20671   },
20672   {
20673     "axioms": [
20674       "propext",
20675       "Classical.choice",
20676       "Quot.sound"
20677     ],
20678     "in_project_namespace": true,
20679     "kind": "definition",
20680     "module": "KomorebiVerification.PacketNaturalityCompletion",
20681     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB",
20682     "runtime_only": false
20683   },
20684   {
20685     "axioms": [
20686       "propext",
20687       "Classical.choice",
20688       "Quot.sound"
20689     ],
20690     "in_project_namespace": true,
20691     "kind": "theorem",
20692     "module": "KomorebiVerification.ProjectorCore",
20693     "name": "Komorebi.Algebra.MatrixSupported.mul",
20694     "runtime_only": false
20695   },
20696   {
20697     "axioms": [],
20698     "in_project_namespace": true,
20699     "kind": "definition",
20700     "module": "KomorebiVerification.ProjectorCore",
20701     "name": "Komorebi.ClaimKind.propositionClaim.elim",
20702     "runtime_only": false
20703   },
20704   {
20705     "axioms": [
20706       "propext",
20707       "Classical.choice",
20708       "Quot.sound"
20709     ],
20710     "in_project_namespace": true,
20711     "kind": "definition",
20712     "module": "KomorebiVerification.TopologicalCompletion",
20713     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.noConfusion",
20714     "runtime_only": false
20715   },
20716   {
20717     "axioms": [
20718       "propext",
20719       "Classical.choice",
20720       "Quot.sound"
20721     ],
20722     "in_project_namespace": true,
20723     "kind": "theorem",
20724     "module": "PaperIRelease.PacketAggregation",
20725     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_2",
20726     "runtime_only": false
20727   },
20728   {
20729     "axioms": [
20730       "propext",
20731       "Classical.choice",
20732       "Quot.sound"
20733     ],
20734     "in_project_namespace": true,
20735     "kind": "definition",
20736     "module": "PaperIRelease.TopologyCategories",
20737     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.comp",
20738     "runtime_only": false
20739   },
20740   {
20741     "axioms": [
20742       "propext",
20743       "Classical.choice",
20744       "Quot.sound"
20745     ],
20746     "in_project_namespace": true,
20747     "kind": "theorem",
20748     "module": "PaperIRelease.GrammarAlgebra",
20749     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.declared",
20750     "runtime_only": false
20751   },
20752   {
20753     "axioms": [
20754       "propext",
20755       "Classical.choice",
20756       "Quot.sound"
20757     ],
20758     "in_project_namespace": false,
20759     "kind": "theorem",
20760     "module": "PaperIRelease.TopologyUnconditionalBridge",
20761     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_5",
20762     "runtime_only": false
20763   },
20764   {
20765     "axioms": [
20766       "propext",
20767       "Classical.choice",
20768       "Quot.sound"
20769     ],
20770     "in_project_namespace": true,
20771     "kind": "theorem",
20772     "module": "PaperIRelease.GraphReachability",
20773     "name": "Komorebi.PaperIRelease.generatedAlgebra_hull_le_reachable",
20774     "runtime_only": false
20775   },
20776   {
20777     "axioms": [
20778       "propext",
20779       "Classical.choice",
20780       "Quot.sound"
20781     ],
20782     "in_project_namespace": true,
20783     "kind": "theorem",
20784     "module": "KomorebiVerification.PacketNaturalityCompletion",
20785     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_eq_zero_iff_of_bijective",
20786     "runtime_only": false
20787   },
20788   {
20789     "axioms": [
20790       "propext",
20791       "Classical.choice",
20792       "Quot.sound"
20793     ],
20794     "in_project_namespace": false,
20795     "kind": "theorem",
20796     "module": "PaperIRelease.TopologyCountablePackets",
20797     "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_3",
20798     "runtime_only": false
20799   },
20800   {
20801     "axioms": [
20802       "propext",
20803       "Classical.choice",
20804       "Quot.sound"
20805     ],
20806     "in_project_namespace": true,
20807     "kind": "definition",
20808     "module": "KomorebiVerification.PathGraphKrylov",
20809     "name": "Komorebi.PathGraphKrylov.walkMatrix",
20810     "runtime_only": false
20811   },
20812   {
20813     "axioms": [
20814       "propext",
20815       "Quot.sound"
20816     ],
20817     "in_project_namespace": true,
20818     "kind": "theorem",
20819     "module": "PaperIRelease.PacketLocalRank",
20820     "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_2",
20821     "runtime_only": false
20822   },
20823   {
20824     "axioms": [],
20825     "in_project_namespace": false,
20826     "kind": "theorem",
20827     "module": "KomorebiVerification.ProjectorCore",
20828     "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.eq_1",
20829     "runtime_only": false
20830   },
20831   {
20832     "axioms": [
20833       "propext",
20834       "Classical.choice",
20835       "Quot.sound"
20836     ],
20837     "in_project_namespace": true,
20838     "kind": "theorem",
20839     "module": "PaperICompletion8.SemisimpleExistence",
20840     "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_finiteAlgebra_seed_formula",
20841     "runtime_only": false
20842   },
20843   {
20844     "axioms": [
20845       "propext",
20846       "Classical.choice",
20847       "Quot.sound"
20848     ],
20849     "in_project_namespace": true,
20850     "kind": "theorem",
20851     "module": "KomorebiVerification.EllipticAlgorithms",
20852     "name": "Komorebi.EllipticCoordinates.P0_idempotent",
20853     "runtime_only": false
20854   },
20855   {
20856     "axioms": [
20857       "propext",
20858       "Classical.choice",
20859       "Quot.sound"
20860     ],
20861     "in_project_namespace": false,
20862     "kind": "definition",
20863     "module": "PaperIRelease.TopologyDenseCompletion",
20864     "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion",
20865     "runtime_only": false
20866   },
20867   {
20868     "axioms": [
20869       "propext",
20870       "Classical.choice",
20871       "Quot.sound"
20872     ],
20873     "in_project_namespace": true,
20874     "kind": "theorem",
20875     "module": "PaperICompletion3.OperatorPrimaryAPI",
20876     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount.congr_simp",
20877     "runtime_only": false
20878   },
20879   {
20880     "axioms": [
20881       "propext",
20882       "Classical.choice",
20883       "Quot.sound"
20884     ],
20885     "in_project_namespace": true,
20886     "kind": "definition",
20887     "module": "PaperIRelease.TopologyCategories",
20888     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.identity",
20889     "runtime_only": false
20890   },
20891   {
20892     "axioms": [
20893       "propext",
20894       "Classical.choice",
20895       "Quot.sound"
20896     ],
20897     "in_project_namespace": true,
20898     "kind": "theorem",
20899     "module": "KomorebiVerification.EllipticAlgorithms",
20900     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_1",
20901     "runtime_only": false
20902   },
20903   {
20904     "axioms": [
20905       "propext",
20906       "Classical.choice",
20907       "Quot.sound"
20908     ],
20909     "in_project_namespace": true,
20910     "kind": "theorem",
20911     "module": "PaperIRelease.GrammarPaths",
20912     "name": "Komorebi.PaperIRelease.GrammarAlgebra.pathCombinationWord.eq_1",
20913     "runtime_only": false
20914   },
20915   {
20916     "axioms": [],
20917     "in_project_namespace": true,
20918     "kind": "definition",
20919     "module": "KomorebiVerification.PacketNaturalityCompletion",
20920     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._unsafe_rec",
20921     "runtime_only": true
20922   },
20923   {
20924     "axioms": [
20925       "propext",
20926       "Classical.choice",
20927       "Quot.sound"
20928     ],
20929     "in_project_namespace": true,
20930     "kind": "definition",
20931     "module": "KomorebiVerification.PacketNaturalityCompletion",
20932     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraSemiring",
20933     "runtime_only": false
20934   },
20935   {
20936     "axioms": [
20937       "propext",
20938       "Classical.choice",
20939       "Quot.sound"
20940     ],
20941     "in_project_namespace": false,
20942     "kind": "theorem",
20943     "module": "PaperIRelease.TopologyUnconditional",
20944     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues_nonempty",
20945     "runtime_only": false
20946   },
20947   {
20948     "axioms": [
20949       "propext",
20950       "Classical.choice",
20951       "Quot.sound"
20952     ],
20953     "in_project_namespace": true,
20954     "kind": "theorem",
20955     "module": "PaperIRelease.GrammarAlgebra",
20956     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction.eq_1",
20957     "runtime_only": false
20958   },
20959   {
20960     "axioms": [
20961       "propext",
20962       "Classical.choice",
20963       "Quot.sound"
20964     ],
20965     "in_project_namespace": true,
20966     "kind": "theorem",
20967     "module": "PaperIRelease.GraphReachability",
20968     "name": "Komorebi.PaperIRelease.generatedAlgebra_unreachable_obstruction",
20969     "runtime_only": false
20970   },
20971   {
20972     "axioms": [
20973       "propext",
20974       "Classical.choice",
20975       "Quot.sound"
20976     ],
20977     "in_project_namespace": true,
20978     "kind": "definition",
20979     "module": "KomorebiVerification.EllipticAlgorithms",
20980     "name": "Komorebi.EllipticCoordinates.relationPolynomial",
20981     "runtime_only": false
20982   },
20983   {
20984     "axioms": [
20985       "propext",
20986       "Quot.sound"
20987     ],
20988     "in_project_namespace": true,
20989     "kind": "definition",
20990     "module": "PaperIRelease.GrammarTyped",
20991     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.total",
20992     "runtime_only": false
20993   },
20994   {
20995     "axioms": [],
20996     "in_project_namespace": true,
20997     "kind": "definition",
20998     "module": "KomorebiVerification.PathGraphKrylov",
20999     "name": "Komorebi.PathGraphKrylov.endpoint",
21000     "runtime_only": false
21001   },
21002   {
21003     "axioms": [
21004       "propext",
21005       "Classical.choice",
21006       "Quot.sound"
21007     ],
21008     "in_project_namespace": true,
21009     "kind": "theorem",
21010     "module": "PaperICompletion5.CyclicGeometricCriterion",
21011     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_minpoly_quotient_presentation",
21012     "runtime_only": false
21013   },
21014   {
21015     "axioms": [
21016       "propext",
21017       "Classical.choice",
21018       "Quot.sound"
21019     ],
21020     "in_project_namespace": false,
21021     "kind": "theorem",
21022     "module": "PaperIRelease.TopologyUnconditional",
21023     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm_zero",
21024     "runtime_only": false
21025   },
21026   {
21027     "axioms": [
21028       "propext",
21029       "Classical.choice",
21030       "Quot.sound"
21031     ],
21032     "in_project_namespace": true,
21033     "kind": "definition",
21034     "module": "PaperICompletion8.RegularMultiplicity",
21035     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv",
21036     "runtime_only": false
21037   },
21038   {
21039     "axioms": [
21040       "propext",
21041       "Classical.choice",
21042       "Quot.sound"
21043     ],
21044     "in_project_namespace": true,
21045     "kind": "theorem",
21046     "module": "PaperIRelease.AlgebraDiagonal",
21047     "name": "Komorebi.PaperIRelease.diagonalProjection_of_offdiagonal_zero",
21048     "runtime_only": false
21049   },
21050   {
21051     "axioms": [
21052       "propext",
21053       "Classical.choice",
21054       "Quot.sound"
21055     ],
21056     "in_project_namespace": true,
21057     "kind": "theorem",
21058     "module": "KomorebiVerification.PacketNaturalityCompletion",
21059     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_synthesizeBlocks",
21060     "runtime_only": false
21061   },
21062   {
21063     "axioms": [],
21064     "in_project_namespace": true,
21065     "kind": "definition",
21066     "module": "KomorebiVerification.ProjectorCore",
21067     "name": "Komorebi.instInhabitedFormalizationStatus",
21068     "runtime_only": false
21069   },
21070   {
21071     "axioms": [
21072       "propext",
21073       "Classical.choice",
21074       "Quot.sound"
21075     ],
21076     "in_project_namespace": true,
21077     "kind": "theorem",
21078     "module": "PaperICompletion3.InvariantFactorCount",
21079     "name": "Komorebi.PaperICompletion3.InvariantFactorCount.invariantFactorProduct_seedNumber_isLeast",
21080     "runtime_only": false
21081   },
21082   {
21083     "axioms": [
21084       "propext",
21085       "Classical.choice",
21086       "Quot.sound"
21087     ],
21088     "in_project_namespace": true,
21089     "kind": "theorem",
21090     "module": "PaperIRelease.CategoryPackets",
21091     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.seed_condition",
21092     "runtime_only": false
21093   },
21094   {
21095     "axioms": [
21096       "propext",
21097       "Quot.sound"
21098     ],
21099     "in_project_namespace": false,
21100     "kind": "definition",
21101     "module": "KomorebiVerification.SeedRankOperations",
21102     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule",
21103     "runtime_only": false
21104   },
21105   {
21106     "axioms": [
21107       "propext",
21108       "Quot.sound"
21109     ],
21110     "in_project_namespace": true,
21111     "kind": "theorem",
21112     "module": "PaperIRelease.GrammarModules",
21113     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.injEq",
21114     "runtime_only": false
21115   },
21116   {
21117     "axioms": [
21118       "propext",
21119       "Classical.choice",
21120       "Quot.sound"
21121     ],
21122     "in_project_namespace": false,
21123     "kind": "theorem",
21124     "module": "PaperIRelease.TopologyDenseCompletion",
21125     "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv_apply_coe",
21126     "runtime_only": false
21127   },
21128   {
21129     "axioms": [
21130       "propext",
21131       "Classical.choice",
21132       "Quot.sound"
21133     ],
21134     "in_project_namespace": true,
21135     "kind": "theorem",
21136     "module": "PaperIRelease.GrammarEquivalence",
21137     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total_single",
21138     "runtime_only": false
21139   },
21140   {
21141     "axioms": [
21142       "propext",
21143       "Classical.choice",
21144       "Quot.sound"
21145     ],
21146     "in_project_namespace": true,
21147     "kind": "theorem",
21148     "module": "PaperIRelease.GrammarAlgebra",
21149     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_vertex",
21150     "runtime_only": false
21151   },
21152   {
21153     "axioms": [
21154       "propext",
21155       "Classical.choice",
21156       "Quot.sound"
21157     ],
21158     "in_project_namespace": true,
21159     "kind": "theorem",
21160     "module": "PaperICompletion5.GeometricSeedFormula",
21161     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues_nonempty",
21162     "runtime_only": false
21163   },
21164   {
21165     "axioms": [
21166       "propext",
21167       "Classical.choice",
21168       "Quot.sound"
21169     ],
21170     "in_project_namespace": true,
21171     "kind": "theorem",
21172     "module": "PaperIRelease.GeneralNormedPackets",
21173     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_apply",
21174     "runtime_only": false
21175   },
21176   {
21177     "axioms": [
21178       "propext",
21179       "Classical.choice",
21180       "Quot.sound"
21181     ],
21182     "in_project_namespace": true,
21183     "kind": "definition",
21184     "module": "PaperICompletion3.OperatorPrimaryAPI",
21185     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.indexFintype",
21186     "runtime_only": false
21187   },
21188   {
21189     "axioms": [],
21190     "in_project_namespace": true,
21191     "kind": "definition",
21192     "module": "KomorebiVerification.ProjectorCore",
21193     "name": "Komorebi.ClaimRecord.targetNamespace",
21194     "runtime_only": false
21195   },
21196   {
21197     "axioms": [
21198       "propext",
21199       "Classical.choice",
21200       "Quot.sound"
21201     ],
21202     "in_project_namespace": true,
21203     "kind": "theorem",
21204     "module": "KomorebiVerification.TopologicalCompletion",
21205     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.dense_operatorHull_image",
21206     "runtime_only": false
21207   },
21208   {
21209     "axioms": [],
21210     "in_project_namespace": true,
21211     "kind": "theorem",
21212     "module": "PaperICompletion8.RegularMultiplicity",
21213     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_5",
21214     "runtime_only": false
21215   },
21216   {
21217     "axioms": [
21218       "propext",
21219       "Classical.choice",
21220       "Quot.sound"
21221     ],
21222     "in_project_namespace": true,
21223     "kind": "theorem",
21224     "module": "PaperIRelease.CoordinateTransport",
21225     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_8",
21226     "runtime_only": false
21227   },
21228   {
21229     "axioms": [
21230       "propext",
21231       "Quot.sound"
21232     ],
21233     "in_project_namespace": true,
21234     "kind": "theorem",
21235     "module": "PaperIRelease.GrammarModules",
21236     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_10",
21237     "runtime_only": false
21238   },
21239   {
21240     "axioms": [
21241       "propext",
21242       "Classical.choice",
21243       "Quot.sound"
21244     ],
21245     "in_project_namespace": true,
21246     "kind": "definition",
21247     "module": "KomorebiVerification.PacketNaturalityCompletion",
21248     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock",
21249     "runtime_only": false
21250   },
21251   {
21252     "axioms": [
21253       "propext",
21254       "Classical.choice",
21255       "Quot.sound"
21256     ],
21257     "in_project_namespace": true,
21258     "kind": "definition",
21259     "module": "PaperIRelease.CategoryPackets",
21260     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.packets",
21261     "runtime_only": false
21262   },
21263   {
21264     "axioms": [
21265       "propext",
21266       "Classical.choice",
21267       "Quot.sound"
21268     ],
21269     "in_project_namespace": true,
21270     "kind": "theorem",
21271     "module": "PaperIRelease.PacketSourceUpper",
21272     "name": "Komorebi.PaperIRelease.localCornerAlgebra.congr_simp",
21273     "runtime_only": false
21274   },
21275   {
21276     "axioms": [
21277       "propext"
21278     ],
21279     "in_project_namespace": true,
21280     "kind": "definition",
21281     "module": "PaperIRelease.CategoryExport",
21282     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._sunfold",
21283     "runtime_only": false
21284   },
21285   {
21286     "axioms": [
21287       "propext",
21288       "Classical.choice",
21289       "Quot.sound"
21290     ],
21291     "in_project_namespace": false,
21292     "kind": "definition",
21293     "module": "PaperIRelease.TopologyUnconditional",
21294     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedAddCommGroup",
21295     "runtime_only": false
21296   },
21297   {
21298     "axioms": [
21299       "propext",
21300       "Classical.choice",
21301       "Quot.sound"
21302     ],
21303     "in_project_namespace": true,
21304     "kind": "theorem",
21305     "module": "PaperIRelease.GrammarAlgebra",
21306     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_idempotent",
21307     "runtime_only": false
21308   },
21309   {
21310     "axioms": [
21311       "propext",
21312       "Classical.choice",
21313       "Quot.sound"
21314     ],
21315     "in_project_namespace": true,
21316     "kind": "theorem",
21317     "module": "PaperIRelease.GrammarEquivalence",
21318     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_12",
21319     "runtime_only": false
21320   },
21321   {
21322     "axioms": [
21323       "propext",
21324       "Classical.choice",
21325       "Quot.sound"
21326     ],
21327     "in_project_namespace": true,
21328     "kind": "theorem",
21329     "module": "PaperICompletion8.DivisionBlock",
21330     "name": "Komorebi.PaperICompletion8.DivisionBlock.leftGenerates_iff_familyGenerates",
21331     "runtime_only": false
21332   },
21333   {
21334     "axioms": [
21335       "propext",
21336       "Classical.choice",
21337       "Quot.sound"
21338     ],
21339     "in_project_namespace": true,
21340     "kind": "theorem",
21341     "module": "PaperIRelease.GraphPropagation",
21342     "name": "Komorebi.PaperIRelease.reachable_range_le",
21343     "runtime_only": false
21344   },
21345   {
21346     "axioms": [
21347       "propext",
21348       "Classical.choice",
21349       "Quot.sound"
21350     ],
21351     "in_project_namespace": true,
21352     "kind": "theorem",
21353     "module": "KomorebiVerification.PacketNaturalityCompletion",
21354     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.MappedGeneratedHull.eq_1",
21355     "runtime_only": false
21356   },
21357   {
21358     "axioms": [
21359       "propext",
21360       "Classical.choice",
21361       "Quot.sound"
21362     ],
21363     "in_project_namespace": true,
21364     "kind": "definition",
21365     "module": "PaperIRelease.BoundedStar",
21366     "name": "Komorebi.PaperIRelease.BoundedSupport.underlying",
21367     "runtime_only": false
21368   },
21369   {
21370     "axioms": [
21371       "propext",
21372       "Classical.choice",
21373       "Quot.sound"
21374     ],
21375     "in_project_namespace": true,
21376     "kind": "theorem",
21377     "module": "PaperIRelease.GrammarEquivalence",
21378     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_9",
21379     "runtime_only": false
21380   },
21381   {
21382     "axioms": [
21383       "propext",
21384       "Classical.choice",
21385       "Quot.sound"
21386     ],
21387     "in_project_namespace": true,
21388     "kind": "definition",
21389     "module": "PaperIRelease.GeneralNormedPackets",
21390     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet",
21391     "runtime_only": false
21392   },
21393   {
21394     "axioms": [
21395       "propext",
21396       "Classical.choice",
21397       "Quot.sound"
21398     ],
21399     "in_project_namespace": true,
21400     "kind": "theorem",
21401     "module": "PaperIRelease.PacketAggregation",
21402     "name": "Komorebi.PaperIRelease.PacketAggregation.proj_groupedProjection",
21403     "runtime_only": false
21404   },
21405   {
21406     "axioms": [
21407       "propext",
21408       "Classical.choice",
21409       "Quot.sound"
21410     ],
21411     "in_project_namespace": true,
21412     "kind": "theorem",
21413     "module": "PaperICompletion4.ResidueQuotient",
21414     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_2",
21415     "runtime_only": false
21416   },
21417   {
21418     "axioms": [
21419       "propext",
21420       "Classical.choice",
21421       "Quot.sound"
21422     ],
21423     "in_project_namespace": true,
21424     "kind": "theorem",
21425     "module": "KomorebiVerification.TopologicalCompletion",
21426     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet._proof_1",
21427     "runtime_only": false
21428   },
21429   {
21430     "axioms": [
21431       "propext",
21432       "Classical.choice",
21433       "Quot.sound"
21434     ],
21435     "in_project_namespace": false,
21436     "kind": "theorem",
21437     "module": "PaperIRelease.TopologyCountablePackets",
21438     "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound._proof_1",
21439     "runtime_only": false
21440   },
21441   {
21442     "axioms": [
21443       "propext",
21444       "Classical.choice",
21445       "Quot.sound"
21446     ],
21447     "in_project_namespace": true,
21448     "kind": "theorem",
21449     "module": "PaperIRelease.GraphPropagation",
21450     "name": "Komorebi.PaperIRelease.reachable_range_le_in_component",
21451     "runtime_only": false
21452   },
21453   {
21454     "axioms": [
21455       "propext",
21456       "Classical.choice",
21457       "Quot.sound"
21458     ],
21459     "in_project_namespace": true,
21460     "kind": "theorem",
21461     "module": "PaperIRelease.GrammarTyped",
21462     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_freeAction",
21463     "runtime_only": false
21464   },
21465   {
21466     "axioms": [
21467       "propext",
21468       "Classical.choice",
21469       "Quot.sound"
21470     ],
21471     "in_project_namespace": true,
21472     "kind": "definition",
21473     "module": "PaperICompletion3.OperatorPrimaryAPI",
21474     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.noConfusion",
21475     "runtime_only": false
21476   },
21477   {
21478     "axioms": [
21479       "propext",
21480       "Classical.choice",
21481       "Quot.sound"
21482     ],
21483     "in_project_namespace": true,
21484     "kind": "theorem",
21485     "module": "PaperICompletion4.OperatorIntrinsicFormula",
21486     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_3",
21487     "runtime_only": false
21488   },
21489   {
21490     "axioms": [
21491       "propext",
21492       "Classical.choice",
21493       "Quot.sound"
21494     ],
21495     "in_project_namespace": true,
21496     "kind": "theorem",
21497     "module": "PaperIRelease.GeneralFiniteCompletion",
21498     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_2",
21499     "runtime_only": false
21500   },
21501   {
21502     "axioms": [
21503       "propext",
21504       "Quot.sound"
21505     ],
21506     "in_project_namespace": true,
21507     "kind": "theorem",
21508     "module": "PaperICompletion5.GeometricSeedFormula",
21509     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues._proof_1",
21510     "runtime_only": false
21511   },
21512   {
21513     "axioms": [
21514       "propext",
21515       "Classical.choice",
21516       "Quot.sound"
21517     ],
21518     "in_project_namespace": true,
21519     "kind": "definition",
21520     "module": "PaperIRelease.AlgebraQuotient",
21521     "name": "Komorebi.PaperIRelease.diagonalClassQuotientEquiv",
21522     "runtime_only": false
21523   },
21524   {
21525     "axioms": [
21526       "propext",
21527       "Classical.choice",
21528       "Quot.sound"
21529     ],
21530     "in_project_namespace": true,
21531     "kind": "constructor",
21532     "module": "PaperIRelease.GrammarTyped",
21533     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk",
21534     "runtime_only": false
21535   },
21536   {
21537     "axioms": [
21538       "propext",
21539       "Classical.choice",
21540       "Quot.sound"
21541     ],
21542     "in_project_namespace": true,
21543     "kind": "theorem",
21544     "module": "PaperIRelease.GrammarEquivalence",
21545     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ext",
21546     "runtime_only": false
21547   },
21548   {
21549     "axioms": [
21550       "propext",
21551       "Quot.sound"
21552     ],
21553     "in_project_namespace": true,
21554     "kind": "theorem",
21555     "module": "KomorebiVerification.SeedRankBasics",
21556     "name": "Komorebi.SeedRankBasics.generates_mono",
21557     "runtime_only": false
21558   },
21559   {
21560     "axioms": [
21561       "propext",
21562       "Classical.choice",
21563       "Quot.sound"
21564     ],
21565     "in_project_namespace": true,
21566     "kind": "theorem",
21567     "module": "KomorebiVerification.PacketNaturalityCompletion",
21568     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_end_eq_finrank_blocks",
21569     "runtime_only": false
21570   },
21571   {
21572     "axioms": [
21573       "propext",
21574       "Classical.choice",
21575       "Quot.sound"
21576     ],
21577     "in_project_namespace": false,
21578     "kind": "theorem",
21579     "module": "PaperIRelease.TopologyUnconditional",
21580     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_uniform_limit",
21581     "runtime_only": false
21582   },
21583   {
21584     "axioms": [
21585       "propext",
21586       "Classical.choice",
21587       "Quot.sound"
21588     ],
21589     "in_project_namespace": false,
21590     "kind": "theorem",
21591     "module": "PaperIRelease.TopologyTransport",
21592     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_4",
21593     "runtime_only": false
21594   },
21595   {
21596     "axioms": [
21597       "propext",
21598       "Classical.choice",
21599       "Quot.sound"
21600     ],
21601     "in_project_namespace": true,
21602     "kind": "theorem",
21603     "module": "KomorebiVerification.PacketNaturalityCompletion",
21604     "name": "Komorebi.PacketNaturalityCompletion.Reachability.reachable_forward",
21605     "runtime_only": false
21606   },
21607   {
21608     "axioms": [
21609       "Classical.choice"
21610     ],
21611     "in_project_namespace": true,
21612     "kind": "theorem",
21613     "module": "PaperIRelease.AlgebraClassGrouping",
21614     "name": "Komorebi.PaperIRelease.preorderClassesFintype._proof_1",
21615     "runtime_only": false
21616   },
21617   {
21618     "axioms": [
21619       "propext",
21620       "Classical.choice",
21621       "Quot.sound"
21622     ],
21623     "in_project_namespace": true,
21624     "kind": "recursor",
21625     "module": "PaperIRelease.GrammarAlgebra",
21626     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.rec",
21627     "runtime_only": false
21628   },
21629   {
21630     "axioms": [
21631       "propext",
21632       "Classical.choice",
21633       "Quot.sound"
21634     ],
21635     "in_project_namespace": true,
21636     "kind": "definition",
21637     "module": "KomorebiVerification.ProjectorCore",
21638     "name": "Komorebi.Operator.lowRankApply",
21639     "runtime_only": false
21640   },
21641   {
21642     "axioms": [
21643       "propext",
21644       "Quot.sound"
21645     ],
21646     "in_project_namespace": true,
21647     "kind": "theorem",
21648     "module": "PaperIRelease.AlgebraTransfer",
21649     "name": "Komorebi.PaperIRelease.operatorWord._proof_1",
21650     "runtime_only": false
21651   },
21652   {
21653     "axioms": [
21654       "propext",
21655       "Classical.choice",
21656       "Quot.sound"
21657     ],
21658     "in_project_namespace": true,
21659     "kind": "theorem",
21660     "module": "PaperIRelease.GeneralPacketBounds",
21661     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_bound",
21662     "runtime_only": false
21663   },
21664   {
21665     "axioms": [
21666       "propext",
21667       "Classical.choice",
21668       "Quot.sound"
21669     ],
21670     "in_project_namespace": true,
21671     "kind": "theorem",
21672     "module": "PaperIRelease.AlgebraSupport",
21673     "name": "Komorebi.PaperIRelease.support_mul_closed_iff",
21674     "runtime_only": false
21675   },
21676   {
21677     "axioms": [
21678       "propext",
21679       "Classical.choice",
21680       "Quot.sound"
21681     ],
21682     "in_project_namespace": true,
21683     "kind": "theorem",
21684     "module": "PaperICompletion8.SemisimpleFormula",
21685     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.exists_finite_simple_decomposition",
21686     "runtime_only": false
21687   },
21688   {
21689     "axioms": [
21690       "propext",
21691       "Classical.choice",
21692       "Quot.sound"
21693     ],
21694     "in_project_namespace": true,
21695     "kind": "theorem",
21696     "module": "PaperIRelease.GrammarAlgebra",
21697     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors._proof_1",
21698     "runtime_only": false
21699   },
21700   {
21701     "axioms": [
21702       "propext",
21703       "Classical.choice",
21704       "Quot.sound"
21705     ],
21706     "in_project_namespace": true,
21707     "kind": "theorem",
21708     "module": "KomorebiVerification.ProjectorCore",
21709     "name": "Komorebi.Packet.fibreProj_reconstruction",
21710     "runtime_only": false
21711   },
21712   {
21713     "axioms": [
21714       "propext",
21715       "Classical.choice",
21716       "Quot.sound"
21717     ],
21718     "in_project_namespace": true,
21719     "kind": "theorem",
21720     "module": "PaperICompletion.SpectralCertificates",
21721     "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedNumber_isLeast",
21722     "runtime_only": false
21723   },
21724   {
21725     "axioms": [
21726       "propext",
21727       "Classical.choice",
21728       "Quot.sound"
21729     ],
21730     "in_project_namespace": true,
21731     "kind": "recursor",
21732     "module": "PaperIRelease.TopologyCategories",
21733     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.rec",
21734     "runtime_only": false
21735   },
21736   {
21737     "axioms": [
21738       "propext",
21739       "Classical.choice",
21740       "Quot.sound"
21741     ],
21742     "in_project_namespace": true,
21743     "kind": "definition",
21744     "module": "PaperIRelease.GeneralNormedPackets",
21745     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk._flat_ctor",
21746     "runtime_only": false
21747   },
21748   {
21749     "axioms": [
21750       "propext",
21751       "Classical.choice",
21752       "Quot.sound"
21753     ],
21754     "in_project_namespace": true,
21755     "kind": "theorem",
21756     "module": "PaperIRelease.PacketTopology",
21757     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL._proof_2",
21758     "runtime_only": false
21759   },
21760   {
21761     "axioms": [
21762       "propext",
21763       "Classical.choice",
21764       "Quot.sound"
21765     ],
21766     "in_project_namespace": true,
21767     "kind": "theorem",
21768     "module": "PaperIRelease.GrammarTyped",
21769     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_vertex",
21770     "runtime_only": false
21771   },
21772   {
21773     "axioms": [
21774       "propext",
21775       "Classical.choice",
21776       "Quot.sound"
21777     ],
21778     "in_project_namespace": true,
21779     "kind": "theorem",
21780     "module": "PaperIRelease.PacketSourceLower",
21781     "name": "Komorebi.PaperIRelease.sum_localPureSeedRank_le_of_compression",
21782     "runtime_only": false
21783   },
21784   {
21785     "axioms": [
21786       "propext",
21787       "Classical.choice",
21788       "Quot.sound"
21789     ],
21790     "in_project_namespace": true,
21791     "kind": "theorem",
21792     "module": "PaperIRelease.CategoryPackets",
21793     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_5",
21794     "runtime_only": false
21795   },
21796   {
21797     "axioms": [
21798       "propext",
21799       "Classical.choice",
21800       "Quot.sound"
21801     ],
21802     "in_project_namespace": true,
21803     "kind": "theorem",
21804     "module": "KomorebiVerification.SingleOperatorGraph",
21805     "name": "Komorebi.SingleOperatorGraph.multiplicity_le_of_generates",
21806     "runtime_only": false
21807   },
21808   {
21809     "axioms": [
21810       "propext",
21811       "Classical.choice",
21812       "Quot.sound"
21813     ],
21814     "in_project_namespace": true,
21815     "kind": "definition",
21816     "module": "KomorebiVerification.KernelAudit",
21817     "name": "Komorebi.Verification.fourCoordinateFamily",
21818     "runtime_only": false
21819   },
21820   {
21821     "axioms": [
21822       "propext",
21823       "Classical.choice",
21824       "Quot.sound"
21825     ],
21826     "in_project_namespace": false,
21827     "kind": "definition",
21828     "module": "PaperIRelease.TopologyCountablePackets",
21829     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_12",
21830     "runtime_only": false
21831   },
21832   {
21833     "axioms": [],
21834     "in_project_namespace": true,
21835     "kind": "definition",
21836     "module": "PaperIRelease.GraphSourceBoundary",
21837     "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow",
21838     "runtime_only": false
21839   },
21840   {
21841     "axioms": [
21842       "propext",
21843       "Classical.choice",
21844       "Quot.sound"
21845     ],
21846     "in_project_namespace": false,
21847     "kind": "theorem",
21848     "module": "PaperIRelease.TopologyUnconditional",
21849     "name": "PaperIRelease.TopologyUnconditional.finiteSum.eq_1",
21850     "runtime_only": false
21851   },
21852   {
21853     "axioms": [
21854       "propext",
21855       "Classical.choice",
21856       "Quot.sound"
21857     ],
21858     "in_project_namespace": false,
21859     "kind": "theorem",
21860     "module": "PaperIRelease.TopologyCountablePackets",
21861     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_norm_le",
21862     "runtime_only": false
21863   },
21864   {
21865     "axioms": [
21866       "propext",
21867       "Classical.choice",
21868       "Quot.sound"
21869     ],
21870     "in_project_namespace": true,
21871     "kind": "definition",
21872     "module": "PaperIRelease.PacketAggregation",
21873     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection",
21874     "runtime_only": false
21875   },
21876   {
21877     "axioms": [],
21878     "in_project_namespace": true,
21879     "kind": "definition",
21880     "module": "PaperIRelease.AlgebraPreorder",
21881     "name": "Komorebi.PaperIRelease.StrictPath._sunfold",
21882     "runtime_only": false
21883   },
21884   {
21885     "axioms": [
21886       "propext",
21887       "Classical.choice",
21888       "Quot.sound"
21889     ],
21890     "in_project_namespace": true,
21891     "kind": "definition",
21892     "module": "KomorebiVerification.TopologicalCompletion",
21893     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic",
21894     "runtime_only": false
21895   },
21896   {
21897     "axioms": [
21898       "propext",
21899       "Classical.choice",
21900       "Quot.sound"
21901     ],
21902     "in_project_namespace": false,
21903     "kind": "theorem",
21904     "module": "PaperIRelease.TopologyUnconditional",
21905     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_6",
21906     "runtime_only": false
21907   },
21908   {
21909     "axioms": [
21910       "propext",
21911       "Classical.choice",
21912       "Quot.sound"
21913     ],
21914     "in_project_namespace": true,
21915     "kind": "definition",
21916     "module": "KomorebiVerification.EllipticAlgorithms",
21917     "name": "Komorebi.FiniteAlgorithms.exactGraphSeedRank",
21918     "runtime_only": false
21919   },
21920   {
21921     "axioms": [
21922       "propext",
21923       "Quot.sound"
21924     ],
21925     "in_project_namespace": true,
21926     "kind": "theorem",
21927     "module": "PaperIRelease.AlgebraPreorder",
21928     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_2",
21929     "runtime_only": false
21930   },
21931   {
21932     "axioms": [
21933       "propext",
21934       "Classical.choice",
21935       "Quot.sound"
21936     ],
21937     "in_project_namespace": false,
21938     "kind": "theorem",
21939     "module": "PaperIRelease.TopologyCountablePackets",
21940     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_4",
21941     "runtime_only": false
21942   },
21943   {
21944     "axioms": [],
21945     "in_project_namespace": true,
21946     "kind": "constructor",
21947     "module": "KomorebiVerification.ProjectorCore",
21948     "name": "Komorebi.FormalizationStatus.partialFormalization",
21949     "runtime_only": false
21950   },
21951   {
21952     "axioms": [
21953       "propext",
21954       "Classical.choice",
21955       "Quot.sound"
21956     ],
21957     "in_project_namespace": true,
21958     "kind": "theorem",
21959     "module": "PaperICompletion8.ProductPresentation",
21960     "name": "Komorebi.PaperICompletion8.ProductPresentation.exists_multiplicity_presentation",
21961     "runtime_only": false
21962   },
21963   {
21964     "axioms": [
21965       "propext",
21966       "Classical.choice",
21967       "Quot.sound"
21968     ],
21969     "in_project_namespace": true,
21970     "kind": "theorem",
21971     "module": "PaperIRelease.PacketUniversal",
21972     "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut_packet",
21973     "runtime_only": false
21974   },
21975   {
21976     "axioms": [
21977       "propext",
21978       "Classical.choice",
21979       "Quot.sound"
21980     ],
21981     "in_project_namespace": true,
21982     "kind": "theorem",
21983     "module": "PaperIRelease.BoundedStar",
21984     "name": "Komorebi.PaperIRelease.BoundedSupport.proj_mem",
21985     "runtime_only": false
21986   },
21987   {
21988     "axioms": [
21989       "propext",
21990       "Classical.choice",
21991       "Quot.sound"
21992     ],
21993     "in_project_namespace": false,
21994     "kind": "definition",
21995     "module": "PaperIRelease.TopologyCountablePackets",
21996     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis",
21997     "runtime_only": false
21998   },
21999   {
22000     "axioms": [],
22001     "in_project_namespace": true,
22002     "kind": "definition",
22003     "module": "PaperIRelease.GrammarPaths",
22004     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil.elim",
22005     "runtime_only": false
22006   },
22007   {
22008     "axioms": [
22009       "propext",
22010       "Quot.sound"
22011     ],
22012     "in_project_namespace": true,
22013     "kind": "definition",
22014     "module": "PaperIRelease.PacketBoundaryTests",
22015     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.horizontal",
22016     "runtime_only": false
22017   },
22018   {
22019     "axioms": [
22020       "propext",
22021       "Classical.choice",
22022       "Quot.sound"
22023     ],
22024     "in_project_namespace": true,
22025     "kind": "theorem",
22026     "module": "PaperIRelease.TensorPackets",
22027     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_3",
22028     "runtime_only": false
22029   },
22030   {
22031     "axioms": [
22032       "propext",
22033       "Quot.sound"
22034     ],
22035     "in_project_namespace": true,
22036     "kind": "theorem",
22037     "module": "KomorebiVerification.PathGraphKrylov",
22038     "name": "Komorebi.PathGraphKrylov.leftStep.eq_1",
22039     "runtime_only": false
22040   },
22041   {
22042     "axioms": [
22043       "propext",
22044       "Quot.sound"
22045     ],
22046     "in_project_namespace": true,
22047     "kind": "definition",
22048     "module": "KomorebiVerification.PathGraphKrylov",
22049     "name": "Komorebi.PathGraphKrylov.krylov._f",
22050     "runtime_only": false
22051   },
22052   {
22053     "axioms": [
22054       "propext",
22055       "Classical.choice",
22056       "Quot.sound"
22057     ],
22058     "in_project_namespace": true,
22059     "kind": "theorem",
22060     "module": "PaperIRelease.PacketPureBoundaryTests",
22061     "name": "Komorebi.PaperIRelease.PureBoundaryTests.deleted_zero_rank",
22062     "runtime_only": false
22063   },
22064   {
22065     "axioms": [],
22066     "in_project_namespace": false,
22067     "kind": "theorem",
22068     "module": "PaperIRelease.CategoryExport",
22069     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_2",
22070     "runtime_only": false
22071   },
22072   {
22073     "axioms": [
22074       "propext",
22075       "Classical.choice",
22076       "Quot.sound"
22077     ],
22078     "in_project_namespace": true,
22079     "kind": "definition",
22080     "module": "KomorebiVerification.EllipticAlgorithms",
22081     "name": "Komorebi.FiniteAlgorithms.transferBlockTable",
22082     "runtime_only": false
22083   },
22084   {
22085     "axioms": [
22086       "propext",
22087       "Classical.choice",
22088       "Quot.sound"
22089     ],
22090     "in_project_namespace": true,
22091     "kind": "definition",
22092     "module": "PaperIRelease.PacketTopology",
22093     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL",
22094     "runtime_only": false
22095   },
22096   {
22097     "axioms": [
22098       "propext",
22099       "Classical.choice",
22100       "Quot.sound"
22101     ],
22102     "in_project_namespace": true,
22103     "kind": "theorem",
22104     "module": "PaperIRelease.PacketTopologyGeneral",
22105     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_2",
22106     "runtime_only": false
22107   },
22108   {
22109     "axioms": [
22110       "propext",
22111       "Classical.choice",
22112       "Quot.sound"
22113     ],
22114     "in_project_namespace": true,
22115     "kind": "definition",
22116     "module": "PaperIRelease.TopologyCategories",
22117     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.ctorIdx",
22118     "runtime_only": false
22119   },
22120   {
22121     "axioms": [
22122       "propext",
22123       "Classical.choice",
22124       "Quot.sound"
22125     ],
22126     "in_project_namespace": false,
22127     "kind": "theorem",
22128     "module": "PaperIRelease.TopologySemilinearRank",
22129     "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates.eq_1",
22130     "runtime_only": false
22131   },
22132   {
22133     "axioms": [
22134       "propext",
22135       "Classical.choice",
22136       "Quot.sound"
22137     ],
22138     "in_project_namespace": true,
22139     "kind": "theorem",
22140     "module": "PaperIRelease.PacketDescent",
22141     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_intertwines",
22142     "runtime_only": false
22143   },
22144   {
22145     "axioms": [
22146       "propext",
22147       "Classical.choice",
22148       "Quot.sound"
22149     ],
22150     "in_project_namespace": true,
22151     "kind": "theorem",
22152     "module": "PaperIRelease.PacketTopology",
22153     "name": "Komorebi.Foundation.LinearProjectorFamily.banach_packet_shortExact",
22154     "runtime_only": false
22155   },
22156   {
22157     "axioms": [
22158       "propext",
22159       "Classical.choice",
22160       "Quot.sound"
22161     ],
22162     "in_project_namespace": true,
22163     "kind": "theorem",
22164     "module": "PaperIRelease.GrammarAlgebra",
22165     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_2",
22166     "runtime_only": false
22167   },
22168   {
22169     "axioms": [
22170       "propext",
22171       "Classical.choice",
22172       "Quot.sound"
22173     ],
22174     "in_project_namespace": false,
22175     "kind": "theorem",
22176     "module": "PaperIRelease.TopologyCountablePackets",
22177     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis._proof_2",
22178     "runtime_only": false
22179   },
22180   {
22181     "axioms": [
22182       "propext",
22183       "Classical.choice",
22184       "Quot.sound"
22185     ],
22186     "in_project_namespace": true,
22187     "kind": "definition",
22188     "module": "PaperIRelease.GrammarPaths",
22189     "name": "Komorebi.PaperIRelease.GrammarAlgebra.PathCombination",
22190     "runtime_only": false
22191   },
22192   {
22193     "axioms": [
22194       "propext",
22195       "Classical.choice",
22196       "Quot.sound"
22197     ],
22198     "in_project_namespace": false,
22199     "kind": "theorem",
22200     "module": "PaperIRelease.TopologyUnconditionalBridge",
22201     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_2",
22202     "runtime_only": false
22203   },
22204   {
22205     "axioms": [
22206       "propext"
22207     ],
22208     "in_project_namespace": true,
22209     "kind": "theorem",
22210     "module": "KomorebiVerification.ProjectorCore",
22211     "name": "Komorebi.Algebra.IsUpperTriangular.add",
22212     "runtime_only": false
22213   },
22214   {
22215     "axioms": [
22216       "propext",
22217       "Classical.choice",
22218       "Quot.sound"
22219     ],
22220     "in_project_namespace": true,
22221     "kind": "theorem",
22222     "module": "KomorebiVerification.TopologicalCompletion",
22223     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_7",
22224     "runtime_only": false
22225   },
22226   {
22227     "axioms": [
22228       "propext"
22229     ],
22230     "in_project_namespace": true,
22231     "kind": "theorem",
22232     "module": "PaperIRelease.CategoryExport",
22233     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_7",
22234     "runtime_only": false
22235   },
22236   {
22237     "axioms": [
22238       "propext",
22239       "Classical.choice",
22240       "Quot.sound"
22241     ],
22242     "in_project_namespace": true,
22243     "kind": "theorem",
22244     "module": "PaperIRelease.CategoryBoundaries",
22245     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_4",
22246     "runtime_only": false
22247   },
22248   {
22249     "axioms": [
22250       "propext",
22251       "Classical.choice",
22252       "Quot.sound"
22253     ],
22254     "in_project_namespace": true,
22255     "kind": "theorem",
22256     "module": "PaperIRelease.TopologyCategories",
22257     "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull._proof_1",
22258     "runtime_only": false
22259   },
22260   {
22261     "axioms": [
22262       "propext",
22263       "Classical.choice",
22264       "Quot.sound"
22265     ],
22266     "in_project_namespace": true,
22267     "kind": "theorem",
22268     "module": "PaperICompletion5.CyclicGeometricCriterion",
22269     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff._proof_1_1",
22270     "runtime_only": false
22271   },
22272   {
22273     "axioms": [],
22274     "in_project_namespace": true,
22275     "kind": "definition",
22276     "module": "KomorebiVerification.ProjectorCore",
22277     "name": "Komorebi.ClaimRecord.noConfusion",
22278     "runtime_only": false
22279   },
22280   {
22281     "axioms": [],
22282     "in_project_namespace": true,
22283     "kind": "definition",
22284     "module": "PaperIRelease.CategoryExport",
22285     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.match_1",
22286     "runtime_only": false
22287   },
22288   {
22289     "axioms": [
22290       "propext",
22291       "Quot.sound"
22292     ],
22293     "in_project_namespace": true,
22294     "kind": "constructor",
22295     "module": "PaperIRelease.GrammarModules",
22296     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk",
22297     "runtime_only": false
22298   },
22299   {
22300     "axioms": [
22301       "propext",
22302       "Classical.choice",
22303       "Quot.sound"
22304     ],
22305     "in_project_namespace": true,
22306     "kind": "theorem",
22307     "module": "PaperIRelease.CategoryPackets",
22308     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.operator_apply",
22309     "runtime_only": false
22310   },
22311   {
22312     "axioms": [],
22313     "in_project_namespace": true,
22314     "kind": "definition",
22315     "module": "KomorebiVerification.ProjectorCore",
22316     "name": "Komorebi.Seed.OperatorRelation._sizeOf_1",
22317     "runtime_only": false
22318   },
22319   {
22320     "axioms": [
22321       "propext",
22322       "Classical.choice",
22323       "Quot.sound"
22324     ],
22325     "in_project_namespace": true,
22326     "kind": "theorem",
22327     "module": "PaperIRelease.GrammarEquivalence",
22328     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_isEquivalence",
22329     "runtime_only": false
22330   },
22331   {
22332     "axioms": [
22333       "propext",
22334       "Classical.choice",
22335       "Quot.sound"
22336     ],
22337     "in_project_namespace": true,
22338     "kind": "theorem",
22339     "module": "PaperIRelease.GraphSourceObstruction",
22340     "name": "Komorebi.PaperIRelease.generatedAlgebra_source_obstruction",
22341     "runtime_only": false
22342   },
22343   {
22344     "axioms": [
22345       "propext",
22346       "Classical.choice",
22347       "Quot.sound"
22348     ],
22349     "in_project_namespace": true,
22350     "kind": "theorem",
22351     "module": "PaperIRelease.PacketTopologyGeneral",
22352     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorCLM._proof_1",
22353     "runtime_only": false
22354   },
22355   {
22356     "axioms": [
22357       "propext",
22358       "Classical.choice",
22359       "Quot.sound"
22360     ],
22361     "in_project_namespace": true,
22362     "kind": "theorem",
22363     "module": "PaperICompletion4.ResidueQuotient",
22364     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryProductQuotientEquiv._proof_1",
22365     "runtime_only": false
22366   },
22367   {
22368     "axioms": [
22369       "propext",
22370       "Classical.choice",
22371       "Quot.sound"
22372     ],
22373     "in_project_namespace": true,
22374     "kind": "theorem",
22375     "module": "PaperIRelease.GraphSourceProjection",
22376     "name": "Komorebi.PaperIRelease.componentProjection_mem",
22377     "runtime_only": false
22378   },
22379   {
22380     "axioms": [
22381       "propext",
22382       "Classical.choice",
22383       "Quot.sound"
22384     ],
22385     "in_project_namespace": true,
22386     "kind": "theorem",
22387     "module": "PaperIRelease.TensorPackets",
22388     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_1",
22389     "runtime_only": false
22390   },
22391   {
22392     "axioms": [
22393       "propext",
22394       "Classical.choice",
22395       "Quot.sound"
22396     ],
22397     "in_project_namespace": true,
22398     "kind": "theorem",
22399     "module": "KomorebiVerification.PacketNaturalityCompletion",
22400     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_not_mem_range_arrowA",
22401     "runtime_only": false
22402   },
22403   {
22404     "axioms": [
22405       "propext",
22406       "Classical.choice",
22407       "Quot.sound"
22408     ],
22409     "in_project_namespace": true,
22410     "kind": "theorem",
22411     "module": "PaperIRelease.AlgebraClassGrouping",
22412     "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_2",
22413     "runtime_only": false
22414   },
22415   {
22416     "axioms": [
22417       "propext",
22418       "Quot.sound"
22419     ],
22420     "in_project_namespace": true,
22421     "kind": "theorem",
22422     "module": "PaperICompletion4.GroupedPrimary",
22423     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_1",
22424     "runtime_only": false
22425   },
22426   {
22427     "axioms": [
22428       "propext",
22429       "Quot.sound"
22430     ],
22431     "in_project_namespace": true,
22432     "kind": "recursor",
22433     "module": "PaperIRelease.GrammarTyped",
22434     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.rec",
22435     "runtime_only": false
22436   },
22437   {
22438     "axioms": [
22439       "propext",
22440       "Classical.choice",
22441       "Quot.sound"
22442     ],
22443     "in_project_namespace": true,
22444     "kind": "constructor",
22445     "module": "PaperIRelease.TopologyCategories",
22446     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk",
22447     "runtime_only": false
22448   },
22449   {
22450     "axioms": [
22451       "propext",
22452       "Classical.choice",
22453       "Quot.sound"
22454     ],
22455     "in_project_namespace": true,
22456     "kind": "definition",
22457     "module": "KomorebiVerification.TopologicalCompletion",
22458     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk._flat_ctor",
22459     "runtime_only": false
22460   },
22461   {
22462     "axioms": [
22463       "propext",
22464       "Classical.choice",
22465       "Quot.sound"
22466     ],
22467     "in_project_namespace": true,
22468     "kind": "theorem",
22469     "module": "PaperIRelease.AlgebraClassGrouping",
22470     "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_3",
22471     "runtime_only": false
22472   },
22473   {
22474     "axioms": [
22475       "propext",
22476       "Classical.choice",
22477       "Quot.sound"
22478     ],
22479     "in_project_namespace": true,
22480     "kind": "theorem",
22481     "module": "PaperICompletion6.SixWayCyclicCriterion",
22482     "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_six_way_algebraicClosure",
22483     "runtime_only": false
22484   },
22485   {
22486     "axioms": [
22487       "propext",
22488       "Classical.choice",
22489       "Quot.sound"
22490     ],
22491     "in_project_namespace": true,
22492     "kind": "theorem",
22493     "module": "PaperICompletion8.SemisimpleFormula",
22494     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.exists_wedderburn_decomposition",
22495     "runtime_only": false
22496   },
22497   {
22498     "axioms": [
22499       "propext",
22500       "Quot.sound"
22501     ],
22502     "in_project_namespace": true,
22503     "kind": "theorem",
22504     "module": "PaperICompletion5.LinearPrimaryEigenspace",
22505     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_4",
22506     "runtime_only": false
22507   },
22508   {
22509     "axioms": [
22510       "propext",
22511       "Classical.choice",
22512       "Quot.sound"
22513     ],
22514     "in_project_namespace": true,
22515     "kind": "definition",
22516     "module": "PaperICompletion.SpectralCertificates",
22517     "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis",
22518     "runtime_only": false
22519   },
22520   {
22521     "axioms": [
22522       "propext",
22523       "Classical.choice",
22524       "Quot.sound"
22525     ],
22526     "in_project_namespace": true,
22527     "kind": "theorem",
22528     "module": "PaperICompletion4.IntrinsicPrimary",
22529     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_2",
22530     "runtime_only": false
22531   },
22532   {
22533     "axioms": [
22534       "propext",
22535       "Quot.sound"
22536     ],
22537     "in_project_namespace": true,
22538     "kind": "definition",
22539     "module": "PaperIRelease.GrammarIdeal",
22540     "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeGrammar",
22541     "runtime_only": false
22542   },
22543   {
22544     "axioms": [],
22545     "in_project_namespace": true,
22546     "kind": "definition",
22547     "module": "KomorebiVerification.ProjectorCore",
22548     "name": "Komorebi.instInhabitedClaimKind",
22549     "runtime_only": false
22550   },
22551   {
22552     "axioms": [
22553       "propext",
22554       "Classical.choice",
22555       "Quot.sound"
22556     ],
22557     "in_project_namespace": true,
22558     "kind": "theorem",
22559     "module": "PaperIRelease.GeneralNormedPackets",
22560     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.idempotent",
22561     "runtime_only": false
22562   },
22563   {
22564     "axioms": [
22565       "propext",
22566       "Classical.choice",
22567       "Quot.sound"
22568     ],
22569     "in_project_namespace": true,
22570     "kind": "theorem",
22571     "module": "PaperICompletion3.OperatorPrimaryAPI",
22572     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_of_cyclic",
22573     "runtime_only": false
22574   },
22575   {
22576     "axioms": [
22577       "propext",
22578       "Classical.choice",
22579       "Quot.sound"
22580     ],
22581     "in_project_namespace": true,
22582     "kind": "theorem",
22583     "module": "PaperIRelease.AlgebraSupport",
22584     "name": "Komorebi.PaperIRelease.operatorSupported_iff_ambient",
22585     "runtime_only": false
22586   },
22587   {
22588     "axioms": [
22589       "propext",
22590       "Classical.choice",
22591       "Quot.sound"
22592     ],
22593     "in_project_namespace": true,
22594     "kind": "definition",
22595     "module": "KomorebiVerification.ExactCoordinates",
22596     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates",
22597     "runtime_only": false
22598   },
22599   {
22600     "axioms": [
22601       "propext",
22602       "Classical.choice",
22603       "Quot.sound"
22604     ],
22605     "in_project_namespace": true,
22606     "kind": "theorem",
22607     "module": "PaperIRelease.PacketPureRank",
22608     "name": "Komorebi.PaperIRelease.all_pure_generates",
22609     "runtime_only": false
22610   },
22611   {
22612     "axioms": [
22613       "propext",
22614       "Classical.choice",
22615       "Quot.sound"
22616     ],
22617     "in_project_namespace": true,
22618     "kind": "theorem",
22619     "module": "KomorebiVerification.PacketNaturalityCompletion",
22620     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_eq_sum_packet_finrank",
22621     "runtime_only": false
22622   },
22623   {
22624     "axioms": [
22625       "propext",
22626       "Classical.choice",
22627       "Quot.sound"
22628     ],
22629     "in_project_namespace": true,
22630     "kind": "theorem",
22631     "module": "PaperIRelease.GrammarTyped",
22632     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_1",
22633     "runtime_only": false
22634   },
22635   {
22636     "axioms": [
22637       "propext",
22638       "Classical.choice",
22639       "Quot.sound"
22640     ],
22641     "in_project_namespace": false,
22642     "kind": "theorem",
22643     "module": "PaperIRelease.TopologyCountablePackets",
22644     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_11",
22645     "runtime_only": false
22646   },
22647   {
22648     "axioms": [
22649       "propext",
22650       "Classical.choice",
22651       "Quot.sound"
22652     ],
22653     "in_project_namespace": false,
22654     "kind": "theorem",
22655     "module": "ReleaseBoundary",
22656     "name": "_private.ReleaseBoundary.0.PaperIBlock08Tests.mixed_count",
22657     "runtime_only": false
22658   },
22659   {
22660     "axioms": [
22661       "propext",
22662       "Classical.choice",
22663       "Quot.sound"
22664     ],
22665     "in_project_namespace": true,
22666     "kind": "theorem",
22667     "module": "PaperIRelease.AlgebraPreorder",
22668     "name": "Komorebi.PaperIRelease.strictIdeal_power_mem",
22669     "runtime_only": false
22670   },
22671   {
22672     "axioms": [
22673       "propext",
22674       "Classical.choice",
22675       "Quot.sound"
22676     ],
22677     "in_project_namespace": true,
22678     "kind": "theorem",
22679     "module": "KomorebiVerification.SeedRankBasics",
22680     "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv_apply_mk",
22681     "runtime_only": false
22682   },
22683   {
22684     "axioms": [
22685       "propext",
22686       "Classical.choice",
22687       "Quot.sound"
22688     ],
22689     "in_project_namespace": false,
22690     "kind": "definition",
22691     "module": "PaperIRelease.TopologyCountablePackets",
22692     "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms",
22693     "runtime_only": false
22694   },
22695   {
22696     "axioms": [
22697       "propext",
22698       "Classical.choice",
22699       "Quot.sound"
22700     ],
22701     "in_project_namespace": true,
22702     "kind": "theorem",
22703     "module": "PaperICompletion4.OperatorIntrinsicFormula",
22704     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues_nonempty",
22705     "runtime_only": false
22706   },
22707   {
22708     "axioms": [
22709       "propext",
22710       "Classical.choice",
22711       "Quot.sound"
22712     ],
22713     "in_project_namespace": true,
22714     "kind": "theorem",
22715     "module": "PaperICompletion6.ScalarExtension",
22716     "name": "Komorebi.PaperICompletion6.ScalarExtension.baseChange_nontrivial",
22717     "runtime_only": false
22718   },
22719   {
22720     "axioms": [
22721       "propext"
22722     ],
22723     "in_project_namespace": true,
22724     "kind": "theorem",
22725     "module": "PaperIRelease.CategoryExport",
22726     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_1",
22727     "runtime_only": false
22728   },
22729   {
22730     "axioms": [
22731       "propext",
22732       "Classical.choice",
22733       "Quot.sound"
22734     ],
22735     "in_project_namespace": true,
22736     "kind": "theorem",
22737     "module": "PaperIRelease.GrammarEquivalence",
22738     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_13",
22739     "runtime_only": false
22740   },
22741   {
22742     "axioms": [
22743       "propext",
22744       "Classical.choice",
22745       "Quot.sound"
22746     ],
22747     "in_project_namespace": true,
22748     "kind": "theorem",
22749     "module": "PaperIRelease.GrammarPaths",
22750     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_2",
22751     "runtime_only": false
22752   },
22753   {
22754     "axioms": [
22755       "propext",
22756       "Classical.choice",
22757       "Quot.sound"
22758     ],
22759     "in_project_namespace": true,
22760     "kind": "theorem",
22761     "module": "KomorebiVerification.ExactCoordinates",
22762     "name": "Komorebi.Foundation.LinearProjectorFamily.proj_packet_self",
22763     "runtime_only": false
22764   },
22765   {
22766     "axioms": [
22767       "propext",
22768       "Classical.choice",
22769       "Quot.sound"
22770     ],
22771     "in_project_namespace": false,
22772     "kind": "definition",
22773     "module": "ReleaseBoundary",
22774     "name": "PaperIBlock08Tests.dualLinearEquiv",
22775     "runtime_only": false
22776   },
22777   {
22778     "axioms": [],
22779     "in_project_namespace": false,
22780     "kind": "definition",
22781     "module": "KomorebiVerification.PacketNaturalityCompletion",
22782     "name": "_private.KomorebiVerification.PacketNaturalityCompletion.0.Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1.splitter",
22783     "runtime_only": false
22784   },
22785   {
22786     "axioms": [
22787       "propext",
22788       "Quot.sound"
22789     ],
22790     "in_project_namespace": true,
22791     "kind": "theorem",
22792     "module": "PaperICompletion5.CyclicGeometricCriterion",
22793     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_3",
22794     "runtime_only": false
22795   },
22796   {
22797     "axioms": [
22798       "propext",
22799       "Classical.choice",
22800       "Quot.sound"
22801     ],
22802     "in_project_namespace": false,
22803     "kind": "definition",
22804     "module": "PaperIRelease.TopologyUnconditionalBridge",
22805     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv",
22806     "runtime_only": false
22807   },
22808   {
22809     "axioms": [
22810       "propext",
22811       "Classical.choice",
22812       "Quot.sound"
22813     ],
22814     "in_project_namespace": true,
22815     "kind": "theorem",
22816     "module": "PaperIRelease.PolynomialMonic",
22817     "name": "Komorebi.PaperIRelease.PolynomialModule.monic_primary_internal_decomposition",
22818     "runtime_only": false
22819   },
22820   {
22821     "axioms": [
22822       "propext",
22823       "Classical.choice",
22824       "Quot.sound"
22825     ],
22826     "in_project_namespace": true,
22827     "kind": "definition",
22828     "module": "PaperIRelease.GeneralNormedPackets",
22829     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.noConfusionType",
22830     "runtime_only": false
22831   },
22832   {
22833     "axioms": [
22834       "propext",
22835       "Classical.choice",
22836       "Quot.sound"
22837     ],
22838     "in_project_namespace": true,
22839     "kind": "definition",
22840     "module": "PaperIRelease.GrammarPaths",
22841     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word",
22842     "runtime_only": false
22843   },
22844   {
22845     "axioms": [
22846       "propext",
22847       "Classical.choice",
22848       "Quot.sound"
22849     ],
22850     "in_project_namespace": true,
22851     "kind": "theorem",
22852     "module": "PaperICompletion4.ResidueQuotient",
22853     "name": "Komorebi.PaperICompletion4.ResidueQuotient.quotientAfterEquiv_ker",
22854     "runtime_only": false
22855   },
22856   {
22857     "axioms": [
22858       "propext",
22859       "Classical.choice",
22860       "Quot.sound"
22861     ],
22862     "in_project_namespace": true,
22863     "kind": "theorem",
22864     "module": "PaperICompletion5.CyclicGeometricCriterion",
22865     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_geometricSeedMaximum_one",
22866     "runtime_only": false
22867   },
22868   {
22869     "axioms": [
22870       "propext",
22871       "Classical.choice",
22872       "Quot.sound"
22873     ],
22874     "in_project_namespace": true,
22875     "kind": "theorem",
22876     "module": "PaperIRelease.GrammarEquivalence",
22877     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_4",
22878     "runtime_only": false
22879   },
22880   {
22881     "axioms": [
22882       "propext",
22883       "Quot.sound"
22884     ],
22885     "in_project_namespace": true,
22886     "kind": "theorem",
22887     "module": "PaperIRelease.GrammarModules",
22888     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.inj",
22889     "runtime_only": false
22890   },
22891   {
22892     "axioms": [],
22893     "in_project_namespace": true,
22894     "kind": "theorem",
22895     "module": "KomorebiVerification.ProjectorCore",
22896     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_2",
22897     "runtime_only": false
22898   },
22899   {
22900     "axioms": [
22901       "propext",
22902       "Classical.choice",
22903       "Quot.sound"
22904     ],
22905     "in_project_namespace": true,
22906     "kind": "definition",
22907     "module": "PaperIRelease.PacketDescent",
22908     "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroQuotient",
22909     "runtime_only": false
22910   },
22911   {
22912     "axioms": [
22913       "propext",
22914       "Classical.choice",
22915       "Quot.sound"
22916     ],
22917     "in_project_namespace": true,
22918     "kind": "theorem",
22919     "module": "KomorebiVerification.SingleOperatorGraph",
22920     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor.eq_1",
22921     "runtime_only": false
22922   },
22923   {
22924     "axioms": [
22925       "propext",
22926       "Classical.choice",
22927       "Quot.sound"
22928     ],
22929     "in_project_namespace": true,
22930     "kind": "theorem",
22931     "module": "PaperICompletion4.OperatorIntrinsicFormula",
22932     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_2",
22933     "runtime_only": false
22934   },
22935   {
22936     "axioms": [
22937       "propext",
22938       "Classical.choice",
22939       "Quot.sound"
22940     ],
22941     "in_project_namespace": true,
22942     "kind": "theorem",
22943     "module": "PaperIRelease.SeedOperations",
22944     "name": "Komorebi.PaperIRelease.SeedOperations.regular_generates_one",
22945     "runtime_only": false
22946   },
22947   {
22948     "axioms": [
22949       "propext",
22950       "Classical.choice",
22951       "Quot.sound"
22952     ],
22953     "in_project_namespace": true,
22954     "kind": "definition",
22955     "module": "PaperIRelease.PacketTopologyGeneral",
22956     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM",
22957     "runtime_only": false
22958   },
22959   {
22960     "axioms": [
22961       "propext",
22962       "Classical.choice",
22963       "Quot.sound"
22964     ],
22965     "in_project_namespace": true,
22966     "kind": "theorem",
22967     "module": "PaperIRelease.CategoryBoundaries",
22968     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_2",
22969     "runtime_only": false
22970   },
22971   {
22972     "axioms": [],
22973     "in_project_namespace": true,
22974     "kind": "theorem",
22975     "module": "KomorebiVerification.ProjectorCore",
22976     "name": "Komorebi.Seed.OperatorExpr.id.sizeOf_spec",
22977     "runtime_only": false
22978   },
22979   {
22980     "axioms": [
22981       "propext",
22982       "Classical.choice",
22983       "Quot.sound"
22984     ],
22985     "in_project_namespace": true,
22986     "kind": "constructor",
22987     "module": "PaperIRelease.GrammarAlgebra",
22988     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_orthogonal",
22989     "runtime_only": false
22990   },
22991   {
22992     "axioms": [
22993       "propext",
22994       "Classical.choice",
22995       "Quot.sound"
22996     ],
22997     "in_project_namespace": true,
22998     "kind": "theorem",
22999     "module": "PaperIRelease.PacketDescent",
23000     "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_2",
23001     "runtime_only": false
23002   },
23003   {
23004     "axioms": [],
23005     "in_project_namespace": true,
23006     "kind": "definition",
23007     "module": "KomorebiVerification.ProjectorCore",
23008     "name": "Komorebi.ClaimKind.ctorElimType",
23009     "runtime_only": false
23010   },
23011   {
23012     "axioms": [
23013       "propext",
23014       "Classical.choice",
23015       "Quot.sound"
23016     ],
23017     "in_project_namespace": true,
23018     "kind": "definition",
23019     "module": "KomorebiVerification.EllipticAlgorithms",
23020     "name": "Komorebi.FiniteAlgorithms.assembleTransferBlockTable",
23021     "runtime_only": false
23022   },
23023   {
23024     "axioms": [
23025       "propext",
23026       "Classical.choice",
23027       "Quot.sound"
23028     ],
23029     "in_project_namespace": true,
23030     "kind": "theorem",
23031     "module": "PaperIRelease.GrammarTyped",
23032     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_on_range",
23033     "runtime_only": false
23034   },
23035   {
23036     "axioms": [
23037       "propext",
23038       "Classical.choice",
23039       "Quot.sound"
23040     ],
23041     "in_project_namespace": true,
23042     "kind": "definition",
23043     "module": "KomorebiVerification.TopologicalCompletion",
23044     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk._flat_ctor",
23045     "runtime_only": false
23046   },
23047   {
23048     "axioms": [
23049       "propext",
23050       "Classical.choice",
23051       "Quot.sound"
23052     ],
23053     "in_project_namespace": true,
23054     "kind": "theorem",
23055     "module": "PaperIRelease.GeneralNormedPackets",
23056     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.sizeOf_spec",
23057     "runtime_only": false
23058   },
23059   {
23060     "axioms": [],
23061     "in_project_namespace": true,
23062     "kind": "definition",
23063     "module": "PaperICompletion8.DivisionBlock",
23064     "name": "Komorebi.PaperICompletion8.DivisionBlock.BlockModule",
23065     "runtime_only": false
23066   },
23067   {
23068     "axioms": [
23069       "propext",
23070       "Classical.choice",
23071       "Quot.sound"
23072     ],
23073     "in_project_namespace": true,
23074     "kind": "theorem",
23075     "module": "PaperIRelease.TopologyCategories",
23076     "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_3",
23077     "runtime_only": false
23078   },
23079   {
23080     "axioms": [
23081       "propext",
23082       "Classical.choice",
23083       "Quot.sound"
23084     ],
23085     "in_project_namespace": true,
23086     "kind": "theorem",
23087     "module": "PaperICompletion3.PrimarySeedFormula",
23088     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity.eq_1",
23089     "runtime_only": false
23090   },
23091   {
23092     "axioms": [
23093       "propext"
23094     ],
23095     "in_project_namespace": true,
23096     "kind": "theorem",
23097     "module": "PaperIRelease.CategoryExport",
23098     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_5",
23099     "runtime_only": false
23100   },
23101   {
23102     "axioms": [
23103       "propext",
23104       "Classical.choice",
23105       "Quot.sound"
23106     ],
23107     "in_project_namespace": false,
23108     "kind": "definition",
23109     "module": "PaperIRelease.TopologyUnconditional",
23110     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNorm",
23111     "runtime_only": false
23112   },
23113   {
23114     "axioms": [
23115       "propext",
23116       "Classical.choice",
23117       "Quot.sound"
23118     ],
23119     "in_project_namespace": true,
23120     "kind": "definition",
23121     "module": "PaperIRelease.TopologyCategories",
23122     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.noConfusionType",
23123     "runtime_only": false
23124   },
23125   {
23126     "axioms": [],
23127     "in_project_namespace": true,
23128     "kind": "theorem",
23129     "module": "PaperIRelease.GrammarPaths",
23130     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.inj",
23131     "runtime_only": false
23132   },
23133   {
23134     "axioms": [
23135       "propext",
23136       "Quot.sound"
23137     ],
23138     "in_project_namespace": true,
23139     "kind": "theorem",
23140     "module": "KomorebiVerification.ProjectorCore",
23141     "name": "Komorebi.Foundation.transferBlock._proof_1",
23142     "runtime_only": false
23143   },
23144   {
23145     "axioms": [
23146       "propext",
23147       "Classical.choice",
23148       "Quot.sound"
23149     ],
23150     "in_project_namespace": true,
23151     "kind": "theorem",
23152     "module": "PaperIRelease.GrammarTyped",
23153     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_complete",
23154     "runtime_only": false
23155   },
23156   {
23157     "axioms": [
23158       "propext",
23159       "Classical.choice",
23160       "Quot.sound"
23161     ],
23162     "in_project_namespace": true,
23163     "kind": "theorem",
23164     "module": "PaperIRelease.AlgebraDiagonal",
23165     "name": "Komorebi.PaperIRelease.diagonalProjection_of_commutes",
23166     "runtime_only": false
23167   },
23168   {
23169     "axioms": [],
23170     "in_project_namespace": true,
23171     "kind": "definition",
23172     "module": "PaperIRelease.GrammarPaths",
23173     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath._sizeOf_inst",
23174     "runtime_only": false
23175   },
23176   {
23177     "axioms": [
23178       "propext",
23179       "Classical.choice",
23180       "Quot.sound"
23181     ],
23182     "in_project_namespace": true,
23183     "kind": "theorem",
23184     "module": "PaperICompletion8.SemisimpleFormula",
23185     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.seedRank_eq_radicalTop_restricted",
23186     "runtime_only": false
23187   },
23188   {
23189     "axioms": [
23190       "propext",
23191       "Classical.choice",
23192       "Quot.sound"
23193     ],
23194     "in_project_namespace": true,
23195     "kind": "definition",
23196     "module": "KomorebiVerification.PacketNaturalityCompletion",
23197     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.BlocksSupported",
23198     "runtime_only": false
23199   },
23200   {
23201     "axioms": [
23202       "propext"
23203     ],
23204     "in_project_namespace": true,
23205     "kind": "theorem",
23206     "module": "PaperICompletion4.IntrinsicPrimary",
23207     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_1",
23208     "runtime_only": false
23209   },
23210   {
23211     "axioms": [
23212       "propext"
23213     ],
23214     "in_project_namespace": true,
23215     "kind": "theorem",
23216     "module": "KomorebiVerification.SingleOperatorGraph",
23217     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_9",
23218     "runtime_only": false
23219   },
23220   {
23221     "axioms": [
23222       "propext",
23223       "Quot.sound"
23224     ],
23225     "in_project_namespace": true,
23226     "kind": "theorem",
23227     "module": "KomorebiVerification.PathGraphKrylov",
23228     "name": "Komorebi.PathGraphKrylov.krylov_zero",
23229     "runtime_only": false
23230   },
23231   {
23232     "axioms": [
23233       "propext",
23234       "Classical.choice",
23235       "Quot.sound"
23236     ],
23237     "in_project_namespace": true,
23238     "kind": "definition",
23239     "module": "PaperIRelease.TopologyCategories",
23240     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject._sizeOf_1",
23241     "runtime_only": false
23242   },
23243   {
23244     "axioms": [
23245       "propext",
23246       "Classical.choice",
23247       "Quot.sound"
23248     ],
23249     "in_project_namespace": true,
23250     "kind": "theorem",
23251     "module": "KomorebiVerification.TopologicalCompletion",
23252     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.coordinate",
23253     "runtime_only": false
23254   },
23255   {
23256     "axioms": [
23257       "propext",
23258       "Quot.sound"
23259     ],
23260     "in_project_namespace": true,
23261     "kind": "definition",
23262     "module": "PaperIRelease.GrammarModules",
23263     "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom",
23264     "runtime_only": false
23265   },
23266   {
23267     "axioms": [],
23268     "in_project_namespace": true,
23269     "kind": "theorem",
23270     "module": "KomorebiVerification.ProjectorCore",
23271     "name": "Komorebi.instDecidableEqFormalizationStatus._proof_1",
23272     "runtime_only": false
23273   },
23274   {
23275     "axioms": [
23276       "propext",
23277       "Classical.choice",
23278       "Quot.sound"
23279     ],
23280     "in_project_namespace": true,
23281     "kind": "theorem",
23282     "module": "PaperIRelease.PacketUniversal",
23283     "name": "Komorebi.PaperIRelease.PacketUniversal.block_intertwining_iff",
23284     "runtime_only": false
23285   },
23286   {
23287     "axioms": [
23288       "propext",
23289       "Classical.choice",
23290       "Quot.sound"
23291     ],
23292     "in_project_namespace": true,
23293     "kind": "definition",
23294     "module": "PaperIRelease.PacketLocalRank",
23295     "name": "Komorebi.PaperIRelease.localPacketFamily",
23296     "runtime_only": false
23297   },
23298   {
23299     "axioms": [
23300       "propext",
23301       "Classical.choice",
23302       "Quot.sound"
23303     ],
23304     "in_project_namespace": true,
23305     "kind": "theorem",
23306     "module": "KomorebiVerification.PacketNaturalityCompletion",
23307     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum_zero_ne",
23308     "runtime_only": false
23309   },
23310   {
23311     "axioms": [
23312       "propext",
23313       "Classical.choice",
23314       "Quot.sound"
23315     ],
23316     "in_project_namespace": true,
23317     "kind": "definition",
23318     "module": "PaperIRelease.AlgebraTransfer",
23319     "name": "Komorebi.PaperIRelease.packetWordSum",
23320     "runtime_only": false
23321   },
23322   {
23323     "axioms": [
23324       "propext",
23325       "Classical.choice",
23326       "Quot.sound"
23327     ],
23328     "in_project_namespace": true,
23329     "kind": "theorem",
23330     "module": "PaperIRelease.PacketExactSequence",
23331     "name": "Komorebi.Foundation.LinearProjectorFamily.packet_sequence_exact",
23332     "runtime_only": false
23333   },
23334   {
23335     "axioms": [
23336       "propext",
23337       "Classical.choice",
23338       "Quot.sound"
23339     ],
23340     "in_project_namespace": true,
23341     "kind": "theorem",
23342     "module": "PaperIRelease.PacketCorners",
23343     "name": "Komorebi.PaperIRelease.cornerCompression._proof_5",
23344     "runtime_only": false
23345   },
23346   {
23347     "axioms": [
23348       "propext",
23349       "Quot.sound"
23350     ],
23351     "in_project_namespace": true,
23352     "kind": "definition",
23353     "module": "KomorebiVerification.PathGraphKrylov",
23354     "name": "Komorebi.PathGraphKrylov.pathStep",
23355     "runtime_only": false
23356   },
23357   {
23358     "axioms": [
23359       "propext",
23360       "Quot.sound"
23361     ],
23362     "in_project_namespace": true,
23363     "kind": "theorem",
23364     "module": "KomorebiVerification.EllipticAlgorithms",
23365     "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity._proof_1",
23366     "runtime_only": false
23367   },
23368   {
23369     "axioms": [
23370       "propext",
23371       "Classical.choice",
23372       "Quot.sound"
23373     ],
23374     "in_project_namespace": true,
23375     "kind": "theorem",
23376     "module": "KomorebiVerification.PacketNaturalityCompletion",
23377     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.sizeOf_spec",
23378     "runtime_only": false
23379   },
23380   {
23381     "axioms": [
23382       "propext",
23383       "Classical.choice",
23384       "Quot.sound"
23385     ],
23386     "in_project_namespace": true,
23387     "kind": "definition",
23388     "module": "PaperIRelease.GrammarAlgebra",
23389     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization._sizeOf_inst",
23390     "runtime_only": false
23391   },
23392   {
23393     "axioms": [],
23394     "in_project_namespace": true,
23395     "kind": "definition",
23396     "module": "KomorebiVerification.ProjectorCore",
23397     "name": "Komorebi.ClaimRecord.heading",
23398     "runtime_only": false
23399   },
23400   {
23401     "axioms": [
23402       "propext",
23403       "Classical.choice",
23404       "Quot.sound"
23405     ],
23406     "in_project_namespace": true,
23407     "kind": "theorem",
23408     "module": "PaperIRelease.CategoryPackets",
23409     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.injEq",
23410     "runtime_only": false
23411   },
23412   {
23413     "axioms": [
23414       "propext",
23415       "Classical.choice",
23416       "Quot.sound"
23417     ],
23418     "in_project_namespace": true,
23419     "kind": "definition",
23420     "module": "KomorebiVerification.TopologicalCompletion",
23421     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.HasTopologicalSeedRankOne",
23422     "runtime_only": false
23423   },
23424   {
23425     "axioms": [
23426       "propext",
23427       "Quot.sound"
23428     ],
23429     "in_project_namespace": true,
23430     "kind": "theorem",
23431     "module": "PaperIRelease.AlgebraTransfer",
23432     "name": "Komorebi.PaperIRelease.operatorWord.eq_def",
23433     "runtime_only": false
23434   },
23435   {
23436     "axioms": [
23437       "propext",
23438       "Classical.choice",
23439       "Quot.sound"
23440     ],
23441     "in_project_namespace": true,
23442     "kind": "theorem",
23443     "module": "KomorebiVerification.SingleOperatorGraph",
23444     "name": "Komorebi.SingleOperatorGraph.singleOperator_seedNumber_isLeast_of_primary_decomposition",
23445     "runtime_only": false
23446   },
23447   {
23448     "axioms": [
23449       "propext",
23450       "Quot.sound"
23451     ],
23452     "in_project_namespace": true,
23453     "kind": "definition",
23454     "module": "PaperIRelease.ScalarExtension",
23455     "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease_2",
23456     "runtime_only": false
23457   },
23458   {
23459     "axioms": [
23460       "propext",
23461       "Classical.choice",
23462       "Quot.sound"
23463     ],
23464     "in_project_namespace": true,
23465     "kind": "definition",
23466     "module": "KomorebiVerification.SingleOperatorGraph",
23467     "name": "Komorebi.SingleOperatorGraph.cycleSeeds",
23468     "runtime_only": false
23469   },
23470   {
23471     "axioms": [
23472       "propext",
23473       "Classical.choice",
23474       "Quot.sound"
23475     ],
23476     "in_project_namespace": true,
23477     "kind": "definition",
23478     "module": "PaperIRelease.PacketTopology",
23479     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM",
23480     "runtime_only": false
23481   },
23482   {
23483     "axioms": [
23484       "propext",
23485       "Classical.choice",
23486       "Quot.sound"
23487     ],
23488     "in_project_namespace": true,
23489     "kind": "theorem",
23490     "module": "PaperIRelease.PacketCorners",
23491     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_9",
23492     "runtime_only": false
23493   },
23494   {
23495     "axioms": [
23496       "propext",
23497       "Quot.sound"
23498     ],
23499     "in_project_namespace": true,
23500     "kind": "definition",
23501     "module": "PaperIRelease.GrammarAlgebra",
23502     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.noConfusionType",
23503     "runtime_only": false
23504   },
23505   {
23506     "axioms": [
23507       "propext",
23508       "Classical.choice",
23509       "Quot.sound"
23510     ],
23511     "in_project_namespace": true,
23512     "kind": "definition",
23513     "module": "PaperIRelease.PacketAggregation",
23514     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv",
23515     "runtime_only": false
23516   },
23517   {
23518     "axioms": [
23519       "propext",
23520       "Classical.choice",
23521       "Quot.sound"
23522     ],
23523     "in_project_namespace": true,
23524     "kind": "theorem",
23525     "module": "PaperICompletion4.ResidueQuotient",
23526     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv_mk",
23527     "runtime_only": false
23528   },
23529   {
23530     "axioms": [
23531       "propext",
23532       "Classical.choice",
23533       "Quot.sound"
23534     ],
23535     "in_project_namespace": true,
23536     "kind": "theorem",
23537     "module": "PaperICompletion8.ProductPresentation",
23538     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_6",
23539     "runtime_only": false
23540   },
23541   {
23542     "axioms": [],
23543     "in_project_namespace": true,
23544     "kind": "definition",
23545     "module": "PaperIRelease.CategoryExport",
23546     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.noConfusion",
23547     "runtime_only": false
23548   },
23549   {
23550     "axioms": [
23551       "propext",
23552       "Classical.choice",
23553       "Quot.sound"
23554     ],
23555     "in_project_namespace": true,
23556     "kind": "theorem",
23557     "module": "PaperIRelease.CategoryPackets",
23558     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ext",
23559     "runtime_only": false
23560   },
23561   {
23562     "axioms": [
23563       "propext",
23564       "Classical.choice",
23565       "Quot.sound"
23566     ],
23567     "in_project_namespace": true,
23568     "kind": "theorem",
23569     "module": "KomorebiVerification.PaperITransport",
23570     "name": "Komorebi.Foundation.transferBlock.eq_1",
23571     "runtime_only": false
23572   },
23573   {
23574     "axioms": [
23575       "propext",
23576       "Classical.choice",
23577       "Quot.sound"
23578     ],
23579     "in_project_namespace": false,
23580     "kind": "definition",
23581     "module": "PaperIRelease.TopologyUnconditional",
23582     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets._sizeOf_1",
23583     "runtime_only": false
23584   },
23585   {
23586     "axioms": [
23587       "propext",
23588       "Classical.choice",
23589       "Quot.sound"
23590     ],
23591     "in_project_namespace": true,
23592     "kind": "theorem",
23593     "module": "PaperIRelease.PacketDescent",
23594     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_3",
23595     "runtime_only": false
23596   },
23597   {
23598     "axioms": [],
23599     "in_project_namespace": true,
23600     "kind": "definition",
23601     "module": "PaperIRelease.CategoryExport",
23602     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.elim",
23603     "runtime_only": false
23604   },
23605   {
23606     "axioms": [],
23607     "in_project_namespace": true,
23608     "kind": "definition",
23609     "module": "KomorebiVerification.ProjectorCore",
23610     "name": "Komorebi.ClaimRecord.statement",
23611     "runtime_only": false
23612   },
23613   {
23614     "axioms": [],
23615     "in_project_namespace": true,
23616     "kind": "theorem",
23617     "module": "PaperIRelease.CategoryExport",
23618     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.sizeOf_spec",
23619     "runtime_only": false
23620   },
23621   {
23622     "axioms": [
23623       "propext",
23624       "Classical.choice",
23625       "Quot.sound"
23626     ],
23627     "in_project_namespace": true,
23628     "kind": "theorem",
23629     "module": "PaperIRelease.PacketDescent",
23630     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_3",
23631     "runtime_only": false
23632   },
23633   {
23634     "axioms": [
23635       "propext",
23636       "Classical.choice",
23637       "Quot.sound"
23638     ],
23639     "in_project_namespace": false,
23640     "kind": "definition",
23641     "module": "PaperIRelease.TopologyDenseCompletion",
23642     "name": "PaperIRelease.TopologyDenseCompletion.transportedUniformity",
23643     "runtime_only": false
23644   },
23645   {
23646     "axioms": [
23647       "propext",
23648       "Classical.choice",
23649       "Quot.sound"
23650     ],
23651     "in_project_namespace": true,
23652     "kind": "definition",
23653     "module": "KomorebiVerification.PacketNaturalityCompletion",
23654     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOps",
23655     "runtime_only": false
23656   },
23657   {
23658     "axioms": [
23659       "propext",
23660       "Quot.sound"
23661     ],
23662     "in_project_namespace": true,
23663     "kind": "definition",
23664     "module": "PaperIRelease.ScalarExtension",
23665     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule",
23666     "runtime_only": false
23667   },
23668   {
23669     "axioms": [
23670       "propext",
23671       "Quot.sound"
23672     ],
23673     "in_project_namespace": true,
23674     "kind": "theorem",
23675     "module": "KomorebiVerification.PathGraphKrylov",
23676     "name": "Komorebi.PathGraphKrylov.krylov_succ",
23677     "runtime_only": false
23678   },
23679   {
23680     "axioms": [
23681       "propext"
23682     ],
23683     "in_project_namespace": true,
23684     "kind": "theorem",
23685     "module": "PaperIRelease.CategoryExport",
23686     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.injEq",
23687     "runtime_only": false
23688   },
23689   {
23690     "axioms": [
23691       "propext",
23692       "Classical.choice",
23693       "Quot.sound"
23694     ],
23695     "in_project_namespace": true,
23696     "kind": "theorem",
23697     "module": "PaperICompletion4.IntrinsicPrimary",
23698     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary",
23699     "runtime_only": false
23700   },
23701   {
23702     "axioms": [
23703       "propext",
23704       "Classical.choice",
23705       "Quot.sound"
23706     ],
23707     "in_project_namespace": true,
23708     "kind": "theorem",
23709     "module": "PaperIRelease.AlgebraClassGrouping",
23710     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_7",
23711     "runtime_only": false
23712   },
23713   {
23714     "axioms": [
23715       "propext",
23716       "Classical.choice",
23717       "Quot.sound"
23718     ],
23719     "in_project_namespace": true,
23720     "kind": "theorem",
23721     "module": "KomorebiVerification.PacketNaturalityCompletion",
23722     "name": "Komorebi.PacketNaturalityCompletion.Packets.eq_iff_projectors_eq",
23723     "runtime_only": false
23724   },
23725   {
23726     "axioms": [
23727       "propext",
23728       "Classical.choice",
23729       "Quot.sound"
23730     ],
23731     "in_project_namespace": true,
23732     "kind": "theorem",
23733     "module": "PaperIRelease.CategoryPackets",
23734     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_2",
23735     "runtime_only": false
23736   },
23737   {
23738     "axioms": [
23739       "propext",
23740       "Classical.choice",
23741       "Quot.sound"
23742     ],
23743     "in_project_namespace": true,
23744     "kind": "definition",
23745     "module": "PaperIRelease.AlgebraTransfer",
23746     "name": "Komorebi.PaperIRelease.packetWordSum._f",
23747     "runtime_only": false
23748   },
23749   {
23750     "axioms": [
23751       "propext",
23752       "Classical.choice",
23753       "Quot.sound"
23754     ],
23755     "in_project_namespace": true,
23756     "kind": "definition",
23757     "module": "PaperIRelease.GrammarEquivalence",
23758     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.casesOn",
23759     "runtime_only": false
23760   },
23761   {
23762     "axioms": [
23763       "propext",
23764       "Classical.choice",
23765       "Quot.sound"
23766     ],
23767     "in_project_namespace": true,
23768     "kind": "theorem",
23769     "module": "PaperICompletion4.ResidueQuotient",
23770     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_8",
23771     "runtime_only": false
23772   },
23773   {
23774     "axioms": [
23775       "propext",
23776       "Classical.choice",
23777       "Quot.sound"
23778     ],
23779     "in_project_namespace": true,
23780     "kind": "definition",
23781     "module": "PaperICompletion.SpectralCertificates",
23782     "name": "Komorebi.PaperICompletion.SpectralCertificates.maxEigenMultiplicity",
23783     "runtime_only": false
23784   },
23785   {
23786     "axioms": [
23787       "propext",
23788       "Classical.choice",
23789       "Quot.sound"
23790     ],
23791     "in_project_namespace": true,
23792     "kind": "definition",
23793     "module": "PaperIRelease.CategoryPackets",
23794     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.noConfusionType",
23795     "runtime_only": false
23796   },
23797   {
23798     "axioms": [
23799       "propext",
23800       "Classical.choice",
23801       "Quot.sound"
23802     ],
23803     "in_project_namespace": true,
23804     "kind": "definition",
23805     "module": "PaperIRelease.CategoryPackets",
23806     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism._sizeOf_inst",
23807     "runtime_only": false
23808   },
23809   {
23810     "axioms": [
23811       "propext",
23812       "Classical.choice",
23813       "Quot.sound"
23814     ],
23815     "in_project_namespace": true,
23816     "kind": "theorem",
23817     "module": "PaperIRelease.PacketAggregation",
23818     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_3",
23819     "runtime_only": false
23820   },
23821   {
23822     "axioms": [
23823       "propext",
23824       "Classical.choice",
23825       "Quot.sound"
23826     ],
23827     "in_project_namespace": true,
23828     "kind": "definition",
23829     "module": "PaperICompletion4.OperatorIntrinsicFormula",
23830     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicSeedMaximum",
23831     "runtime_only": false
23832   },
23833   {
23834     "axioms": [
23835       "propext",
23836       "Classical.choice",
23837       "Quot.sound"
23838     ],
23839     "in_project_namespace": false,
23840     "kind": "definition",
23841     "module": "ReleaseBoundary",
23842     "name": "PaperIBlock08Tests.MixedD",
23843     "runtime_only": false
23844   },
23845   {
23846     "axioms": [
23847       "propext",
23848       "Classical.choice",
23849       "Quot.sound"
23850     ],
23851     "in_project_namespace": false,
23852     "kind": "theorem",
23853     "module": "PaperIRelease.TopologyCountablePackets",
23854     "name": "PaperIRelease.TopologyCountablePackets.Projectors.eq_zero_of_unconditionalNorm_eq_zero",
23855     "runtime_only": false
23856   },
23857   {
23858     "axioms": [
23859       "propext",
23860       "Classical.choice",
23861       "Quot.sound"
23862     ],
23863     "in_project_namespace": true,
23864     "kind": "theorem",
23865     "module": "KomorebiVerification.TopologicalCompletion",
23866     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_3",
23867     "runtime_only": false
23868   },
23869   {
23870     "axioms": [
23871       "propext",
23872       "Classical.choice",
23873       "Quot.sound"
23874     ],
23875     "in_project_namespace": true,
23876     "kind": "theorem",
23877     "module": "PaperICompletion3.OperatorPrimaryAPI",
23878     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount_eq_zero_iff",
23879     "runtime_only": false
23880   },
23881   {
23882     "axioms": [
23883       "propext",
23884       "Classical.choice",
23885       "Quot.sound"
23886     ],
23887     "in_project_namespace": true,
23888     "kind": "definition",
23889     "module": "PaperIRelease.TensorPackets",
23890     "name": "Komorebi.PaperIRelease.tensorPacketCoordinates",
23891     "runtime_only": false
23892   },
23893   {
23894     "axioms": [
23895       "propext",
23896       "Classical.choice",
23897       "Quot.sound"
23898     ],
23899     "in_project_namespace": true,
23900     "kind": "constructor",
23901     "module": "PaperIRelease.TopologyCategories",
23902     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk",
23903     "runtime_only": false
23904   },
23905   {
23906     "axioms": [],
23907     "in_project_namespace": true,
23908     "kind": "definition",
23909     "module": "PaperIRelease.CategoryExport",
23910     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.noConfusion",
23911     "runtime_only": false
23912   },
23913   {
23914     "axioms": [
23915       "propext",
23916       "Classical.choice",
23917       "Quot.sound"
23918     ],
23919     "in_project_namespace": true,
23920     "kind": "theorem",
23921     "module": "PaperIRelease.CategoryPackets",
23922     "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_2",
23923     "runtime_only": false
23924   },
23925   {
23926     "axioms": [
23927       "propext",
23928       "Classical.choice",
23929       "Quot.sound"
23930     ],
23931     "in_project_namespace": true,
23932     "kind": "definition",
23933     "module": "PaperIRelease.AlgebraPreorder",
23934     "name": "Komorebi.PaperIRelease.strictSupportPower",
23935     "runtime_only": false
23936   },
23937   {
23938     "axioms": [
23939       "propext",
23940       "Classical.choice",
23941       "Quot.sound"
23942     ],
23943     "in_project_namespace": true,
23944     "kind": "theorem",
23945     "module": "KomorebiVerification.ProjectorCore",
23946     "name": "Komorebi.Packet.coordinateProj_reconstruction",
23947     "runtime_only": false
23948   },
23949   {
23950     "axioms": [
23951       "propext",
23952       "Classical.choice",
23953       "Quot.sound"
23954     ],
23955     "in_project_namespace": true,
23956     "kind": "theorem",
23957     "module": "PaperIRelease.AlgebraQuotient",
23958     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_8",
23959     "runtime_only": false
23960   },
23961   {
23962     "axioms": [
23963       "propext",
23964       "Classical.choice",
23965       "Quot.sound"
23966     ],
23967     "in_project_namespace": true,
23968     "kind": "theorem",
23969     "module": "PaperICompletion.CyclicClassification",
23970     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap_ker_eq_annihilator_of_surjective",
23971     "runtime_only": false
23972   },
23973   {
23974     "axioms": [
23975       "propext",
23976       "Classical.choice",
23977       "Quot.sound"
23978     ],
23979     "in_project_namespace": true,
23980     "kind": "theorem",
23981     "module": "KomorebiVerification.SingleOperatorGraph",
23982     "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate",
23983     "runtime_only": false
23984   },
23985   {
23986     "axioms": [
23987       "propext",
23988       "Classical.choice",
23989       "Quot.sound"
23990     ],
23991     "in_project_namespace": true,
23992     "kind": "theorem",
23993     "module": "PaperIRelease.BoundedStar",
23994     "name": "Komorebi.PaperIRelease.BoundedSupport.universal_pattern_boundary",
23995     "runtime_only": false
23996   },
23997   {
23998     "axioms": [
23999       "propext",
24000       "Classical.choice",
24001       "Quot.sound"
24002     ],
24003     "in_project_namespace": true,
24004     "kind": "theorem",
24005     "module": "PaperIRelease.TopologyCategories",
24006     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.identity._proof_1",
24007     "runtime_only": false
24008   },
24009   {
24010     "axioms": [],
24011     "in_project_namespace": true,
24012     "kind": "constructor",
24013     "module": "KomorebiVerification.ProjectorCore",
24014     "name": "Komorebi.FormalizationStatus.boundaryOnly",
24015     "runtime_only": false
24016   },
24017   {
24018     "axioms": [
24019       "propext",
24020       "Classical.choice",
24021       "Quot.sound"
24022     ],
24023     "in_project_namespace": false,
24024     "kind": "theorem",
24025     "module": "PaperIRelease.TopologyDenseCompletion",
24026     "name": "PaperIRelease.TopologyDenseCompletion.transported_locallyConvex",
24027     "runtime_only": false
24028   },
24029   {
24030     "axioms": [
24031       "propext",
24032       "Classical.choice",
24033       "Quot.sound"
24034     ],
24035     "in_project_namespace": true,
24036     "kind": "theorem",
24037     "module": "PaperICompletion7.Nakayama",
24038     "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_module_jacobson",
24039     "runtime_only": false
24040   },
24041   {
24042     "axioms": [
24043       "propext",
24044       "Classical.choice",
24045       "Quot.sound"
24046     ],
24047     "in_project_namespace": false,
24048     "kind": "definition",
24049     "module": "PaperIRelease.TopologyUnconditional",
24050     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_14",
24051     "runtime_only": false
24052   },
24053   {
24054     "axioms": [
24055       "propext",
24056       "Quot.sound"
24057     ],
24058     "in_project_namespace": true,
24059     "kind": "theorem",
24060     "module": "KomorebiVerification.PathGraphKrylov",
24061     "name": "Komorebi.PathGraphKrylov.pathStep_apply",
24062     "runtime_only": false
24063   },
24064   {
24065     "axioms": [
24066       "propext",
24067       "Classical.choice",
24068       "Quot.sound"
24069     ],
24070     "in_project_namespace": true,
24071     "kind": "theorem",
24072     "module": "KomorebiVerification.SingleOperatorGraph",
24073     "name": "Komorebi.SingleOperatorGraph.hasCyclicVector_iff_seedNumber_eq_one",
24074     "runtime_only": false
24075   },
24076   {
24077     "axioms": [
24078       "propext",
24079       "Classical.choice",
24080       "Quot.sound"
24081     ],
24082     "in_project_namespace": false,
24083     "kind": "definition",
24084     "module": "PaperIRelease.TopologyDenseCompletion",
24085     "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding",
24086     "runtime_only": false
24087   },
24088   {
24089     "axioms": [
24090       "propext",
24091       "Classical.choice",
24092       "Quot.sound"
24093     ],
24094     "in_project_namespace": true,
24095     "kind": "theorem",
24096     "module": "KomorebiVerification.PacketNaturalityCompletion",
24097     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply_preserves_reachable_support",
24098     "runtime_only": false
24099   },
24100   {
24101     "axioms": [
24102       "propext",
24103       "Quot.sound"
24104     ],
24105     "in_project_namespace": true,
24106     "kind": "definition",
24107     "module": "PaperIRelease.GrammarAlgebra",
24108     "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrowWord",
24109     "runtime_only": false
24110   },
24111   {
24112     "axioms": [
24113       "propext",
24114       "Classical.choice",
24115       "Quot.sound"
24116     ],
24117     "in_project_namespace": true,
24118     "kind": "definition",
24119     "module": "PaperIRelease.TopologyCategories",
24120     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.noConfusionType",
24121     "runtime_only": false
24122   },
24123   {
24124     "axioms": [
24125       "propext",
24126       "Classical.choice",
24127       "Quot.sound"
24128     ],
24129     "in_project_namespace": true,
24130     "kind": "theorem",
24131     "module": "PaperIRelease.AlgebraClassGrouping",
24132     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_10",
24133     "runtime_only": false
24134   },
24135   {
24136     "axioms": [],
24137     "in_project_namespace": true,
24138     "kind": "definition",
24139     "module": "KomorebiVerification.ProjectorCore",
24140     "name": "Komorebi.Packet.coordinateProj",
24141     "runtime_only": false
24142   },
24143   {
24144     "axioms": [
24145       "propext",
24146       "Classical.choice",
24147       "Quot.sound"
24148     ],
24149     "in_project_namespace": true,
24150     "kind": "theorem",
24151     "module": "PaperIRelease.PacketPureBoundaryTests",
24152     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_3",
24153     "runtime_only": false
24154   },
24155   {
24156     "axioms": [
24157       "propext",
24158       "Quot.sound"
24159     ],
24160     "in_project_namespace": true,
24161     "kind": "theorem",
24162     "module": "KomorebiVerification.PathGraphKrylov",
24163     "name": "Komorebi.PathGraphKrylov.IsCyclic.eq_1",
24164     "runtime_only": false
24165   },
24166   {
24167     "axioms": [
24168       "propext",
24169       "Classical.choice",
24170       "Quot.sound"
24171     ],
24172     "in_project_namespace": true,
24173     "kind": "theorem",
24174     "module": "KomorebiVerification.EllipticAlgorithms",
24175     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_2",
24176     "runtime_only": false
24177   },
24178   {
24179     "axioms": [
24180       "propext",
24181       "Classical.choice",
24182       "Quot.sound"
24183     ],
24184     "in_project_namespace": true,
24185     "kind": "theorem",
24186     "module": "PaperIRelease.PacketEquivalentNorm",
24187     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_2",
24188     "runtime_only": false
24189   },
24190   {
24191     "axioms": [],
24192     "in_project_namespace": true,
24193     "kind": "theorem",
24194     "module": "KomorebiVerification.ProjectorCore",
24195     "name": "Komorebi.FiniteDifference.iteratedDiff.eq_def",
24196     "runtime_only": false
24197   },
24198   {
24199     "axioms": [
24200       "propext",
24201       "Quot.sound"
24202     ],
24203     "in_project_namespace": true,
24204     "kind": "theorem",
24205     "module": "PaperIRelease.GrammarModules",
24206     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_1",
24207     "runtime_only": false
24208   },
24209   {
24210     "axioms": [
24211       "propext",
24212       "Quot.sound"
24213     ],
24214     "in_project_namespace": true,
24215     "kind": "theorem",
24216     "module": "PaperIRelease.ScalarExtension",
24217     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_6",
24218     "runtime_only": false
24219   },
24220   {
24221     "axioms": [
24222       "propext",
24223       "Classical.choice",
24224       "Quot.sound"
24225     ],
24226     "in_project_namespace": true,
24227     "kind": "theorem",
24228     "module": "PaperICompletion4.GroupedPrimary",
24229     "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv._proof_2",
24230     "runtime_only": false
24231   },
24232   {
24233     "axioms": [],
24234     "in_project_namespace": false,
24235     "kind": "definition",
24236     "module": "KomorebiVerification.ProjectorCore",
24237     "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.splitter",
24238     "runtime_only": false
24239   },
24240   {
24241     "axioms": [
24242       "propext",
24243       "Classical.choice",
24244       "Quot.sound"
24245     ],
24246     "in_project_namespace": false,
24247     "kind": "theorem",
24248     "module": "PaperIRelease.TopologyUnconditional",
24249     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_zero_val",
24250     "runtime_only": false
24251   },
24252   {
24253     "axioms": [
24254       "propext",
24255       "Classical.choice",
24256       "Quot.sound"
24257     ],
24258     "in_project_namespace": false,
24259     "kind": "theorem",
24260     "module": "PaperIRelease.TopologyUnconditionalBridge",
24261     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_9",
24262     "runtime_only": false
24263   },
24264   {
24265     "axioms": [
24266       "propext",
24267       "Classical.choice",
24268       "Quot.sound"
24269     ],
24270     "in_project_namespace": true,
24271     "kind": "theorem",
24272     "module": "PaperIRelease.GraphPropagation",
24273     "name": "Komorebi.PaperIRelease.edge_range_le",
24274     "runtime_only": false
24275   },
24276   {
24277     "axioms": [
24278       "propext",
24279       "Classical.choice",
24280       "Quot.sound"
24281     ],
24282     "in_project_namespace": true,
24283     "kind": "definition",
24284     "module": "PaperIRelease.TopologyCategories",
24285     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.toPacketObject",
24286     "runtime_only": false
24287   },
24288   {
24289     "axioms": [
24290       "propext",
24291       "Quot.sound"
24292     ],
24293     "in_project_namespace": true,
24294     "kind": "theorem",
24295     "module": "PaperIRelease.GrammarModules",
24296     "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_3",
24297     "runtime_only": false
24298   },
24299   {
24300     "axioms": [
24301       "propext",
24302       "Classical.choice",
24303       "Quot.sound"
24304     ],
24305     "in_project_namespace": true,
24306     "kind": "theorem",
24307     "module": "PaperICompletion4.ResidueQuotient",
24308     "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff",
24309     "runtime_only": false
24310   },
24311   {
24312     "axioms": [
24313       "propext",
24314       "Classical.choice",
24315       "Quot.sound"
24316     ],
24317     "in_project_namespace": true,
24318     "kind": "theorem",
24319     "module": "PaperICompletion8.DivisionBlock",
24320     "name": "Komorebi.PaperICompletion8.DivisionBlock.oneBlock_seedRank_eq_ceilDiv",
24321     "runtime_only": false
24322   },
24323   {
24324     "axioms": [
24325       "propext",
24326       "Classical.choice",
24327       "Quot.sound"
24328     ],
24329     "in_project_namespace": true,
24330     "kind": "theorem",
24331     "module": "PaperICompletion3.PrimarySeedFormula",
24332     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.seedNumber_isLeast_linearEquiv",
24333     "runtime_only": false
24334   },
24335   {
24336     "axioms": [
24337       "propext",
24338       "Classical.choice",
24339       "Quot.sound"
24340     ],
24341     "in_project_namespace": true,
24342     "kind": "theorem",
24343     "module": "PaperICompletion5.GeometricSeedFormula",
24344     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues_bddAbove",
24345     "runtime_only": false
24346   },
24347   {
24348     "axioms": [
24349       "propext",
24350       "Classical.choice",
24351       "Quot.sound"
24352     ],
24353     "in_project_namespace": false,
24354     "kind": "theorem",
24355     "module": "PaperIRelease.TopologyCountablePackets",
24356     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_7",
24357     "runtime_only": false
24358   },
24359   {
24360     "axioms": [],
24361     "in_project_namespace": true,
24362     "kind": "recursor",
24363     "module": "PaperIRelease.GrammarPaths",
24364     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.rec",
24365     "runtime_only": false
24366   },
24367   {
24368     "axioms": [
24369       "propext",
24370       "Classical.choice",
24371       "Quot.sound"
24372     ],
24373     "in_project_namespace": false,
24374     "kind": "definition",
24375     "module": "PaperIRelease.TopologyTransport",
24376     "name": "PaperIRelease.TopologyTransport.quotientEquiv",
24377     "runtime_only": false
24378   },
24379   {
24380     "axioms": [
24381       "propext",
24382       "Classical.choice",
24383       "Quot.sound"
24384     ],
24385     "in_project_namespace": true,
24386     "kind": "theorem",
24387     "module": "PaperIRelease.CategoryPackets",
24388     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ext_iff",
24389     "runtime_only": false
24390   },
24391   {
24392     "axioms": [
24393       "propext",
24394       "Classical.choice",
24395       "Quot.sound"
24396     ],
24397     "in_project_namespace": true,
24398     "kind": "theorem",
24399     "module": "PaperIRelease.CategoryPackets",
24400     "name": "Komorebi.PaperIRelease.CategoryPackets.sum_conditions_comm",
24401     "runtime_only": false
24402   },
24403   {
24404     "axioms": [
24405       "propext",
24406       "Quot.sound"
24407     ],
24408     "in_project_namespace": true,
24409     "kind": "theorem",
24410     "module": "KomorebiVerification.FibreRefinement",
24411     "name": "Komorebi.Packet.fibreLinearProjectorFamily._proof_2",
24412     "runtime_only": false
24413   },
24414   {
24415     "axioms": [
24416       "propext",
24417       "Classical.choice",
24418       "Quot.sound"
24419     ],
24420     "in_project_namespace": true,
24421     "kind": "definition",
24422     "module": "PaperICompletion.SpectralCertificates",
24423     "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedIndexEquiv",
24424     "runtime_only": false
24425   },
24426   {
24427     "axioms": [],
24428     "in_project_namespace": true,
24429     "kind": "definition",
24430     "module": "KomorebiVerification.ProjectorCore",
24431     "name": "Komorebi.FormalizationStatus.kernelChecked.elim",
24432     "runtime_only": false
24433   },
24434   {
24435     "axioms": [
24436       "propext",
24437       "Classical.choice",
24438       "Quot.sound"
24439     ],
24440     "in_project_namespace": true,
24441     "kind": "definition",
24442     "module": "KomorebiVerification.SingleOperatorGraph",
24443     "name": "Komorebi.SingleOperatorGraph.HasCyclicVector",
24444     "runtime_only": false
24445   },
24446   {
24447     "axioms": [
24448       "propext",
24449       "Classical.choice",
24450       "Quot.sound"
24451     ],
24452     "in_project_namespace": false,
24453     "kind": "theorem",
24454     "module": "ReleaseBoundary",
24455     "name": "PaperIBlock08Tests.abstract_quaternion_presentation",
24456     "runtime_only": false
24457   },
24458   {
24459     "axioms": [
24460       "propext",
24461       "Quot.sound"
24462     ],
24463     "in_project_namespace": true,
24464     "kind": "theorem",
24465     "module": "PaperIRelease.GrammarTyped",
24466     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.splitData._proof_1",
24467     "runtime_only": false
24468   },
24469   {
24470     "axioms": [
24471       "propext",
24472       "Classical.choice",
24473       "Quot.sound"
24474     ],
24475     "in_project_namespace": true,
24476     "kind": "theorem",
24477     "module": "KomorebiVerification.PacketNaturalityCompletion",
24478     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_2",
24479     "runtime_only": false
24480   },
24481   {
24482     "axioms": [
24483       "propext",
24484       "Classical.choice",
24485       "Quot.sound"
24486     ],
24487     "in_project_namespace": false,
24488     "kind": "theorem",
24489     "module": "PaperIRelease.TopologyUnconditional",
24490     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_8",
24491     "runtime_only": false
24492   },
24493   {
24494     "axioms": [
24495       "propext",
24496       "Classical.choice",
24497       "Quot.sound"
24498     ],
24499     "in_project_namespace": true,
24500     "kind": "theorem",
24501     "module": "PaperIRelease.PacketDescent",
24502     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap_ker",
24503     "runtime_only": false
24504   },
24505   {
24506     "axioms": [
24507       "propext",
24508       "Quot.sound"
24509     ],
24510     "in_project_namespace": true,
24511     "kind": "theorem",
24512     "module": "PaperIRelease.AlgebraClassGrouping",
24513     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_1",
24514     "runtime_only": false
24515   },
24516   {
24517     "axioms": [
24518       "propext",
24519       "Classical.choice",
24520       "Quot.sound"
24521     ],
24522     "in_project_namespace": true,
24523     "kind": "definition",
24524     "module": "PaperIRelease.CategoryPackets",
24525     "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory",
24526     "runtime_only": false
24527   },
24528   {
24529     "axioms": [
24530       "propext",
24531       "Quot.sound"
24532     ],
24533     "in_project_namespace": true,
24534     "kind": "theorem",
24535     "module": "KomorebiVerification.SingleOperatorGraph",
24536     "name": "Komorebi.SingleOperatorGraph.evalVector._proof_4",
24537     "runtime_only": false
24538   },
24539   {
24540     "axioms": [
24541       "propext",
24542       "Classical.choice",
24543       "Quot.sound"
24544     ],
24545     "in_project_namespace": true,
24546     "kind": "theorem",
24547     "module": "KomorebiVerification.PathGraphKrylov",
24548     "name": "Komorebi.PathGraphKrylov.pathAdjacency_mulVec",
24549     "runtime_only": false
24550   },
24551   {
24552     "axioms": [
24553       "propext",
24554       "Classical.choice",
24555       "Quot.sound"
24556     ],
24557     "in_project_namespace": true,
24558     "kind": "theorem",
24559     "module": "KomorebiVerification.EllipticAlgorithms",
24560     "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_2",
24561     "runtime_only": false
24562   },
24563   {
24564     "axioms": [
24565       "propext",
24566       "Classical.choice",
24567       "Quot.sound"
24568     ],
24569     "in_project_namespace": true,
24570     "kind": "definition",
24571     "module": "KomorebiVerification.TopologicalCompletion",
24572     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.casesOn",
24573     "runtime_only": false
24574   },
24575   {
24576     "axioms": [
24577       "propext",
24578       "Classical.choice",
24579       "Quot.sound"
24580     ],
24581     "in_project_namespace": false,
24582     "kind": "theorem",
24583     "module": "PaperIRelease.TopologyUnconditional",
24584     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues_bddAbove",
24585     "runtime_only": false
24586   },
24587   {
24588     "axioms": [
24589       "propext",
24590       "Classical.choice",
24591       "Quot.sound"
24592     ],
24593     "in_project_namespace": true,
24594     "kind": "theorem",
24595     "module": "PaperICompletion3.PrimarySeedFormula",
24596     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap_surjective",
24597     "runtime_only": false
24598   },
24599   {
24600     "axioms": [],
24601     "in_project_namespace": true,
24602     "kind": "definition",
24603     "module": "PaperIRelease.CategoryExport",
24604     "name": "Komorebi.PaperIRelease.CategoryExport.Expression._sizeOf_1",
24605     "runtime_only": false
24606   },
24607   {
24608     "axioms": [
24609       "propext",
24610       "Classical.choice",
24611       "Quot.sound"
24612     ],
24613     "in_project_namespace": true,
24614     "kind": "theorem",
24615     "module": "PaperICompletion.ConditionedCoordinates",
24616     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber.eq_1",
24617     "runtime_only": false
24618   },
24619   {
24620     "axioms": [
24621       "propext",
24622       "Classical.choice",
24623       "Quot.sound"
24624     ],
24625     "in_project_namespace": true,
24626     "kind": "theorem",
24627     "module": "KomorebiVerification.PacketNaturalityCompletion",
24628     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.algebraTransferEdge_iff_of_bijective",
24629     "runtime_only": false
24630   },
24631   {
24632     "axioms": [
24633       "propext",
24634       "Classical.choice",
24635       "Quot.sound"
24636     ],
24637     "in_project_namespace": true,
24638     "kind": "definition",
24639     "module": "PaperICompletion7.ModuleTop",
24640     "name": "Komorebi.PaperICompletion7.ModuleTop.RadicalTop",
24641     "runtime_only": false
24642   },
24643   {
24644     "axioms": [
24645       "propext",
24646       "Classical.choice",
24647       "Quot.sound"
24648     ],
24649     "in_project_namespace": true,
24650     "kind": "theorem",
24651     "module": "PaperIRelease.PacketLocalRank",
24652     "name": "Komorebi.PaperIRelease.local_packetPure_iff",
24653     "runtime_only": false
24654   },
24655   {
24656     "axioms": [
24657       "propext",
24658       "Classical.choice",
24659       "Quot.sound"
24660     ],
24661     "in_project_namespace": true,
24662     "kind": "theorem",
24663     "module": "PaperIRelease.GrammarEquivalence",
24664     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_faithful",
24665     "runtime_only": false
24666   },
24667   {
24668     "axioms": [
24669       "propext",
24670       "Classical.choice",
24671       "Quot.sound"
24672     ],
24673     "in_project_namespace": true,
24674     "kind": "theorem",
24675     "module": "KomorebiVerification.ProjectorCore",
24676     "name": "Komorebi.Quantum.logPhase.eq_1",
24677     "runtime_only": false
24678   },
24679   {
24680     "axioms": [
24681       "propext",
24682       "Classical.choice",
24683       "Quot.sound"
24684     ],
24685     "in_project_namespace": true,
24686     "kind": "theorem",
24687     "module": "KomorebiVerification.ExactCoordinates",
24688     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates._proof_1",
24689     "runtime_only": false
24690   },
24691   {
24692     "axioms": [
24693       "propext",
24694       "Quot.sound"
24695     ],
24696     "in_project_namespace": true,
24697     "kind": "theorem",
24698     "module": "PaperIRelease.GrammarModules",
24699     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_1",
24700     "runtime_only": false
24701   },
24702   {
24703     "axioms": [
24704       "propext",
24705       "Classical.choice",
24706       "Quot.sound"
24707     ],
24708     "in_project_namespace": true,
24709     "kind": "theorem",
24710     "module": "PaperIRelease.PacketDescent",
24711     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_6",
24712     "runtime_only": false
24713   },
24714   {
24715     "axioms": [
24716       "propext",
24717       "Classical.choice",
24718       "Quot.sound"
24719     ],
24720     "in_project_namespace": true,
24721     "kind": "theorem",
24722     "module": "PaperIRelease.PacketDescent",
24723     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_range_in_ambient",
24724     "runtime_only": false
24725   },
24726   {
24727     "axioms": [
24728       "propext",
24729       "Quot.sound"
24730     ],
24731     "in_project_namespace": true,
24732     "kind": "theorem",
24733     "module": "KomorebiVerification.PathGraphKrylov",
24734     "name": "Komorebi.PathGraphKrylov.krylov_eq_pow",
24735     "runtime_only": false
24736   },
24737   {
24738     "axioms": [
24739       "propext",
24740       "Classical.choice",
24741       "Quot.sound"
24742     ],
24743     "in_project_namespace": false,
24744     "kind": "theorem",
24745     "module": "PaperIRelease.TopologyCountablePackets",
24746     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis_opNorm_le",
24747     "runtime_only": false
24748   },
24749   {
24750     "axioms": [
24751       "propext",
24752       "Quot.sound"
24753     ],
24754     "in_project_namespace": true,
24755     "kind": "definition",
24756     "module": "KomorebiVerification.PathGraphKrylov",
24757     "name": "Komorebi.PathGraphKrylov.rightStep",
24758     "runtime_only": false
24759   },
24760   {
24761     "axioms": [],
24762     "in_project_namespace": true,
24763     "kind": "theorem",
24764     "module": "KomorebiVerification.ProjectorCore",
24765     "name": "Komorebi.ClaimKind.theoremClaim.sizeOf_spec",
24766     "runtime_only": false
24767   },
24768   {
24769     "axioms": [
24770       "propext",
24771       "Classical.choice",
24772       "Quot.sound"
24773     ],
24774     "in_project_namespace": true,
24775     "kind": "definition",
24776     "module": "KomorebiVerification.TopologicalCompletion",
24777     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily._sizeOf_1",
24778     "runtime_only": false
24779   },
24780   {
24781     "axioms": [
24782       "propext",
24783       "Classical.choice",
24784       "Quot.sound"
24785     ],
24786     "in_project_namespace": true,
24787     "kind": "theorem",
24788     "module": "KomorebiVerification.TopologicalCompletion",
24789     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_5",
24790     "runtime_only": false
24791   },
24792   {
24793     "axioms": [
24794       "propext",
24795       "Quot.sound"
24796     ],
24797     "in_project_namespace": true,
24798     "kind": "theorem",
24799     "module": "PaperIRelease.CategoryPackets",
24800     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_4",
24801     "runtime_only": false
24802   },
24803   {
24804     "axioms": [
24805       "propext",
24806       "Classical.choice",
24807       "Quot.sound"
24808     ],
24809     "in_project_namespace": true,
24810     "kind": "definition",
24811     "module": "PaperIRelease.CategoryPackets",
24812     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.recOn",
24813     "runtime_only": false
24814   },
24815   {
24816     "axioms": [
24817       "propext",
24818       "Classical.choice",
24819       "Quot.sound"
24820     ],
24821     "in_project_namespace": true,
24822     "kind": "definition",
24823     "module": "KomorebiVerification.PacketNaturalityCompletion",
24824     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packetMap",
24825     "runtime_only": false
24826   },
24827   {
24828     "axioms": [
24829       "propext",
24830       "Classical.choice",
24831       "Quot.sound"
24832     ],
24833     "in_project_namespace": true,
24834     "kind": "definition",
24835     "module": "PaperIRelease.GrammarTyped",
24836     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization._sizeOf_inst",
24837     "runtime_only": false
24838   },
24839   {
24840     "axioms": [
24841       "propext",
24842       "Quot.sound"
24843     ],
24844     "in_project_namespace": true,
24845     "kind": "theorem",
24846     "module": "PaperIRelease.AlgebraSupport",
24847     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_1",
24848     "runtime_only": false
24849   },
24850   {
24851     "axioms": [
24852       "propext",
24853       "Classical.choice",
24854       "Quot.sound"
24855     ],
24856     "in_project_namespace": true,
24857     "kind": "theorem",
24858     "module": "PaperIRelease.PacketCorners",
24859     "name": "Komorebi.PaperIRelease.corner_one_eq_projector",
24860     "runtime_only": false
24861   },
24862   {
24863     "axioms": [
24864       "propext",
24865       "Classical.choice",
24866       "Quot.sound"
24867     ],
24868     "in_project_namespace": true,
24869     "kind": "definition",
24870     "module": "KomorebiVerification.SingleOperatorGraph",
24871     "name": "Komorebi.SingleOperatorGraph.operatorAlgebra",
24872     "runtime_only": false
24873   },
24874   {
24875     "axioms": [
24876       "propext",
24877       "Classical.choice",
24878       "Quot.sound"
24879     ],
24880     "in_project_namespace": false,
24881     "kind": "theorem",
24882     "module": "PaperIRelease.TopologyUnconditional",
24883     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_limit_bound",
24884     "runtime_only": false
24885   },
24886   {
24887     "axioms": [
24888       "propext",
24889       "Classical.choice",
24890       "Quot.sound"
24891     ],
24892     "in_project_namespace": true,
24893     "kind": "theorem",
24894     "module": "PaperICompletion5.GeometricSeedFormula",
24895     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_le_seedFinrank",
24896     "runtime_only": false
24897   },
24898   {
24899     "axioms": [],
24900     "in_project_namespace": true,
24901     "kind": "definition",
24902     "module": "KomorebiVerification.ProjectorCore",
24903     "name": "Komorebi.ClaimRecord.mk._flat_ctor",
24904     "runtime_only": false
24905   },
24906   {
24907     "axioms": [
24908       "propext",
24909       "Quot.sound"
24910     ],
24911     "in_project_namespace": true,
24912     "kind": "theorem",
24913     "module": "PaperIRelease.CategoryBoundaries",
24914     "name": "Komorebi.Packet.fibreLinearProj.eq_1",
24915     "runtime_only": false
24916   },
24917   {
24918     "axioms": [
24919       "propext",
24920       "Quot.sound"
24921     ],
24922     "in_project_namespace": true,
24923     "kind": "theorem",
24924     "module": "PaperIRelease.GraphSources",
24925     "name": "Komorebi.PaperIRelease.FiniteDigraph.component_le_iff",
24926     "runtime_only": false
24927   },
24928   {
24929     "axioms": [
24930       "propext",
24931       "Classical.choice",
24932       "Quot.sound"
24933     ],
24934     "in_project_namespace": true,
24935     "kind": "theorem",
24936     "module": "PaperIRelease.PacketCorners",
24937     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_5",
24938     "runtime_only": false
24939   },
24940   {
24941     "axioms": [
24942       "propext",
24943       "Classical.choice",
24944       "Quot.sound"
24945     ],
24946     "in_project_namespace": true,
24947     "kind": "theorem",
24948     "module": "PaperIRelease.PacketDescent",
24949     "name": "Komorebi.Foundation.LinearProjectorFamily.transferBlock_preserves_packet",
24950     "runtime_only": false
24951   },
24952   {
24953     "axioms": [
24954       "propext",
24955       "Classical.choice",
24956       "Quot.sound"
24957     ],
24958     "in_project_namespace": true,
24959     "kind": "theorem",
24960     "module": "PaperICompletion8.RegularMultiplicity",
24961     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_smul",
24962     "runtime_only": false
24963   },
24964   {
24965     "axioms": [],
24966     "in_project_namespace": true,
24967     "kind": "constructor",
24968     "module": "KomorebiVerification.ProjectorCore",
24969     "name": "Komorebi.ClaimKind.lemmaClaim",
24970     "runtime_only": false
24971   },
24972   {
24973     "axioms": [],
24974     "in_project_namespace": true,
24975     "kind": "definition",
24976     "module": "KomorebiVerification.ProjectorCore",
24977     "name": "Komorebi.ClaimRecord.kind",
24978     "runtime_only": false
24979   },
24980   {
24981     "axioms": [
24982       "propext",
24983       "Classical.choice",
24984       "Quot.sound"
24985     ],
24986     "in_project_namespace": true,
24987     "kind": "theorem",
24988     "module": "PaperIRelease.GrammarIdeal",
24989     "name": "Komorebi.PaperIRelease.GrammarAlgebra.base_respects",
24990     "runtime_only": false
24991   },
24992   {
24993     "axioms": [
24994       "propext",
24995       "Quot.sound"
24996     ],
24997     "in_project_namespace": true,
24998     "kind": "theorem",
24999     "module": "KomorebiVerification.PaperITransport",
25000     "name": "Komorebi.Foundation.conjugateEnd_apply",
25001     "runtime_only": false
25002   },
25003   {
25004     "axioms": [
25005       "propext"
25006     ],
25007     "in_project_namespace": true,
25008     "kind": "theorem",
25009     "module": "KomorebiVerification.PacketNaturalityCompletion",
25010     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_1",
25011     "runtime_only": false
25012   },
25013   {
25014     "axioms": [
25015       "propext",
25016       "Classical.choice",
25017       "Quot.sound"
25018     ],
25019     "in_project_namespace": true,
25020     "kind": "theorem",
25021     "module": "KomorebiVerification.SingleOperatorGraph",
25022     "name": "Komorebi.SingleOperatorGraph.cycle_seedNumber_isLeast_two_of_root",
25023     "runtime_only": false
25024   },
25025   {
25026     "axioms": [
25027       "propext",
25028       "Classical.choice",
25029       "Quot.sound"
25030     ],
25031     "in_project_namespace": true,
25032     "kind": "theorem",
25033     "module": "PaperICompletion4.OperatorIntrinsicFormula",
25034     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_8",
25035     "runtime_only": false
25036   },
25037   {
25038     "axioms": [
25039       "propext",
25040       "Quot.sound"
25041     ],
25042     "in_project_namespace": false,
25043     "kind": "theorem",
25044     "module": "PaperIRelease.TopologyDenseCompletion",
25045     "name": "PaperIRelease.TopologyDenseCompletion.completedAction._proof_1",
25046     "runtime_only": false
25047   },
25048   {
25049     "axioms": [
25050       "propext",
25051       "Quot.sound"
25052     ],
25053     "in_project_namespace": true,
25054     "kind": "theorem",
25055     "module": "PaperIRelease.GraphSources",
25056     "name": "Komorebi.PaperIRelease.FiniteDigraph.component_eq_iff._simp_1",
25057     "runtime_only": false
25058   },
25059   {
25060     "axioms": [
25061       "propext",
25062       "Classical.choice",
25063       "Quot.sound"
25064     ],
25065     "in_project_namespace": true,
25066     "kind": "theorem",
25067     "module": "KomorebiVerification.PacketNaturalityCompletion",
25068     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.exists_packet_maps_nonzero_comp",
25069     "runtime_only": false
25070   },
25071   {
25072     "axioms": [
25073       "propext",
25074       "Classical.choice",
25075       "Quot.sound"
25076     ],
25077     "in_project_namespace": false,
25078     "kind": "theorem",
25079     "module": "ReleaseBoundary",
25080     "name": "PaperIBlock08Tests.qj.eq_1",
25081     "runtime_only": false
25082   },
25083   {
25084     "axioms": [
25085       "propext",
25086       "Classical.choice",
25087       "Quot.sound"
25088     ],
25089     "in_project_namespace": true,
25090     "kind": "theorem",
25091     "module": "KomorebiVerification.PathGraphKrylov",
25092     "name": "Komorebi.PathGraphKrylov.walkMatrix.eq_1",
25093     "runtime_only": false
25094   },
25095   {
25096     "axioms": [
25097       "propext",
25098       "Classical.choice",
25099       "Quot.sound"
25100     ],
25101     "in_project_namespace": false,
25102     "kind": "definition",
25103     "module": "PaperIRelease.TopologyUnconditional",
25104     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._aux_1",
25105     "runtime_only": false
25106   },
25107   {
25108     "axioms": [
25109       "propext",
25110       "Classical.choice",
25111       "Quot.sound"
25112     ],
25113     "in_project_namespace": false,
25114     "kind": "recursor",
25115     "module": "PaperIRelease.TopologyUnconditional",
25116     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.rec",
25117     "runtime_only": false
25118   },
25119   {
25120     "axioms": [
25121       "propext",
25122       "Classical.choice",
25123       "Quot.sound"
25124     ],
25125     "in_project_namespace": true,
25126     "kind": "theorem",
25127     "module": "KomorebiVerification.PacketNaturalityCompletion",
25128     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_injective",
25129     "runtime_only": false
25130   },
25131   {
25132     "axioms": [
25133       "propext",
25134       "Classical.choice",
25135       "Quot.sound"
25136     ],
25137     "in_project_namespace": true,
25138     "kind": "theorem",
25139     "module": "PaperIRelease.GeneralNormedPackets",
25140     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet.eq_1",
25141     "runtime_only": false
25142   },
25143   {
25144     "axioms": [
25145       "propext",
25146       "Classical.choice",
25147       "Quot.sound"
25148     ],
25149     "in_project_namespace": true,
25150     "kind": "theorem",
25151     "module": "PaperIRelease.AlgebraDiagonal",
25152     "name": "Komorebi.PaperIRelease.diagonalProjection_apply",
25153     "runtime_only": false
25154   },
25155   {
25156     "axioms": [
25157       "propext",
25158       "Classical.choice",
25159       "Quot.sound"
25160     ],
25161     "in_project_namespace": true,
25162     "kind": "theorem",
25163     "module": "PaperIRelease.AlgebraClassGrouping",
25164     "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_3",
25165     "runtime_only": false
25166   },
25167   {
25168     "axioms": [],
25169     "in_project_namespace": true,
25170     "kind": "definition",
25171     "module": "PaperICompletion8.DivisionProduct",
25172     "name": "Komorebi.PaperICompletion8.DivisionProduct.DivisionProductModule",
25173     "runtime_only": false
25174   },
25175   {
25176     "axioms": [
25177       "propext",
25178       "Classical.choice",
25179       "Quot.sound"
25180     ],
25181     "in_project_namespace": true,
25182     "kind": "theorem",
25183     "module": "PaperICompletion.SpectralCertificates",
25184     "name": "Komorebi.PaperICompletion.SpectralCertificates.maxEigenMultiplicity.eq_1",
25185     "runtime_only": false
25186   },
25187   {
25188     "axioms": [
25189       "propext",
25190       "Classical.choice",
25191       "Quot.sound"
25192     ],
25193     "in_project_namespace": true,
25194     "kind": "definition",
25195     "module": "PaperIRelease.BoundedStar",
25196     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra",
25197     "runtime_only": false
25198   },
25199   {
25200     "axioms": [
25201       "propext",
25202       "Classical.choice",
25203       "Quot.sound"
25204     ],
25205     "in_project_namespace": true,
25206     "kind": "theorem",
25207     "module": "KomorebiVerification.SingleOperatorGraph",
25208     "name": "Komorebi.SingleOperatorGraph.seedNumberLE_iff_operatorAlgebra_family",
25209     "runtime_only": false
25210   },
25211   {
25212     "axioms": [
25213       "propext",
25214       "Quot.sound"
25215     ],
25216     "in_project_namespace": true,
25217     "kind": "theorem",
25218     "module": "PaperIRelease.GrammarAlgebra",
25219     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction._proof_2",
25220     "runtime_only": false
25221   },
25222   {
25223     "axioms": [
25224       "propext",
25225       "Classical.choice",
25226       "Quot.sound"
25227     ],
25228     "in_project_namespace": true,
25229     "kind": "theorem",
25230     "module": "PaperIRelease.CategoryBoundaries",
25231     "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_3",
25232     "runtime_only": false
25233   },
25234   {
25235     "axioms": [
25236       "propext"
25237     ],
25238     "in_project_namespace": true,
25239     "kind": "theorem",
25240     "module": "KomorebiVerification.SingleOperatorGraph",
25241     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_4",
25242     "runtime_only": false
25243   },
25244   {
25245     "axioms": [],
25246     "in_project_namespace": true,
25247     "kind": "definition",
25248     "module": "KomorebiVerification.PacketNaturalityCompletion",
25249     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.V",
25250     "runtime_only": false
25251   },
25252   {
25253     "axioms": [],
25254     "in_project_namespace": true,
25255     "kind": "definition",
25256     "module": "KomorebiVerification.ProjectorCore",
25257     "name": "Komorebi.ClaimKind.ofNat",
25258     "runtime_only": false
25259   },
25260   {
25261     "axioms": [
25262       "propext",
25263       "Classical.choice",
25264       "Quot.sound"
25265     ],
25266     "in_project_namespace": true,
25267     "kind": "theorem",
25268     "module": "KomorebiVerification.ProjectorCore",
25269     "name": "Komorebi.Foundation.LinearProjectorFamily.mk.sizeOf_spec",
25270     "runtime_only": false
25271   },
25272   {
25273     "axioms": [
25274       "propext",
25275       "Classical.choice",
25276       "Quot.sound"
25277     ],
25278     "in_project_namespace": false,
25279     "kind": "theorem",
25280     "module": "PaperIRelease.TopologyUnconditional",
25281     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_1",
25282     "runtime_only": false
25283   },
25284   {
25285     "axioms": [
25286       "propext",
25287       "Classical.choice",
25288       "Quot.sound"
25289     ],
25290     "in_project_namespace": true,
25291     "kind": "theorem",
25292     "module": "PaperIRelease.AlgebraClassGrouping",
25293     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_14",
25294     "runtime_only": false
25295   },
25296   {
25297     "axioms": [
25298       "propext",
25299       "Classical.choice",
25300       "Quot.sound"
25301     ],
25302     "in_project_namespace": true,
25303     "kind": "definition",
25304     "module": "PaperICompletion7.LocalResidue",
25305     "name": "Komorebi.PaperICompletion7.LocalResidue.residueDivisionRing",
25306     "runtime_only": false
25307   },
25308   {
25309     "axioms": [
25310       "propext",
25311       "Classical.choice",
25312       "Quot.sound"
25313     ],
25314     "in_project_namespace": true,
25315     "kind": "theorem",
25316     "module": "PaperIRelease.AlgebraQuotient",
25317     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_11",
25318     "runtime_only": false
25319   },
25320   {
25321     "axioms": [
25322       "propext",
25323       "Quot.sound"
25324     ],
25325     "in_project_namespace": true,
25326     "kind": "theorem",
25327     "module": "PaperICompletion4.ResidueQuotient",
25328     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_4",
25329     "runtime_only": false
25330   },
25331   {
25332     "axioms": [],
25333     "in_project_namespace": true,
25334     "kind": "constructor",
25335     "module": "KomorebiVerification.ProjectorCore",
25336     "name": "Komorebi.FormalizationStatus.proofTermPresent",
25337     "runtime_only": false
25338   },
25339   {
25340     "axioms": [
25341       "propext",
25342       "Quot.sound"
25343     ],
25344     "in_project_namespace": true,
25345     "kind": "theorem",
25346     "module": "KomorebiVerification.SingleOperatorGraph",
25347     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_2",
25348     "runtime_only": false
25349   },
25350   {
25351     "axioms": [
25352       "propext",
25353       "Classical.choice",
25354       "Quot.sound"
25355     ],
25356     "in_project_namespace": true,
25357     "kind": "inductive",
25358     "module": "PaperIRelease.TopologyCategories",
25359     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject",
25360     "runtime_only": false
25361   },
25362   {
25363     "axioms": [
25364       "propext",
25365       "Classical.choice",
25366       "Quot.sound"
25367     ],
25368     "in_project_namespace": true,
25369     "kind": "theorem",
25370     "module": "PaperIRelease.AlgebraPreorder",
25371     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_5",
25372     "runtime_only": false
25373   },
25374   {
25375     "axioms": [
25376       "propext",
25377       "Classical.choice",
25378       "Quot.sound"
25379     ],
25380     "in_project_namespace": true,
25381     "kind": "theorem",
25382     "module": "PaperIRelease.CategoryPackets",
25383     "name": "Komorebi.PaperIRelease.CategoryPackets.transferBlock_naturality",
25384     "runtime_only": false
25385   },
25386   {
25387     "axioms": [
25388       "propext",
25389       "Quot.sound"
25390     ],
25391     "in_project_namespace": true,
25392     "kind": "theorem",
25393     "module": "PaperICompletion4.OperatorIntrinsicFormula",
25394     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_3",
25395     "runtime_only": false
25396   },
25397   {
25398     "axioms": [
25399       "propext",
25400       "Classical.choice",
25401       "Quot.sound"
25402     ],
25403     "in_project_namespace": true,
25404     "kind": "theorem",
25405     "module": "PaperIRelease.PacketTopologyGeneral",
25406     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_4",
25407     "runtime_only": false
25408   },
25409   {
25410     "axioms": [
25411       "propext",
25412       "Quot.sound"
25413     ],
25414     "in_project_namespace": true,
25415     "kind": "theorem",
25416     "module": "PaperICompletion4.GroupedPrimary",
25417     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primary_equiv_mem_iff",
25418     "runtime_only": false
25419   },
25420   {
25421     "axioms": [
25422       "propext",
25423       "Classical.choice",
25424       "Quot.sound"
25425     ],
25426     "in_project_namespace": true,
25427     "kind": "theorem",
25428     "module": "KomorebiVerification.TopologicalCompletion",
25429     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.sizeOf_spec",
25430     "runtime_only": false
25431   },
25432   {
25433     "axioms": [
25434       "propext",
25435       "Classical.choice",
25436       "Quot.sound"
25437     ],
25438     "in_project_namespace": true,
25439     "kind": "theorem",
25440     "module": "PaperICompletion.CyclicClassification",
25441     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap_apply",
25442     "runtime_only": false
25443   },
25444   {
25445     "axioms": [
25446       "propext",
25447       "Classical.choice",
25448       "Quot.sound"
25449     ],
25450     "in_project_namespace": false,
25451     "kind": "theorem",
25452     "module": "PaperIRelease.TopologyTransport",
25453     "name": "PaperIRelease.TopologyTransport.map_packetRange_eq",
25454     "runtime_only": false
25455   },
25456   {
25457     "axioms": [],
25458     "in_project_namespace": true,
25459     "kind": "constructor",
25460     "module": "PaperIRelease.CategoryExport",
25461     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator",
25462     "runtime_only": false
25463   },
25464   {
25465     "axioms": [
25466       "propext",
25467       "Classical.choice",
25468       "Quot.sound"
25469     ],
25470     "in_project_namespace": true,
25471     "kind": "theorem",
25472     "module": "PaperICompletion5.LinearPrimaryEigenspace",
25473     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.finrank_cokernel_eq_finrank_kernel._proof_1_1",
25474     "runtime_only": false
25475   },
25476   {
25477     "axioms": [
25478       "propext",
25479       "Classical.choice",
25480       "Quot.sound"
25481     ],
25482     "in_project_namespace": true,
25483     "kind": "theorem",
25484     "module": "KomorebiVerification.TopologicalCompletion",
25485     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_seedCardinality_isLeast",
25486     "runtime_only": false
25487   },
25488   {
25489     "axioms": [
25490       "propext",
25491       "Classical.choice",
25492       "Quot.sound"
25493     ],
25494     "in_project_namespace": true,
25495     "kind": "theorem",
25496     "module": "KomorebiVerification.SemisimpleCompletion",
25497     "name": "Komorebi.SemisimpleCompletion.oneBlock_seedFinrank_eq_ceilDiv",
25498     "runtime_only": false
25499   },
25500   {
25501     "axioms": [
25502       "propext",
25503       "Classical.choice",
25504       "Quot.sound"
25505     ],
25506     "in_project_namespace": true,
25507     "kind": "theorem",
25508     "module": "KomorebiVerification.EllipticAlgorithms",
25509     "name": "Komorebi.FiniteAlgorithms.orbitHull_invariant",
25510     "runtime_only": false
25511   },
25512   {
25513     "axioms": [
25514       "propext",
25515       "Classical.choice",
25516       "Quot.sound"
25517     ],
25518     "in_project_namespace": true,
25519     "kind": "theorem",
25520     "module": "KomorebiVerification.PacketNaturalityCompletion",
25521     "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_transferBlock_ne_zero_iff",
25522     "runtime_only": false
25523   },
25524   {
25525     "axioms": [
25526       "propext",
25527       "Classical.choice",
25528       "Quot.sound"
25529     ],
25530     "in_project_namespace": true,
25531     "kind": "theorem",
25532     "module": "KomorebiVerification.SeedRankOperations",
25533     "name": "Komorebi.SeedRankOperations.seedRank_prod_productAlgebra",
25534     "runtime_only": false
25535   },
25536   {
25537     "axioms": [
25538       "propext",
25539       "Classical.choice",
25540       "Quot.sound"
25541     ],
25542     "in_project_namespace": false,
25543     "kind": "theorem",
25544     "module": "PaperIRelease.TopologyCountablePackets",
25545     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_1",
25546     "runtime_only": false
25547   },
25548   {
25549     "axioms": [
25550       "propext",
25551       "Quot.sound"
25552     ],
25553     "in_project_namespace": false,
25554     "kind": "theorem",
25555     "module": "KomorebiVerification.SeedRankOperations",
25556     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_6",
25557     "runtime_only": false
25558   },
25559   {
25560     "axioms": [
25561       "propext",
25562       "Classical.choice",
25563       "Quot.sound"
25564     ],
25565     "in_project_namespace": false,
25566     "kind": "theorem",
25567     "module": "PaperIRelease.AlgebraPreorder",
25568     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono._simp_1_3",
25569     "runtime_only": false
25570   },
25571   {
25572     "axioms": [
25573       "propext",
25574       "Classical.choice",
25575       "Quot.sound"
25576     ],
25577     "in_project_namespace": true,
25578     "kind": "theorem",
25579     "module": "KomorebiVerification.PacketNaturalityCompletion",
25580     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebra_mul_eq_blockMul",
25581     "runtime_only": false
25582   },
25583   {
25584     "axioms": [
25585       "propext",
25586       "Classical.choice",
25587       "Quot.sound"
25588     ],
25589     "in_project_namespace": true,
25590     "kind": "theorem",
25591     "module": "PaperICompletion5.LinearPrimaryEigenspace",
25592     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.linearResidue_finrank",
25593     "runtime_only": false
25594   },
25595   {
25596     "axioms": [
25597       "propext",
25598       "Quot.sound"
25599     ],
25600     "in_project_namespace": true,
25601     "kind": "definition",
25602     "module": "PaperIRelease.GrammarModules",
25603     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.recOn",
25604     "runtime_only": false
25605   },
25606   {
25607     "axioms": [
25608       "propext",
25609       "Quot.sound"
25610     ],
25611     "in_project_namespace": true,
25612     "kind": "definition",
25613     "module": "KomorebiVerification.PathGraphKrylov",
25614     "name": "Komorebi.PathGraphKrylov.leftStep",
25615     "runtime_only": false
25616   },
25617   {
25618     "axioms": [],
25619     "in_project_namespace": true,
25620     "kind": "definition",
25621     "module": "PaperIRelease.GraphSources",
25622     "name": "Komorebi.PaperIRelease.FiniteDigraph.CondensationEdge",
25623     "runtime_only": false
25624   },
25625   {
25626     "axioms": [
25627       "propext",
25628       "Classical.choice",
25629       "Quot.sound"
25630     ],
25631     "in_project_namespace": true,
25632     "kind": "definition",
25633     "module": "KomorebiVerification.TopologicalCompletion",
25634     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.noConfusion",
25635     "runtime_only": false
25636   },
25637   {
25638     "axioms": [
25639       "propext",
25640       "Classical.choice",
25641       "Quot.sound"
25642     ],
25643     "in_project_namespace": true,
25644     "kind": "theorem",
25645     "module": "PaperIRelease.TopologyCategories",
25646     "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_1",
25647     "runtime_only": false
25648   },
25649   {
25650     "axioms": [
25651       "propext",
25652       "Classical.choice",
25653       "Quot.sound"
25654     ],
25655     "in_project_namespace": true,
25656     "kind": "theorem",
25657     "module": "KomorebiVerification.PacketNaturalityCompletion",
25658     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation.eq_1",
25659     "runtime_only": false
25660   },
25661   {
25662     "axioms": [
25663       "propext",
25664       "Classical.choice",
25665       "Quot.sound"
25666     ],
25667     "in_project_namespace": true,
25668     "kind": "theorem",
25669     "module": "PaperIRelease.PacketTopologyGeneral",
25670     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packet_spaces_complete",
25671     "runtime_only": false
25672   },
25673   {
25674     "axioms": [
25675       "propext",
25676       "Classical.choice",
25677       "Quot.sound"
25678     ],
25679     "in_project_namespace": true,
25680     "kind": "theorem",
25681     "module": "PaperIRelease.CategoryPackets",
25682     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_3",
25683     "runtime_only": false
25684   },
25685   {
25686     "axioms": [
25687       "propext",
25688       "Classical.choice",
25689       "Quot.sound"
25690     ],
25691     "in_project_namespace": true,
25692     "kind": "definition",
25693     "module": "PaperIRelease.AlgebraSupport",
25694     "name": "Komorebi.PaperIRelease.supportSubmodule",
25695     "runtime_only": false
25696   },
25697   {
25698     "axioms": [
25699       "propext",
25700       "Classical.choice",
25701       "Quot.sound"
25702     ],
25703     "in_project_namespace": true,
25704     "kind": "theorem",
25705     "module": "PaperIRelease.TopologyCategories",
25706     "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_1",
25707     "runtime_only": false
25708   },
25709   {
25710     "axioms": [
25711       "propext",
25712       "Classical.choice",
25713       "Quot.sound"
25714     ],
25715     "in_project_namespace": false,
25716     "kind": "theorem",
25717     "module": "PaperIRelease.TopologyCountablePackets",
25718     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_19",
25719     "runtime_only": false
25720   },
25721   {
25722     "axioms": [
25723       "propext",
25724       "Classical.choice",
25725       "Quot.sound"
25726     ],
25727     "in_project_namespace": true,
25728     "kind": "definition",
25729     "module": "KomorebiVerification.PacketNaturalityCompletion",
25730     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetInclusion",
25731     "runtime_only": false
25732   },
25733   {
25734     "axioms": [
25735       "propext",
25736       "Classical.choice",
25737       "Quot.sound"
25738     ],
25739     "in_project_namespace": true,
25740     "kind": "theorem",
25741     "module": "PaperIRelease.CategoryPackets",
25742     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.packet_nonzero",
25743     "runtime_only": false
25744   },
25745   {
25746     "axioms": [
25747       "propext",
25748       "Classical.choice",
25749       "Quot.sound"
25750     ],
25751     "in_project_namespace": true,
25752     "kind": "theorem",
25753     "module": "PaperIRelease.CategoryPackets",
25754     "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_3",
25755     "runtime_only": false
25756   },
25757   {
25758     "axioms": [
25759       "propext",
25760       "Classical.choice",
25761       "Quot.sound"
25762     ],
25763     "in_project_namespace": true,
25764     "kind": "theorem",
25765     "module": "KomorebiVerification.EllipticAlgorithms",
25766     "name": "Komorebi.EllipticCoordinates.P0._proof_1",
25767     "runtime_only": false
25768   },
25769   {
25770     "axioms": [
25771       "propext",
25772       "Classical.choice",
25773       "Quot.sound"
25774     ],
25775     "in_project_namespace": true,
25776     "kind": "theorem",
25777     "module": "PaperICompletion6.ScalarExtension",
25778     "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_eq_charpoly_baseChange_iff",
25779     "runtime_only": false
25780   },
25781   {
25782     "axioms": [
25783       "propext",
25784       "Classical.choice",
25785       "Quot.sound"
25786     ],
25787     "in_project_namespace": true,
25788     "kind": "definition",
25789     "module": "PaperICompletion6.OneInvariantFactor",
25790     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.HasOneInvariantFactor",
25791     "runtime_only": false
25792   },
25793   {
25794     "axioms": [
25795       "propext",
25796       "Classical.choice",
25797       "Quot.sound"
25798     ],
25799     "in_project_namespace": true,
25800     "kind": "theorem",
25801     "module": "PaperIRelease.CategoryUniversal",
25802     "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial_underlying",
25803     "runtime_only": false
25804   },
25805   {
25806     "axioms": [
25807       "propext",
25808       "Classical.choice",
25809       "Quot.sound"
25810     ],
25811     "in_project_namespace": true,
25812     "kind": "theorem",
25813     "module": "PaperIRelease.PacketBoundaryTests",
25814     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_submodule_packet_exact",
25815     "runtime_only": false
25816   },
25817   {
25818     "axioms": [
25819       "propext",
25820       "Classical.choice",
25821       "Quot.sound"
25822     ],
25823     "in_project_namespace": true,
25824     "kind": "theorem",
25825     "module": "KomorebiVerification.EllipticAlgorithms",
25826     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_2",
25827     "runtime_only": false
25828   },
25829   {
25830     "axioms": [
25831       "propext",
25832       "Quot.sound"
25833     ],
25834     "in_project_namespace": true,
25835     "kind": "theorem",
25836     "module": "PaperICompletion.CyclicClassification",
25837     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_1",
25838     "runtime_only": false
25839   },
25840   {
25841     "axioms": [],
25842     "in_project_namespace": true,
25843     "kind": "theorem",
25844     "module": "PaperIRelease.CategoryExport",
25845     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.inj",
25846     "runtime_only": false
25847   },
25848   {
25849     "axioms": [
25850       "propext",
25851       "Classical.choice",
25852       "Quot.sound"
25853     ],
25854     "in_project_namespace": true,
25855     "kind": "theorem",
25856     "module": "PaperIRelease.BoundedStar",
25857     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_2",
25858     "runtime_only": false
25859   },
25860   {
25861     "axioms": [
25862       "propext",
25863       "Classical.choice",
25864       "Quot.sound"
25865     ],
25866     "in_project_namespace": true,
25867     "kind": "theorem",
25868     "module": "KomorebiVerification.SemisimpleSeedRank",
25869     "name": "Komorebi.SemisimpleSeedRank.exists_leftGenerators_of_le",
25870     "runtime_only": false
25871   },
25872   {
25873     "axioms": [
25874       "propext",
25875       "Classical.choice",
25876       "Quot.sound"
25877     ],
25878     "in_project_namespace": true,
25879     "kind": "theorem",
25880     "module": "PaperICompletion5.CyclicGeometricCriterion",
25881     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.eigenspace_finrank_pos_iff_mem_spectrum",
25882     "runtime_only": false
25883   },
25884   {
25885     "axioms": [
25886       "propext",
25887       "Classical.choice",
25888       "Quot.sound"
25889     ],
25890     "in_project_namespace": true,
25891     "kind": "theorem",
25892     "module": "PaperIRelease.CategoryPackets",
25893     "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_1",
25894     "runtime_only": false
25895   },
25896   {
25897     "axioms": [
25898       "propext",
25899       "Quot.sound"
25900     ],
25901     "in_project_namespace": true,
25902     "kind": "definition",
25903     "module": "PaperIRelease.GrammarTyped",
25904     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrow",
25905     "runtime_only": false
25906   },
25907   {
25908     "axioms": [
25909       "propext",
25910       "Classical.choice",
25911       "Quot.sound"
25912     ],
25913     "in_project_namespace": true,
25914     "kind": "theorem",
25915     "module": "PaperIRelease.GrammarAlgebra",
25916     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_orthogonal",
25917     "runtime_only": false
25918   },
25919   {
25920     "axioms": [
25921       "propext",
25922       "Classical.choice",
25923       "Quot.sound"
25924     ],
25925     "in_project_namespace": true,
25926     "kind": "theorem",
25927     "module": "PaperIRelease.AlgebraSupport",
25928     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_6",
25929     "runtime_only": false
25930   },
25931   {
25932     "axioms": [],
25933     "in_project_namespace": false,
25934     "kind": "theorem",
25935     "module": "KomorebiVerification.EllipticAlgorithms",
25936     "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.eq_1",
25937     "runtime_only": false
25938   },
25939   {
25940     "axioms": [],
25941     "in_project_namespace": true,
25942     "kind": "theorem",
25943     "module": "KomorebiVerification.ProjectorCore",
25944     "name": "Komorebi.ClaimKind.lemmaClaim.sizeOf_spec",
25945     "runtime_only": false
25946   },
25947   {
25948     "axioms": [
25949       "propext",
25950       "Classical.choice",
25951       "Quot.sound"
25952     ],
25953     "in_project_namespace": true,
25954     "kind": "theorem",
25955     "module": "PaperICompletion5.GeometricSeedFormula",
25956     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum_attained",
25957     "runtime_only": false
25958   },
25959   {
25960     "axioms": [
25961       "propext",
25962       "Classical.choice",
25963       "Quot.sound"
25964     ],
25965     "in_project_namespace": true,
25966     "kind": "definition",
25967     "module": "PaperIRelease.PacketPureBoundaryTests",
25968     "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket",
25969     "runtime_only": false
25970   },
25971   {
25972     "axioms": [
25973       "propext"
25974     ],
25975     "in_project_namespace": true,
25976     "kind": "theorem",
25977     "module": "PaperICompletion4.IntrinsicPrimary",
25978     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.power_kills_of_le",
25979     "runtime_only": false
25980   },
25981   {
25982     "axioms": [
25983       "propext",
25984       "Classical.choice",
25985       "Quot.sound"
25986     ],
25987     "in_project_namespace": true,
25988     "kind": "theorem",
25989     "module": "KomorebiVerification.EllipticAlgorithms",
25990     "name": "Komorebi.EllipticCoordinates.P1.eq_1",
25991     "runtime_only": false
25992   },
25993   {
25994     "axioms": [
25995       "propext",
25996       "Classical.choice",
25997       "Quot.sound"
25998     ],
25999     "in_project_namespace": true,
26000     "kind": "definition",
26001     "module": "PaperICompletion.CyclicClassification",
26002     "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap",
26003     "runtime_only": false
26004   },
26005   {
26006     "axioms": [
26007       "propext",
26008       "Classical.choice",
26009       "Quot.sound"
26010     ],
26011     "in_project_namespace": true,
26012     "kind": "definition",
26013     "module": "KomorebiVerification.EllipticAlgorithms",
26014     "name": "Komorebi.EllipticCoordinates.normalFormToQuotient",
26015     "runtime_only": false
26016   },
26017   {
26018     "axioms": [],
26019     "in_project_namespace": true,
26020     "kind": "definition",
26021     "module": "KomorebiVerification.ProjectorCore",
26022     "name": "Komorebi.ClaimRecord.ctorIdx",
26023     "runtime_only": false
26024   },
26025   {
26026     "axioms": [
26027       "propext",
26028       "Classical.choice",
26029       "Quot.sound"
26030     ],
26031     "in_project_namespace": true,
26032     "kind": "definition",
26033     "module": "PaperIRelease.TopologyCategories",
26034     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk._flat_ctor",
26035     "runtime_only": false
26036   },
26037   {
26038     "axioms": [
26039       "propext",
26040       "Classical.choice",
26041       "Quot.sound"
26042     ],
26043     "in_project_namespace": true,
26044     "kind": "definition",
26045     "module": "PaperIRelease.GraphSourceCount",
26046     "name": "Komorebi.PaperIRelease.PacketCornerCyclic",
26047     "runtime_only": false
26048   },
26049   {
26050     "axioms": [
26051       "propext",
26052       "Quot.sound"
26053     ],
26054     "in_project_namespace": true,
26055     "kind": "theorem",
26056     "module": "PaperIRelease.PacketExactSequence",
26057     "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_2",
26058     "runtime_only": false
26059   },
26060   {
26061     "axioms": [],
26062     "in_project_namespace": true,
26063     "kind": "definition",
26064     "module": "KomorebiVerification.ProjectorCore",
26065     "name": "Komorebi.ClaimRecord.sourceStatus",
26066     "runtime_only": false
26067   },
26068   {
26069     "axioms": [
26070       "propext",
26071       "Quot.sound"
26072     ],
26073     "in_project_namespace": true,
26074     "kind": "theorem",
26075     "module": "KomorebiVerification.SingleOperatorGraph",
26076     "name": "Komorebi.SingleOperatorGraph.evalVector._proof_1",
26077     "runtime_only": false
26078   },
26079   {
26080     "axioms": [
26081       "propext",
26082       "Quot.sound"
26083     ],
26084     "in_project_namespace": true,
26085     "kind": "theorem",
26086     "module": "KomorebiVerification.ProjectorCore",
26087     "name": "Komorebi.Packet.fibreProj_orthogonal",
26088     "runtime_only": false
26089   },
26090   {
26091     "axioms": [
26092       "propext",
26093       "Classical.choice",
26094       "Quot.sound"
26095     ],
26096     "in_project_namespace": true,
26097     "kind": "theorem",
26098     "module": "PaperIRelease.GrammarIdeal",
26099     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv._proof_2",
26100     "runtime_only": false
26101   },
26102   {
26103     "axioms": [
26104       "propext",
26105       "Classical.choice",
26106       "Quot.sound"
26107     ],
26108     "in_project_namespace": false,
26109     "kind": "theorem",
26110     "module": "PaperIRelease.TopologyUnconditional",
26111     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_3",
26112     "runtime_only": false
26113   },
26114   {
26115     "axioms": [
26116       "propext",
26117       "Classical.choice",
26118       "Quot.sound"
26119     ],
26120     "in_project_namespace": true,
26121     "kind": "theorem",
26122     "module": "KomorebiVerification.EllipticAlgorithms",
26123     "name": "Komorebi.EllipticCoordinates.Mx.eq_1",
26124     "runtime_only": false
26125   },
26126   {
26127     "axioms": [
26128       "propext",
26129       "Classical.choice",
26130       "Quot.sound"
26131     ],
26132     "in_project_namespace": true,
26133     "kind": "theorem",
26134     "module": "KomorebiVerification.TopologicalCompletion",
26135     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_4",
26136     "runtime_only": false
26137   },
26138   {
26139     "axioms": [
26140       "propext",
26141       "Classical.choice",
26142       "Quot.sound"
26143     ],
26144     "in_project_namespace": true,
26145     "kind": "theorem",
26146     "module": "KomorebiVerification.TopologicalCompletion",
26147     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic._proof_1",
26148     "runtime_only": false
26149   },
26150   {
26151     "axioms": [
26152       "propext",
26153       "Classical.choice",
26154       "Quot.sound"
26155     ],
26156     "in_project_namespace": true,
26157     "kind": "theorem",
26158     "module": "PaperIRelease.GrammarEquivalence",
26159     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.injEq",
26160     "runtime_only": false
26161   },
26162   {
26163     "axioms": [
26164       "propext",
26165       "Classical.choice",
26166       "Quot.sound"
26167     ],
26168     "in_project_namespace": true,
26169     "kind": "theorem",
26170     "module": "PaperIRelease.GrammarEquivalence",
26171     "name": "Komorebi.PaperIRelease.GrammarAlgebra.liftActionHom.eq_1",
26172     "runtime_only": false
26173   },
26174   {
26175     "axioms": [
26176       "propext",
26177       "Classical.choice",
26178       "Quot.sound"
26179     ],
26180     "in_project_namespace": true,
26181     "kind": "theorem",
26182     "module": "KomorebiVerification.SingleOperatorGraph",
26183     "name": "Komorebi.SingleOperatorGraph.aeval_mem_span_orbit_of_mem",
26184     "runtime_only": false
26185   },
26186   {
26187     "axioms": [
26188       "propext",
26189       "Classical.choice",
26190       "Quot.sound"
26191     ],
26192     "in_project_namespace": true,
26193     "kind": "theorem",
26194     "module": "PaperIRelease.GrammarPaths",
26195     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.path_action",
26196     "runtime_only": false
26197   },
26198   {
26199     "axioms": [
26200       "propext",
26201       "Classical.choice",
26202       "Quot.sound"
26203     ],
26204     "in_project_namespace": true,
26205     "kind": "definition",
26206     "module": "KomorebiVerification.PacketNaturalityCompletion",
26207     "name": "Komorebi.PacketNaturalityCompletion.Reachability.TransferEdge",
26208     "runtime_only": false
26209   },
26210   {
26211     "axioms": [
26212       "propext",
26213       "Classical.choice",
26214       "Quot.sound"
26215     ],
26216     "in_project_namespace": true,
26217     "kind": "definition",
26218     "module": "KomorebiVerification.ExactCoordinates",
26219     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis",
26220     "runtime_only": false
26221   },
26222   {
26223     "axioms": [
26224       "propext",
26225       "Classical.choice",
26226       "Quot.sound"
26227     ],
26228     "in_project_namespace": true,
26229     "kind": "theorem",
26230     "module": "KomorebiVerification.EllipticAlgorithms",
26231     "name": "Komorebi.EllipticCoordinates.P1_apply",
26232     "runtime_only": false
26233   },
26234   {
26235     "axioms": [
26236       "propext",
26237       "Classical.choice",
26238       "Quot.sound"
26239     ],
26240     "in_project_namespace": true,
26241     "kind": "theorem",
26242     "module": "KomorebiVerification.TopologicalCompletion",
26243     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.transferBlock.eq_1",
26244     "runtime_only": false
26245   },
26246   {
26247     "axioms": [
26248       "propext",
26249       "Quot.sound"
26250     ],
26251     "in_project_namespace": true,
26252     "kind": "definition",
26253     "module": "PaperIRelease.GrammarAlgebra",
26254     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.casesOn",
26255     "runtime_only": false
26256   },
26257   {
26258     "axioms": [],
26259     "in_project_namespace": true,
26260     "kind": "theorem",
26261     "module": "KomorebiVerification.ProjectorCore",
26262     "name": "Komorebi.Seed.OperatorRelation.mk.sizeOf_spec",
26263     "runtime_only": false
26264   },
26265   {
26266     "axioms": [],
26267     "in_project_namespace": true,
26268     "kind": "definition",
26269     "module": "KomorebiVerification.ProjectorCore",
26270     "name": "Komorebi.instInhabitedClaimKind.default",
26271     "runtime_only": false
26272   },
26273   {
26274     "axioms": [
26275       "propext",
26276       "Classical.choice",
26277       "Quot.sound"
26278     ],
26279     "in_project_namespace": true,
26280     "kind": "theorem",
26281     "module": "PaperIRelease.AlgebraSupport",
26282     "name": "Komorebi.PaperIRelease.support_pattern_algebra_criterion",
26283     "runtime_only": false
26284   },
26285   {
26286     "axioms": [],
26287     "in_project_namespace": true,
26288     "kind": "definition",
26289     "module": "KomorebiVerification.ProjectorCore",
26290     "name": "Komorebi.instReprClaimKind",
26291     "runtime_only": false
26292   },
26293   {
26294     "axioms": [
26295       "propext",
26296       "Classical.choice",
26297       "Quot.sound"
26298     ],
26299     "in_project_namespace": false,
26300     "kind": "theorem",
26301     "module": "ReleaseBoundary",
26302     "name": "PaperIBlock08Tests.right_division_coefficient",
26303     "runtime_only": false
26304   },
26305   {
26306     "axioms": [
26307       "propext",
26308       "Classical.choice",
26309       "Quot.sound"
26310     ],
26311     "in_project_namespace": true,
26312     "kind": "theorem",
26313     "module": "KomorebiVerification.PacketNaturalityCompletion",
26314     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_comp",
26315     "runtime_only": false
26316   },
26317   {
26318     "axioms": [
26319       "propext",
26320       "Quot.sound"
26321     ],
26322     "in_project_namespace": false,
26323     "kind": "definition",
26324     "module": "PaperIRelease.TopologySemilinearRank",
26325     "name": "PaperIRelease.TopologySemilinearRank.Generates",
26326     "runtime_only": false
26327   },
26328   {
26329     "axioms": [
26330       "propext",
26331       "Classical.choice",
26332       "Quot.sound"
26333     ],
26334     "in_project_namespace": true,
26335     "kind": "theorem",
26336     "module": "KomorebiVerification.PacketNaturalityCompletion",
26337     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMulClosed_iff_transitive",
26338     "runtime_only": false
26339   },
26340   {
26341     "axioms": [
26342       "propext",
26343       "Classical.choice",
26344       "Quot.sound"
26345     ],
26346     "in_project_namespace": true,
26347     "kind": "definition",
26348     "module": "PaperICompletion4.ResidueQuotient",
26349     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv",
26350     "runtime_only": false
26351   },
26352   {
26353     "axioms": [
26354       "propext",
26355       "Classical.choice",
26356       "Quot.sound"
26357     ],
26358     "in_project_namespace": true,
26359     "kind": "theorem",
26360     "module": "PaperIRelease.PacketAggregation",
26361     "name": "Komorebi.PaperIRelease.PacketAggregation.original_mem_grouped",
26362     "runtime_only": false
26363   },
26364   {
26365     "axioms": [
26366       "propext",
26367       "Classical.choice",
26368       "Quot.sound"
26369     ],
26370     "in_project_namespace": true,
26371     "kind": "theorem",
26372     "module": "PaperIRelease.GeneralNormedPackets",
26373     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetRange_eq_closure_map",
26374     "runtime_only": false
26375   },
26376   {
26377     "axioms": [
26378       "propext",
26379       "Classical.choice",
26380       "Quot.sound"
26381     ],
26382     "in_project_namespace": true,
26383     "kind": "recursor",
26384     "module": "PaperICompletion3.OperatorPrimaryAPI",
26385     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.rec",
26386     "runtime_only": false
26387   },
26388   {
26389     "axioms": [
26390       "propext",
26391       "Classical.choice",
26392       "Quot.sound"
26393     ],
26394     "in_project_namespace": true,
26395     "kind": "definition",
26396     "module": "KomorebiVerification.PaperIBlockCompletion",
26397     "name": "Komorebi.Algebra.MatrixSupportMulClosed",
26398     "runtime_only": false
26399   },
26400   {
26401     "axioms": [
26402       "propext",
26403       "Classical.choice",
26404       "Quot.sound"
26405     ],
26406     "in_project_namespace": false,
26407     "kind": "theorem",
26408     "module": "ReleaseBoundary",
26409     "name": "PaperIBlock08Tests.dualFinite",
26410     "runtime_only": false
26411   },
26412   {
26413     "axioms": [
26414       "propext",
26415       "Quot.sound"
26416     ],
26417     "in_project_namespace": true,
26418     "kind": "theorem",
26419     "module": "PaperIRelease.GrammarModules",
26420     "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_3",
26421     "runtime_only": false
26422   },
26423   {
26424     "axioms": [
26425       "propext",
26426       "Classical.choice",
26427       "Quot.sound"
26428     ],
26429     "in_project_namespace": true,
26430     "kind": "theorem",
26431     "module": "KomorebiVerification.PacketNaturalityCompletion",
26432     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA._proof_1",
26433     "runtime_only": false
26434   },
26435   {
26436     "axioms": [
26437       "propext",
26438       "Classical.choice",
26439       "Quot.sound"
26440     ],
26441     "in_project_namespace": true,
26442     "kind": "theorem",
26443     "module": "PaperIRelease.AlgebraDiagonal",
26444     "name": "Komorebi.PaperIRelease.diagonalProjection_range",
26445     "runtime_only": false
26446   },
26447   {
26448     "axioms": [
26449       "propext",
26450       "Quot.sound"
26451     ],
26452     "in_project_namespace": true,
26453     "kind": "theorem",
26454     "module": "PaperIRelease.GraphSourceCount",
26455     "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_1",
26456     "runtime_only": false
26457   },
26458   {
26459     "axioms": [
26460       "propext",
26461       "Classical.choice",
26462       "Quot.sound"
26463     ],
26464     "in_project_namespace": true,
26465     "kind": "theorem",
26466     "module": "PaperIRelease.PacketLocalRank",
26467     "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_3",
26468     "runtime_only": false
26469   },
26470   {
26471     "axioms": [
26472       "propext",
26473       "Classical.choice",
26474       "Quot.sound"
26475     ],
26476     "in_project_namespace": true,
26477     "kind": "theorem",
26478     "module": "PaperICompletion5.GeometricSeedFormula",
26479     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum",
26480     "runtime_only": false
26481   },
26482   {
26483     "axioms": [
26484       "propext",
26485       "Classical.choice",
26486       "Quot.sound"
26487     ],
26488     "in_project_namespace": true,
26489     "kind": "theorem",
26490     "module": "PaperIRelease.GrammarEquivalence",
26491     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.inj",
26492     "runtime_only": false
26493   },
26494   {
26495     "axioms": [
26496       "propext",
26497       "Quot.sound"
26498     ],
26499     "in_project_namespace": true,
26500     "kind": "theorem",
26501     "module": "PaperIRelease.TensorPackets",
26502     "name": "Komorebi.PaperIRelease.dualPackets._proof_1",
26503     "runtime_only": false
26504   },
26505   {
26506     "axioms": [
26507       "propext",
26508       "Classical.choice",
26509       "Quot.sound"
26510     ],
26511     "in_project_namespace": true,
26512     "kind": "theorem",
26513     "module": "PaperIRelease.AlgebraClassGrouping",
26514     "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_2",
26515     "runtime_only": false
26516   },
26517   {
26518     "axioms": [
26519       "propext",
26520       "Classical.choice",
26521       "Quot.sound"
26522     ],
26523     "in_project_namespace": true,
26524     "kind": "theorem",
26525     "module": "PaperICompletion.ConditionedCoordinates",
26526     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_eq_zero_of_subsingleton",
26527     "runtime_only": false
26528   },
26529   {
26530     "axioms": [
26531       "propext",
26532       "Quot.sound"
26533     ],
26534     "in_project_namespace": true,
26535     "kind": "theorem",
26536     "module": "PaperIRelease.ScalarExtension",
26537     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_5",
26538     "runtime_only": false
26539   },
26540   {
26541     "axioms": [
26542       "propext",
26543       "Classical.choice",
26544       "Quot.sound"
26545     ],
26546     "in_project_namespace": true,
26547     "kind": "definition",
26548     "module": "PaperIRelease.PacketTopology",
26549     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient",
26550     "runtime_only": false
26551   },
26552   {
26553     "axioms": [
26554       "propext",
26555       "Classical.choice",
26556       "Quot.sound"
26557     ],
26558     "in_project_namespace": true,
26559     "kind": "theorem",
26560     "module": "PaperIRelease.CoordinateTransport",
26561     "name": "Komorebi.PaperIRelease.CoordinateTransport.support_pattern_invariant",
26562     "runtime_only": false
26563   },
26564   {
26565     "axioms": [
26566       "propext",
26567       "Quot.sound"
26568     ],
26569     "in_project_namespace": true,
26570     "kind": "theorem",
26571     "module": "KomorebiVerification.ProjectorCore",
26572     "name": "Komorebi.Polyphase.coeffSection_one_zero",
26573     "runtime_only": false
26574   },
26575   {
26576     "axioms": [
26577       "propext",
26578       "Classical.choice",
26579       "Quot.sound"
26580     ],
26581     "in_project_namespace": true,
26582     "kind": "definition",
26583     "module": "KomorebiVerification.ProjectorCore",
26584     "name": "Komorebi.Foundation.LinearProjectorFamily.noConfusionType",
26585     "runtime_only": false
26586   },
26587   {
26588     "axioms": [
26589       "propext",
26590       "Classical.choice",
26591       "Quot.sound"
26592     ],
26593     "in_project_namespace": true,
26594     "kind": "theorem",
26595     "module": "PaperICompletion4.OperatorIntrinsicFormula",
26596     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsicSeedMaximum",
26597     "runtime_only": false
26598   },
26599   {
26600     "axioms": [
26601       "propext",
26602       "Quot.sound"
26603     ],
26604     "in_project_namespace": false,
26605     "kind": "definition",
26606     "module": "PaperIRelease.GrammarPaths",
26607     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.splitter",
26608     "runtime_only": false
26609   },
26610   {
26611     "axioms": [],
26612     "in_project_namespace": true,
26613     "kind": "definition",
26614     "module": "PaperIRelease.GrammarPaths",
26615     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.casesOn",
26616     "runtime_only": false
26617   },
26618   {
26619     "axioms": [
26620       "propext",
26621       "Classical.choice",
26622       "Quot.sound"
26623     ],
26624     "in_project_namespace": true,
26625     "kind": "theorem",
26626     "module": "PaperIRelease.PacketAggregation",
26627     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis_synthesis",
26628     "runtime_only": false
26629   },
26630   {
26631     "axioms": [
26632       "propext",
26633       "Classical.choice",
26634       "Quot.sound"
26635     ],
26636     "in_project_namespace": true,
26637     "kind": "theorem",
26638     "module": "KomorebiVerification.EllipticAlgorithms",
26639     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_5",
26640     "runtime_only": false
26641   },
26642   {
26643     "axioms": [
26644       "propext",
26645       "Classical.choice",
26646       "Quot.sound"
26647     ],
26648     "in_project_namespace": false,
26649     "kind": "theorem",
26650     "module": "PaperIRelease.TopologyCountablePackets",
26651     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_3",
26652     "runtime_only": false
26653   },
26654   {
26655     "axioms": [
26656       "propext",
26657       "Quot.sound"
26658     ],
26659     "in_project_namespace": true,
26660     "kind": "theorem",
26661     "module": "PaperIRelease.GrammarPaths",
26662     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_1",
26663     "runtime_only": false
26664   },
26665   {
26666     "axioms": [
26667       "propext",
26668       "Classical.choice",
26669       "Quot.sound"
26670     ],
26671     "in_project_namespace": true,
26672     "kind": "theorem",
26673     "module": "PaperICompletion8.ProductPresentation",
26674     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_2",
26675     "runtime_only": false
26676   },
26677   {
26678     "axioms": [
26679       "propext",
26680       "Classical.choice",
26681       "Quot.sound"
26682     ],
26683     "in_project_namespace": true,
26684     "kind": "theorem",
26685     "module": "KomorebiVerification.PacketNaturalityCompletion",
26686     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_naturality_package",
26687     "runtime_only": false
26688   },
26689   {
26690     "axioms": [
26691       "propext",
26692       "Classical.choice",
26693       "Quot.sound"
26694     ],
26695     "in_project_namespace": false,
26696     "kind": "theorem",
26697     "module": "PaperIRelease.TopologyUnconditional",
26698     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space.ext_iff",
26699     "runtime_only": false
26700   },
26701   {
26702     "axioms": [
26703       "propext",
26704       "Classical.choice",
26705       "Quot.sound"
26706     ],
26707     "in_project_namespace": true,
26708     "kind": "definition",
26709     "module": "KomorebiVerification.PacketNaturalityCompletion",
26710     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.noConfusion",
26711     "runtime_only": false
26712   },
26713   {
26714     "axioms": [
26715       "propext",
26716       "Classical.choice",
26717       "Quot.sound"
26718     ],
26719     "in_project_namespace": true,
26720     "kind": "definition",
26721     "module": "PaperIRelease.CategoryPackets",
26722     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.noConfusion",
26723     "runtime_only": false
26724   },
26725   {
26726     "axioms": [
26727       "propext",
26728       "Classical.choice",
26729       "Quot.sound"
26730     ],
26731     "in_project_namespace": false,
26732     "kind": "theorem",
26733     "module": "PaperIRelease.TopologyUnconditional",
26734     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.sizeOf_spec",
26735     "runtime_only": false
26736   },
26737   {
26738     "axioms": [
26739       "propext",
26740       "Quot.sound"
26741     ],
26742     "in_project_namespace": true,
26743     "kind": "theorem",
26744     "module": "KomorebiVerification.PacketNaturalityCompletion",
26745     "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugateEnd_eq_zero_iff",
26746     "runtime_only": false
26747   },
26748   {
26749     "axioms": [
26750       "propext",
26751       "Classical.choice",
26752       "Quot.sound"
26753     ],
26754     "in_project_namespace": true,
26755     "kind": "theorem",
26756     "module": "PaperIRelease.AlgebraTransfer",
26757     "name": "Komorebi.PaperIRelease.packetPure_of_mem_range",
26758     "runtime_only": false
26759   },
26760   {
26761     "axioms": [
26762       "propext",
26763       "Classical.choice",
26764       "Quot.sound"
26765     ],
26766     "in_project_namespace": true,
26767     "kind": "theorem",
26768     "module": "PaperICompletion4.OperatorIntrinsicFormula",
26769     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_6",
26770     "runtime_only": false
26771   },
26772   {
26773     "axioms": [
26774       "propext",
26775       "Quot.sound"
26776     ],
26777     "in_project_namespace": true,
26778     "kind": "theorem",
26779     "module": "PaperIRelease.GrammarTyped",
26780     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction._proof_1",
26781     "runtime_only": false
26782   },
26783   {
26784     "axioms": [
26785       "propext",
26786       "Classical.choice",
26787       "Quot.sound"
26788     ],
26789     "in_project_namespace": true,
26790     "kind": "definition",
26791     "module": "KomorebiVerification.TopologicalCompletion",
26792     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower",
26793     "runtime_only": false
26794   },
26795   {
26796     "axioms": [
26797       "propext",
26798       "Classical.choice",
26799       "Quot.sound"
26800     ],
26801     "in_project_namespace": true,
26802     "kind": "theorem",
26803     "module": "KomorebiVerification.PacketNaturalityCompletion",
26804     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.no_u_supported_seeds_generate",
26805     "runtime_only": false
26806   },
26807   {
26808     "axioms": [],
26809     "in_project_namespace": true,
26810     "kind": "theorem",
26811     "module": "KomorebiVerification.ProjectorCore",
26812     "name": "Komorebi.instDecidableEqClaimKind._proof_1",
26813     "runtime_only": false
26814   },
26815   {
26816     "axioms": [],
26817     "in_project_namespace": true,
26818     "kind": "definition",
26819     "module": "KomorebiVerification.ProjectorCore",
26820     "name": "Komorebi.instBEqFormalizationStatus",
26821     "runtime_only": false
26822   },
26823   {
26824     "axioms": [
26825       "propext",
26826       "Classical.choice",
26827       "Quot.sound"
26828     ],
26829     "in_project_namespace": true,
26830     "kind": "theorem",
26831     "module": "PaperIRelease.PacketTopologyGeneral",
26832     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM._proof_1",
26833     "runtime_only": false
26834   },
26835   {
26836     "axioms": [
26837       "propext",
26838       "Classical.choice",
26839       "Quot.sound"
26840     ],
26841     "in_project_namespace": true,
26842     "kind": "theorem",
26843     "module": "PaperICompletion3.PrimarySeedFormula",
26844     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.familyGenerates_iff_polynomialModule",
26845     "runtime_only": false
26846   },
26847   {
26848     "axioms": [
26849       "propext",
26850       "Classical.choice",
26851       "Quot.sound"
26852     ],
26853     "in_project_namespace": true,
26854     "kind": "theorem",
26855     "module": "KomorebiVerification.PacketNaturalityCompletion",
26856     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_4",
26857     "runtime_only": false
26858   },
26859   {
26860     "axioms": [
26861       "propext",
26862       "Classical.choice",
26863       "Quot.sound"
26864     ],
26865     "in_project_namespace": true,
26866     "kind": "theorem",
26867     "module": "PaperICompletion6.ScalarExtension",
26868     "name": "Komorebi.PaperICompletion6.ScalarExtension.tensor_endHom_eq_baseChange",
26869     "runtime_only": false
26870   },
26871   {
26872     "axioms": [],
26873     "in_project_namespace": true,
26874     "kind": "definition",
26875     "module": "KomorebiVerification.ProjectorCore",
26876     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._sunfold",
26877     "runtime_only": false
26878   },
26879   {
26880     "axioms": [],
26881     "in_project_namespace": true,
26882     "kind": "definition",
26883     "module": "KomorebiVerification.ProjectorCore",
26884     "name": "Komorebi.FiniteDifference.iteratedDiff._f",
26885     "runtime_only": false
26886   },
26887   {
26888     "axioms": [
26889       "propext",
26890       "Quot.sound"
26891     ],
26892     "in_project_namespace": true,
26893     "kind": "theorem",
26894     "module": "KomorebiVerification.ProjectorCore",
26895     "name": "Komorebi.Quantum.diagonalApply_one",
26896     "runtime_only": false
26897   },
26898   {
26899     "axioms": [
26900       "propext",
26901       "Classical.choice",
26902       "Quot.sound"
26903     ],
26904     "in_project_namespace": true,
26905     "kind": "theorem",
26906     "module": "PaperICompletion4.ResidueQuotient",
26907     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_7",
26908     "runtime_only": false
26909   },
26910   {
26911     "axioms": [
26912       "propext",
26913       "Classical.choice",
26914       "Quot.sound"
26915     ],
26916     "in_project_namespace": true,
26917     "kind": "theorem",
26918     "module": "PaperICompletion.ConditionedCoordinates",
26919     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.norm_coordinateOperator_le",
26920     "runtime_only": false
26921   },
26922   {
26923     "axioms": [],
26924     "in_project_namespace": true,
26925     "kind": "definition",
26926     "module": "KomorebiVerification.ProjectorCore",
26927     "name": "Komorebi.Seed.OperatorExpr.eval._sunfold",
26928     "runtime_only": false
26929   },
26930   {
26931     "axioms": [
26932       "propext",
26933       "Classical.choice",
26934       "Quot.sound"
26935     ],
26936     "in_project_namespace": true,
26937     "kind": "theorem",
26938     "module": "KomorebiVerification.SingleOperatorGraph",
26939     "name": "Komorebi.SingleOperatorGraph.diagonalizable_seedNumber_isLeast",
26940     "runtime_only": false
26941   },
26942   {
26943     "axioms": [
26944       "propext",
26945       "Classical.choice",
26946       "Quot.sound"
26947     ],
26948     "in_project_namespace": true,
26949     "kind": "theorem",
26950     "module": "PaperICompletion8.SemisimpleExistence",
26951     "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_semisimple_seed_formula",
26952     "runtime_only": false
26953   },
26954   {
26955     "axioms": [
26956       "propext",
26957       "Classical.choice",
26958       "Quot.sound"
26959     ],
26960     "in_project_namespace": false,
26961     "kind": "theorem",
26962     "module": "PaperIRelease.TopologySemilinearRank",
26963     "name": "PaperIRelease.TopologySemilinearRank.generates_iff_operator_generates",
26964     "runtime_only": false
26965   },
26966   {
26967     "axioms": [
26968       "propext",
26969       "Classical.choice",
26970       "Quot.sound"
26971     ],
26972     "in_project_namespace": true,
26973     "kind": "theorem",
26974     "module": "PaperIRelease.PacketAggregation",
26975     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_3",
26976     "runtime_only": false
26977   },
26978   {
26979     "axioms": [
26980       "propext",
26981       "Classical.choice",
26982       "Quot.sound"
26983     ],
26984     "in_project_namespace": true,
26985     "kind": "theorem",
26986     "module": "PaperIRelease.GeneralConditionedCoordinates",
26987     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.coordinateOperator_inverse",
26988     "runtime_only": false
26989   },
26990   {
26991     "axioms": [
26992       "propext",
26993       "Classical.choice",
26994       "Quot.sound"
26995     ],
26996     "in_project_namespace": true,
26997     "kind": "theorem",
26998     "module": "KomorebiVerification.TopologicalCompletion",
26999     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.isClosed_packet",
27000     "runtime_only": false
27001   },
27002   {
27003     "axioms": [
27004       "propext",
27005       "Classical.choice",
27006       "Quot.sound"
27007     ],
27008     "in_project_namespace": true,
27009     "kind": "theorem",
27010     "module": "PaperIRelease.PacketAggregation",
27011     "name": "Komorebi.PaperIRelease.PacketAggregation.grouped_nonzero",
27012     "runtime_only": false
27013   },
27014   {
27015     "axioms": [],
27016     "in_project_namespace": true,
27017     "kind": "definition",
27018     "module": "PaperIRelease.GrammarPaths",
27019     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorElim",
27020     "runtime_only": false
27021   },
27022   {
27023     "axioms": [
27024       "propext",
27025       "Quot.sound"
27026     ],
27027     "in_project_namespace": true,
27028     "kind": "theorem",
27029     "module": "KomorebiVerification.SeedRankOperations",
27030     "name": "Komorebi.SeedRankOperations.tensorLeftTowerInstalled",
27031     "runtime_only": false
27032   },
27033   {
27034     "axioms": [],
27035     "in_project_namespace": true,
27036     "kind": "definition",
27037     "module": "PaperIRelease.GrammarPaths",
27038     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorIdx",
27039     "runtime_only": false
27040   },
27041   {
27042     "axioms": [
27043       "propext",
27044       "Classical.choice",
27045       "Quot.sound"
27046     ],
27047     "in_project_namespace": false,
27048     "kind": "theorem",
27049     "module": "ReleaseBoundary",
27050     "name": "PaperIBlock08Tests.regular_direct_sum_roundtrip",
27051     "runtime_only": false
27052   },
27053   {
27054     "axioms": [
27055       "propext",
27056       "Classical.choice",
27057       "Quot.sound"
27058     ],
27059     "in_project_namespace": true,
27060     "kind": "theorem",
27061     "module": "PaperICompletion.ConditionedCoordinates",
27062     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.one_le_conditionNumber",
27063     "runtime_only": false
27064   },
27065   {
27066     "axioms": [
27067       "propext",
27068       "Classical.choice",
27069       "Quot.sound"
27070     ],
27071     "in_project_namespace": true,
27072     "kind": "theorem",
27073     "module": "PaperIRelease.PacketSourceLower",
27074     "name": "Komorebi.PaperIRelease.sum_localNonzeroSeeds_card_le",
27075     "runtime_only": false
27076   },
27077   {
27078     "axioms": [
27079       "propext",
27080       "Classical.choice",
27081       "Quot.sound"
27082     ],
27083     "in_project_namespace": false,
27084     "kind": "definition",
27085     "module": "PaperIRelease.TopologyUnconditional",
27086     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.recOn",
27087     "runtime_only": false
27088   },
27089   {
27090     "axioms": [],
27091     "in_project_namespace": true,
27092     "kind": "definition",
27093     "module": "KomorebiVerification.ProjectorCore",
27094     "name": "Komorebi.ClaimRecord.id",
27095     "runtime_only": false
27096   },
27097   {
27098     "axioms": [
27099       "propext",
27100       "Classical.choice",
27101       "Quot.sound"
27102     ],
27103     "in_project_namespace": true,
27104     "kind": "theorem",
27105     "module": "PaperIRelease.PacketDescent",
27106     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_5",
27107     "runtime_only": false
27108   },
27109   {
27110     "axioms": [
27111       "propext",
27112       "Classical.choice",
27113       "Quot.sound"
27114     ],
27115     "in_project_namespace": true,
27116     "kind": "recursor",
27117     "module": "PaperIRelease.CategoryPackets",
27118     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.rec",
27119     "runtime_only": false
27120   },
27121   {
27122     "axioms": [
27123       "propext",
27124       "Classical.choice",
27125       "Quot.sound"
27126     ],
27127     "in_project_namespace": true,
27128     "kind": "definition",
27129     "module": "PaperICompletion3.OperatorPrimaryAPI",
27130     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.casesOn",
27131     "runtime_only": false
27132   },
27133   {
27134     "axioms": [
27135       "propext",
27136       "Classical.choice",
27137       "Quot.sound"
27138     ],
27139     "in_project_namespace": true,
27140     "kind": "theorem",
27141     "module": "PaperIRelease.GrammarEquivalence",
27142     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_7",
27143     "runtime_only": false
27144   },
27145   {
27146     "axioms": [
27147       "propext",
27148       "Classical.choice",
27149       "Quot.sound"
27150     ],
27151     "in_project_namespace": false,
27152     "kind": "theorem",
27153     "module": "PaperIRelease.TopologyUnconditional",
27154     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.inj",
27155     "runtime_only": false
27156   },
27157   {
27158     "axioms": [
27159       "propext",
27160       "Classical.choice",
27161       "Quot.sound"
27162     ],
27163     "in_project_namespace": true,
27164     "kind": "theorem",
27165     "module": "PaperICompletion3.OperatorPrimaryAPI",
27166     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.inj",
27167     "runtime_only": false
27168   },
27169   {
27170     "axioms": [
27171       "propext",
27172       "Classical.choice",
27173       "Quot.sound"
27174     ],
27175     "in_project_namespace": true,
27176     "kind": "definition",
27177     "module": "PaperIRelease.CategoryPackets",
27178     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.recOn",
27179     "runtime_only": false
27180   },
27181   {
27182     "axioms": [
27183       "propext",
27184       "Classical.choice",
27185       "Quot.sound"
27186     ],
27187     "in_project_namespace": true,
27188     "kind": "definition",
27189     "module": "PaperIRelease.CategoryPackets",
27190     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.casesOn",
27191     "runtime_only": false
27192   },
27193   {
27194     "axioms": [
27195       "propext",
27196       "Classical.choice",
27197       "Quot.sound"
27198     ],
27199     "in_project_namespace": true,
27200     "kind": "theorem",
27201     "module": "PaperICompletion7.ModuleTop",
27202     "name": "Komorebi.PaperICompletion7.ModuleTop.seedRank_eq_idealTop",
27203     "runtime_only": false
27204   },
27205   {
27206     "axioms": [
27207       "propext",
27208       "Classical.choice",
27209       "Quot.sound"
27210     ],
27211     "in_project_namespace": true,
27212     "kind": "theorem",
27213     "module": "PaperIRelease.GrammarEquivalence",
27214     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.arrow_natural",
27215     "runtime_only": false
27216   },
27217   {
27218     "axioms": [
27219       "propext",
27220       "Quot.sound"
27221     ],
27222     "in_project_namespace": true,
27223     "kind": "definition",
27224     "module": "PaperIRelease.GrammarAlgebra",
27225     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.noConfusion",
27226     "runtime_only": false
27227   },
27228   {
27229     "axioms": [
27230       "propext",
27231       "Classical.choice",
27232       "Quot.sound"
27233     ],
27234     "in_project_namespace": true,
27235     "kind": "definition",
27236     "module": "PaperIRelease.PacketTopology",
27237     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseAmbient",
27238     "runtime_only": false
27239   },
27240   {
27241     "axioms": [
27242       "propext"
27243     ],
27244     "in_project_namespace": true,
27245     "kind": "definition",
27246     "module": "KomorebiVerification.PathGraphKrylov",
27247     "name": "Komorebi.PathGraphKrylov.leftTerm",
27248     "runtime_only": false
27249   },
27250   {
27251     "axioms": [
27252       "propext",
27253       "Quot.sound"
27254     ],
27255     "in_project_namespace": true,
27256     "kind": "theorem",
27257     "module": "PaperIRelease.PolynomialModule",
27258     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_2",
27259     "runtime_only": false
27260   },
27261   {
27262     "axioms": [],
27263     "in_project_namespace": true,
27264     "kind": "constructor",
27265     "module": "KomorebiVerification.ProjectorCore",
27266     "name": "Komorebi.ClaimRecord.mk",
27267     "runtime_only": false
27268   },
27269   {
27270     "axioms": [
27271       "propext",
27272       "Classical.choice",
27273       "Quot.sound"
27274     ],
27275     "in_project_namespace": true,
27276     "kind": "theorem",
27277     "module": "KomorebiVerification.EllipticAlgorithms",
27278     "name": "Komorebi.EllipticCoordinates.y_sq",
27279     "runtime_only": false
27280   },
27281   {
27282     "axioms": [
27283       "propext",
27284       "Classical.choice",
27285       "Quot.sound"
27286     ],
27287     "in_project_namespace": true,
27288     "kind": "theorem",
27289     "module": "KomorebiVerification.SingleOperatorGraph",
27290     "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_surjective",
27291     "runtime_only": false
27292   },
27293   {
27294     "axioms": [
27295       "propext",
27296       "Classical.choice",
27297       "Quot.sound"
27298     ],
27299     "in_project_namespace": true,
27300     "kind": "theorem",
27301     "module": "PaperICompletion.ConditionedCoordinates",
27302     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packet_conditioned_coordinate_bounds",
27303     "runtime_only": false
27304   },
27305   {
27306     "axioms": [
27307       "propext",
27308       "Classical.choice",
27309       "Quot.sound"
27310     ],
27311     "in_project_namespace": false,
27312     "kind": "definition",
27313     "module": "PaperIRelease.TopologyCountablePackets",
27314     "name": "PaperIRelease.TopologyCountablePackets.Projectors.noConfusionType",
27315     "runtime_only": false
27316   },
27317   {
27318     "axioms": [
27319       "propext",
27320       "Classical.choice",
27321       "Quot.sound"
27322     ],
27323     "in_project_namespace": true,
27324     "kind": "theorem",
27325     "module": "PaperIRelease.PacketTopology",
27326     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM_toLinearMap",
27327     "runtime_only": false
27328   },
27329   {
27330     "axioms": [],
27331     "in_project_namespace": true,
27332     "kind": "theorem",
27333     "module": "KomorebiVerification.ProjectorCore",
27334     "name": "Komorebi.Seed.OperatorExpr.eval_comp",
27335     "runtime_only": false
27336   },
27337   {
27338     "axioms": [
27339       "propext",
27340       "Classical.choice",
27341       "Quot.sound"
27342     ],
27343     "in_project_namespace": false,
27344     "kind": "theorem",
27345     "module": "PaperIRelease.AlgebraPreorder",
27346     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_length_bound",
27347     "runtime_only": false
27348   },
27349   {
27350     "axioms": [
27351       "propext",
27352       "Classical.choice",
27353       "Quot.sound"
27354     ],
27355     "in_project_namespace": false,
27356     "kind": "theorem",
27357     "module": "ReleaseBoundary",
27358     "name": "PaperIBlock08Tests.dualLinearEquiv._proof_4",
27359     "runtime_only": false
27360   },
27361   {
27362     "axioms": [
27363       "propext",
27364       "Classical.choice",
27365       "Quot.sound"
27366     ],
27367     "in_project_namespace": true,
27368     "kind": "theorem",
27369     "module": "PaperIRelease.PacketUniversal",
27370     "name": "Komorebi.PaperIRelease.PacketUniversal.unique_packet_extension",
27371     "runtime_only": false
27372   },
27373   {
27374     "axioms": [],
27375     "in_project_namespace": true,
27376     "kind": "definition",
27377     "module": "KomorebiVerification.ProjectorCore",
27378     "name": "Komorebi.Seed.OperatorRelation.casesOn",
27379     "runtime_only": false
27380   },
27381   {
27382     "axioms": [
27383       "propext",
27384       "Classical.choice",
27385       "Quot.sound"
27386     ],
27387     "in_project_namespace": true,
27388     "kind": "theorem",
27389     "module": "KomorebiVerification.Basic",
27390     "name": "KomorebiVerification.sumFirstOddNumbers",
27391     "runtime_only": false
27392   },
27393   {
27394     "axioms": [
27395       "propext",
27396       "Classical.choice",
27397       "Quot.sound"
27398     ],
27399     "in_project_namespace": true,
27400     "kind": "definition",
27401     "module": "KomorebiVerification.PacketNaturalityCompletion",
27402     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.algebraMap",
27403     "runtime_only": false
27404   },
27405   {
27406     "axioms": [],
27407     "in_project_namespace": true,
27408     "kind": "definition",
27409     "module": "KomorebiVerification.ProjectorCore",
27410     "name": "Komorebi.Seed.instReprOperatorExpr.repr.match_1",
27411     "runtime_only": false
27412   },
27413   {
27414     "axioms": [],
27415     "in_project_namespace": true,
27416     "kind": "definition",
27417     "module": "KomorebiVerification.PacketNaturalityCompletion",
27418     "name": "Komorebi.PacketNaturalityCompletion.Reachability.OrbitSet",
27419     "runtime_only": false
27420   },
27421   {
27422     "axioms": [
27423       "propext",
27424       "Classical.choice",
27425       "Quot.sound"
27426     ],
27427     "in_project_namespace": true,
27428     "kind": "theorem",
27429     "module": "KomorebiVerification.TopologicalCompletion",
27430     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis._proof_1",
27431     "runtime_only": false
27432   },
27433   {
27434     "axioms": [
27435       "propext"
27436     ],
27437     "in_project_namespace": true,
27438     "kind": "theorem",
27439     "module": "KomorebiVerification.TopologicalCompletion",
27440     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit._simp_1_1",
27441     "runtime_only": false
27442   },
27443   {
27444     "axioms": [],
27445     "in_project_namespace": true,
27446     "kind": "definition",
27447     "module": "PaperIRelease.GrammarPaths",
27448     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn.go",
27449     "runtime_only": false
27450   },
27451   {
27452     "axioms": [
27453       "propext",
27454       "Classical.choice",
27455       "Quot.sound"
27456     ],
27457     "in_project_namespace": true,
27458     "kind": "definition",
27459     "module": "PaperIRelease.BoundedStar",
27460     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra",
27461     "runtime_only": false
27462   },
27463   {
27464     "axioms": [
27465       "propext",
27466       "Classical.choice",
27467       "Quot.sound"
27468     ],
27469     "in_project_namespace": true,
27470     "kind": "theorem",
27471     "module": "KomorebiVerification.SingleOperatorGraph",
27472     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow_basisFun",
27473     "runtime_only": false
27474   },
27475   {
27476     "axioms": [
27477       "propext",
27478       "Classical.choice",
27479       "Quot.sound"
27480     ],
27481     "in_project_namespace": false,
27482     "kind": "theorem",
27483     "module": "PaperIRelease.TopologyUnconditional",
27484     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_3",
27485     "runtime_only": false
27486   },
27487   {
27488     "axioms": [
27489       "propext",
27490       "Classical.choice",
27491       "Quot.sound"
27492     ],
27493     "in_project_namespace": true,
27494     "kind": "definition",
27495     "module": "PaperIRelease.PacketTopology",
27496     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM",
27497     "runtime_only": false
27498   },
27499   {
27500     "axioms": [
27501       "propext",
27502       "Quot.sound"
27503     ],
27504     "in_project_namespace": true,
27505     "kind": "theorem",
27506     "module": "PaperIRelease.GrammarTyped",
27507     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction._proof_2",
27508     "runtime_only": false
27509   },
27510   {
27511     "axioms": [
27512       "propext",
27513       "Classical.choice",
27514       "Quot.sound"
27515     ],
27516     "in_project_namespace": true,
27517     "kind": "theorem",
27518     "module": "KomorebiVerification.EllipticAlgorithms",
27519     "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_1",
27520     "runtime_only": false
27521   },
27522   {
27523     "axioms": [
27524       "propext",
27525       "Classical.choice",
27526       "Quot.sound"
27527     ],
27528     "in_project_namespace": true,
27529     "kind": "theorem",
27530     "module": "KomorebiVerification.EllipticAlgorithms",
27531     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_def",
27532     "runtime_only": false
27533   },
27534   {
27535     "axioms": [
27536       "propext",
27537       "Classical.choice",
27538       "Quot.sound"
27539     ],
27540     "in_project_namespace": true,
27541     "kind": "theorem",
27542     "module": "PaperIRelease.PacketTopology",
27543     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_1",
27544     "runtime_only": false
27545   },
27546   {
27547     "axioms": [],
27548     "in_project_namespace": true,
27549     "kind": "definition",
27550     "module": "KomorebiVerification.ProjectorCore",
27551     "name": "Komorebi.Seed.OperatorExpr.noConfusionType",
27552     "runtime_only": false
27553   },
27554   {
27555     "axioms": [
27556       "propext",
27557       "Classical.choice",
27558       "Quot.sound"
27559     ],
27560     "in_project_namespace": true,
27561     "kind": "recursor",
27562     "module": "PaperIRelease.GrammarEquivalence",
27563     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.rec",
27564     "runtime_only": false
27565   },
27566   {
27567     "axioms": [
27568       "propext",
27569       "Classical.choice",
27570       "Quot.sound"
27571     ],
27572     "in_project_namespace": true,
27573     "kind": "theorem",
27574     "module": "KomorebiVerification.PacketNaturalityCompletion",
27575     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_seedRank_le",
27576     "runtime_only": false
27577   },
27578   {
27579     "axioms": [
27580       "propext",
27581       "Classical.choice",
27582       "Quot.sound"
27583     ],
27584     "in_project_namespace": false,
27585     "kind": "theorem",
27586     "module": "PaperIRelease.TopologyCountablePackets",
27587     "name": "PaperIRelease.TopologyCountablePackets.Projectors.idempotent",
27588     "runtime_only": false
27589   },
27590   {
27591     "axioms": [
27592       "propext",
27593       "Quot.sound"
27594     ],
27595     "in_project_namespace": true,
27596     "kind": "theorem",
27597     "module": "PaperIRelease.GrammarModules",
27598     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_3",
27599     "runtime_only": false
27600   },
27601   {
27602     "axioms": [
27603       "propext",
27604       "Classical.choice",
27605       "Quot.sound"
27606     ],
27607     "in_project_namespace": false,
27608     "kind": "theorem",
27609     "module": "PaperIRelease.TopologyUnconditional",
27610     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.injEq",
27611     "runtime_only": false
27612   },
27613   {
27614     "axioms": [
27615       "propext",
27616       "Classical.choice",
27617       "Quot.sound"
27618     ],
27619     "in_project_namespace": true,
27620     "kind": "theorem",
27621     "module": "KomorebiVerification.ExactCoordinates",
27622     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_4",
27623     "runtime_only": false
27624   },
27625   {
27626     "axioms": [
27627       "propext",
27628       "Classical.choice",
27629       "Quot.sound"
27630     ],
27631     "in_project_namespace": true,
27632     "kind": "definition",
27633     "module": "PaperIRelease.CategoryPackets",
27634     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject._sizeOf_inst",
27635     "runtime_only": false
27636   },
27637   {
27638     "axioms": [
27639       "propext",
27640       "Classical.choice",
27641       "Quot.sound"
27642     ],
27643     "in_project_namespace": true,
27644     "kind": "theorem",
27645     "module": "KomorebiVerification.PathGraphKrylov",
27646     "name": "Komorebi.PathGraphKrylov.walkMatrix_apply",
27647     "runtime_only": false
27648   },
27649   {
27650     "axioms": [
27651       "propext",
27652       "Classical.choice",
27653       "Quot.sound"
27654     ],
27655     "in_project_namespace": true,
27656     "kind": "theorem",
27657     "module": "KomorebiVerification.SingleOperatorGraph",
27658     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective",
27659     "runtime_only": false
27660   },
27661   {
27662     "axioms": [
27663       "propext",
27664       "Quot.sound"
27665     ],
27666     "in_project_namespace": true,
27667     "kind": "theorem",
27668     "module": "KomorebiVerification.PaperITransport",
27669     "name": "Komorebi.Foundation.conjugateEnd.eq_1",
27670     "runtime_only": false
27671   },
27672   {
27673     "axioms": [
27674       "propext",
27675       "Classical.choice",
27676       "Quot.sound"
27677     ],
27678     "in_project_namespace": true,
27679     "kind": "theorem",
27680     "module": "PaperIRelease.GeneralNormedPackets",
27681     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.isClosed_packet",
27682     "runtime_only": false
27683   },
27684   {
27685     "axioms": [
27686       "propext",
27687       "Classical.choice",
27688       "Quot.sound"
27689     ],
27690     "in_project_namespace": true,
27691     "kind": "theorem",
27692     "module": "KomorebiVerification.KernelAudit",
27693     "name": "Komorebi.Verification.parity_refinement",
27694     "runtime_only": false
27695   },
27696   {
27697     "axioms": [
27698       "propext",
27699       "Classical.choice",
27700       "Quot.sound"
27701     ],
27702     "in_project_namespace": true,
27703     "kind": "theorem",
27704     "module": "KomorebiVerification.PacketNaturalityCompletion",
27705     "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_3",
27706     "runtime_only": false
27707   },
27708   {
27709     "axioms": [
27710       "propext",
27711       "Classical.choice",
27712       "Quot.sound"
27713     ],
27714     "in_project_namespace": true,
27715     "kind": "theorem",
27716     "module": "PaperIRelease.GrammarIdeal",
27717     "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented_respects",
27718     "runtime_only": false
27719   },
27720   {
27721     "axioms": [
27722       "propext",
27723       "Quot.sound"
27724     ],
27725     "in_project_namespace": true,
27726     "kind": "theorem",
27727     "module": "KomorebiVerification.SeedRankOperations",
27728     "name": "Komorebi.SeedRankOperations.prodFstSemilinear._proof_2",
27729     "runtime_only": false
27730   },
27731   {
27732     "axioms": [
27733       "propext",
27734       "Classical.choice",
27735       "Quot.sound"
27736     ],
27737     "in_project_namespace": true,
27738     "kind": "definition",
27739     "module": "PaperIRelease.GrammarTyped",
27740     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk._flat_ctor",
27741     "runtime_only": false
27742   },
27743   {
27744     "axioms": [
27745       "propext",
27746       "Classical.choice",
27747       "Quot.sound"
27748     ],
27749     "in_project_namespace": true,
27750     "kind": "recursor",
27751     "module": "PaperIRelease.TopologyCategories",
27752     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.rec",
27753     "runtime_only": false
27754   },
27755   {
27756     "axioms": [
27757       "propext",
27758       "Classical.choice",
27759       "Quot.sound"
27760     ],
27761     "in_project_namespace": false,
27762     "kind": "theorem",
27763     "module": "PaperIRelease.TopologyUnconditional",
27764     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_5",
27765     "runtime_only": false
27766   },
27767   {
27768     "axioms": [
27769       "propext",
27770       "Classical.choice",
27771       "Quot.sound"
27772     ],
27773     "in_project_namespace": false,
27774     "kind": "theorem",
27775     "module": "ReleaseBoundary",
27776     "name": "PaperIBlock08Tests.quaternion_regular_multiplicity_one",
27777     "runtime_only": false
27778   },
27779   {
27780     "axioms": [
27781       "propext",
27782       "Classical.choice",
27783       "Quot.sound"
27784     ],
27785     "in_project_namespace": true,
27786     "kind": "definition",
27787     "module": "PaperIRelease.TopologyCategories",
27788     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism._sizeOf_inst",
27789     "runtime_only": false
27790   },
27791   {
27792     "axioms": [],
27793     "in_project_namespace": true,
27794     "kind": "definition",
27795     "module": "KomorebiVerification.ProjectorCore",
27796     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._unsafe_rec",
27797     "runtime_only": true
27798   },
27799   {
27800     "axioms": [
27801       "propext",
27802       "Classical.choice",
27803       "Quot.sound"
27804     ],
27805     "in_project_namespace": false,
27806     "kind": "theorem",
27807     "module": "ReleaseBoundary",
27808     "name": "PaperIBlock08Tests.regular_columns_intertwines",
27809     "runtime_only": false
27810   },
27811   {
27812     "axioms": [
27813       "propext",
27814       "Classical.choice",
27815       "Quot.sound"
27816     ],
27817     "in_project_namespace": true,
27818     "kind": "definition",
27819     "module": "PaperICompletion3.PrimarySeedFormula",
27820     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity",
27821     "runtime_only": false
27822   },
27823   {
27824     "axioms": [
27825       "propext",
27826       "Classical.choice",
27827       "Quot.sound"
27828     ],
27829     "in_project_namespace": true,
27830     "kind": "definition",
27831     "module": "KomorebiVerification.TopologicalCompletion",
27832     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet",
27833     "runtime_only": false
27834   },
27835   {
27836     "axioms": [
27837       "propext",
27838       "Classical.choice",
27839       "Quot.sound"
27840     ],
27841     "in_project_namespace": true,
27842     "kind": "theorem",
27843     "module": "PaperIRelease.AlgebraTransfer",
27844     "name": "Komorebi.PaperIRelease.packetWordSum.eq_def",
27845     "runtime_only": false
27846   },
27847   {
27848     "axioms": [
27849       "propext",
27850       "Classical.choice",
27851       "Quot.sound"
27852     ],
27853     "in_project_namespace": true,
27854     "kind": "definition",
27855     "module": "PaperIRelease.GrammarEquivalence",
27856     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom._sizeOf_1",
27857     "runtime_only": false
27858   },
27859   {
27860     "axioms": [
27861       "propext",
27862       "Classical.choice",
27863       "Quot.sound"
27864     ],
27865     "in_project_namespace": true,
27866     "kind": "definition",
27867     "module": "PaperIRelease.GrammarIdeal",
27868     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealToPresented",
27869     "runtime_only": false
27870   },
27871   {
27872     "axioms": [
27873       "propext",
27874       "Quot.sound"
27875     ],
27876     "in_project_namespace": true,
27877     "kind": "theorem",
27878     "module": "PaperIRelease.GraphSources",
27879     "name": "Komorebi.PaperIRelease.FiniteDigraph.no_reach_into_source",
27880     "runtime_only": false
27881   },
27882   {
27883     "axioms": [
27884       "propext",
27885       "Classical.choice",
27886       "Quot.sound"
27887     ],
27888     "in_project_namespace": true,
27889     "kind": "theorem",
27890     "module": "KomorebiVerification.TopologicalCompletion",
27891     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.operatorHull.eq_1",
27892     "runtime_only": false
27893   },
27894   {
27895     "axioms": [
27896       "propext",
27897       "Classical.choice",
27898       "Quot.sound"
27899     ],
27900     "in_project_namespace": true,
27901     "kind": "definition",
27902     "module": "KomorebiVerification.PacketNaturalityCompletion",
27903     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.noConfusion",
27904     "runtime_only": false
27905   },
27906   {
27907     "axioms": [
27908       "propext",
27909       "Classical.choice",
27910       "Quot.sound"
27911     ],
27912     "in_project_namespace": true,
27913     "kind": "theorem",
27914     "module": "PaperICompletion.SpectralCertificates",
27915     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenLabelsFintype._proof_1",
27916     "runtime_only": false
27917   },
27918   {
27919     "axioms": [
27920       "propext",
27921       "Classical.choice",
27922       "Quot.sound"
27923     ],
27924     "in_project_namespace": false,
27925     "kind": "theorem",
27926     "module": "PaperIRelease.AlgebraPreorder",
27927     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_length_bound._proof_1_1",
27928     "runtime_only": false
27929   },
27930   {
27931     "axioms": [
27932       "propext",
27933       "Classical.choice",
27934       "Quot.sound"
27935     ],
27936     "in_project_namespace": true,
27937     "kind": "theorem",
27938     "module": "PaperIRelease.GraphSourceProjection",
27939     "name": "Komorebi.PaperIRelease.sourceProjection_compression",
27940     "runtime_only": false
27941   },
27942   {
27943     "axioms": [
27944       "propext",
27945       "Classical.choice",
27946       "Quot.sound"
27947     ],
27948     "in_project_namespace": true,
27949     "kind": "theorem",
27950     "module": "PaperIRelease.AlgebraPreorder",
27951     "name": "Komorebi.PaperIRelease.strictSupport_mul_left",
27952     "runtime_only": false
27953   },
27954   {
27955     "axioms": [
27956       "propext",
27957       "Classical.choice",
27958       "Quot.sound"
27959     ],
27960     "in_project_namespace": true,
27961     "kind": "theorem",
27962     "module": "PaperICompletion5.CyclicGeometricCriterion",
27963     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_7",
27964     "runtime_only": false
27965   },
27966   {
27967     "axioms": [
27968       "propext",
27969       "Classical.choice",
27970       "Quot.sound"
27971     ],
27972     "in_project_namespace": true,
27973     "kind": "definition",
27974     "module": "PaperIRelease.AlgebraClassGrouping",
27975     "name": "Komorebi.PaperIRelease.preorderClassesFintype",
27976     "runtime_only": false
27977   },
27978   {
27979     "axioms": [
27980       "propext",
27981       "Classical.choice",
27982       "Quot.sound"
27983     ],
27984     "in_project_namespace": false,
27985     "kind": "theorem",
27986     "module": "PaperIRelease.TopologyCountablePackets",
27987     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signed_sum_le_norm",
27988     "runtime_only": false
27989   },
27990   {
27991     "axioms": [
27992       "propext",
27993       "Quot.sound"
27994     ],
27995     "in_project_namespace": true,
27996     "kind": "definition",
27997     "module": "KomorebiVerification.SeedRankOperations",
27998     "name": "Komorebi.SeedRankOperations.prodSndSemilinear",
27999     "runtime_only": false
28000   },
28001   {
28002     "axioms": [
28003       "propext",
28004       "Classical.choice",
28005       "Quot.sound"
28006     ],
28007     "in_project_namespace": true,
28008     "kind": "definition",
28009     "module": "PaperIRelease.TopologyCategories",
28010     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk._flat_ctor",
28011     "runtime_only": false
28012   },
28013   {
28014     "axioms": [
28015       "propext",
28016       "Classical.choice",
28017       "Quot.sound"
28018     ],
28019     "in_project_namespace": true,
28020     "kind": "theorem",
28021     "module": "KomorebiVerification.TopologicalCompletion",
28022     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.complete",
28023     "runtime_only": false
28024   },
28025   {
28026     "axioms": [
28027       "propext",
28028       "Classical.choice",
28029       "Quot.sound"
28030     ],
28031     "in_project_namespace": true,
28032     "kind": "definition",
28033     "module": "PaperICompletion5.LinearPrimaryEigenspace",
28034     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap",
28035     "runtime_only": false
28036   },
28037   {
28038     "axioms": [
28039       "propext",
28040       "Quot.sound"
28041     ],
28042     "in_project_namespace": true,
28043     "kind": "theorem",
28044     "module": "PaperIRelease.AlgebraQuotient",
28045     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_4",
28046     "runtime_only": false
28047   },
28048   {
28049     "axioms": [
28050       "propext",
28051       "Classical.choice",
28052       "Quot.sound"
28053     ],
28054     "in_project_namespace": true,
28055     "kind": "theorem",
28056     "module": "PaperIRelease.CategoryPackets",
28057     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_1",
28058     "runtime_only": false
28059   },
28060   {
28061     "axioms": [
28062       "propext",
28063       "Classical.choice",
28064       "Quot.sound"
28065     ],
28066     "in_project_namespace": true,
28067     "kind": "theorem",
28068     "module": "PaperIRelease.PacketAggregation",
28069     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_3",
28070     "runtime_only": false
28071   },
28072   {
28073     "axioms": [],
28074     "in_project_namespace": true,
28075     "kind": "definition",
28076     "module": "KomorebiVerification.ProjectorCore",
28077     "name": "Komorebi.Seed.OperatorExpr.comp.elim",
28078     "runtime_only": false
28079   },
28080   {
28081     "axioms": [
28082       "propext",
28083       "Classical.choice",
28084       "Quot.sound"
28085     ],
28086     "in_project_namespace": false,
28087     "kind": "theorem",
28088     "module": "PaperIRelease.TopologyUnconditional",
28089     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.summable_coordinate_limit",
28090     "runtime_only": false
28091   },
28092   {
28093     "axioms": [
28094       "propext",
28095       "Classical.choice",
28096       "Quot.sound"
28097     ],
28098     "in_project_namespace": true,
28099     "kind": "theorem",
28100     "module": "PaperIRelease.GrammarAlgebra",
28101     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_corner",
28102     "runtime_only": false
28103   },
28104   {
28105     "axioms": [],
28106     "in_project_namespace": true,
28107     "kind": "definition",
28108     "module": "KomorebiVerification.SeedRankBasics",
28109     "name": "Komorebi.SeedRankBasics.oneSeedMap",
28110     "runtime_only": false
28111   },
28112   {
28113     "axioms": [
28114       "propext",
28115       "Classical.choice",
28116       "Quot.sound"
28117     ],
28118     "in_project_namespace": true,
28119     "kind": "theorem",
28120     "module": "KomorebiVerification.TopologicalCompletion",
28121     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense.eq_1",
28122     "runtime_only": false
28123   },
28124   {
28125     "axioms": [
28126       "propext",
28127       "Classical.choice",
28128       "Quot.sound"
28129     ],
28130     "in_project_namespace": true,
28131     "kind": "theorem",
28132     "module": "PaperIRelease.PacketTopologyGeneral",
28133     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_1",
28134     "runtime_only": false
28135   },
28136   {
28137     "axioms": [
28138       "propext",
28139       "Classical.choice",
28140       "Quot.sound"
28141     ],
28142     "in_project_namespace": true,
28143     "kind": "definition",
28144     "module": "PaperIRelease.TopologyCategories",
28145     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.recOn",
28146     "runtime_only": false
28147   },
28148   {
28149     "axioms": [
28150       "propext",
28151       "Classical.choice",
28152       "Quot.sound"
28153     ],
28154     "in_project_namespace": false,
28155     "kind": "theorem",
28156     "module": "PaperIRelease.TopologyCountablePackets",
28157     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_4",
28158     "runtime_only": false
28159   },
28160   {
28161     "axioms": [
28162       "propext"
28163     ],
28164     "in_project_namespace": true,
28165     "kind": "definition",
28166     "module": "PaperIRelease.CategoryExport",
28167     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._f",
28168     "runtime_only": false
28169   },
28170   {
28171     "axioms": [
28172       "propext",
28173       "Classical.choice",
28174       "Quot.sound"
28175     ],
28176     "in_project_namespace": true,
28177     "kind": "theorem",
28178     "module": "PaperIRelease.GrammarTyped",
28179     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_2",
28180     "runtime_only": false
28181   },
28182   {
28183     "axioms": [
28184       "propext",
28185       "Classical.choice",
28186       "Quot.sound"
28187     ],
28188     "in_project_namespace": false,
28189     "kind": "definition",
28190     "module": "PaperIRelease.TopologyUnconditional",
28191     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_16",
28192     "runtime_only": false
28193   },
28194   {
28195     "axioms": [
28196       "propext",
28197       "Classical.choice",
28198       "Quot.sound"
28199     ],
28200     "in_project_namespace": true,
28201     "kind": "theorem",
28202     "module": "PaperICompletion3.PrimarySeedFormula",
28203     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor_injective_on_fiber",
28204     "runtime_only": false
28205   },
28206   {
28207     "axioms": [
28208       "propext",
28209       "Classical.choice",
28210       "Quot.sound"
28211     ],
28212     "in_project_namespace": true,
28213     "kind": "theorem",
28214     "module": "PaperICompletion.SpectralCertificates",
28215     "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList._proof_1",
28216     "runtime_only": false
28217   },
28218   {
28219     "axioms": [
28220       "propext",
28221       "Classical.choice",
28222       "Quot.sound"
28223     ],
28224     "in_project_namespace": false,
28225     "kind": "definition",
28226     "module": "PaperIRelease.TopologyUnconditional",
28227     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.packet",
28228     "runtime_only": false
28229   },
28230   {
28231     "axioms": [
28232       "propext"
28233     ],
28234     "in_project_namespace": true,
28235     "kind": "theorem",
28236     "module": "PaperIRelease.CategoryExport",
28237     "name": "Komorebi.PaperIRelease.CategoryExport.equation_transport",
28238     "runtime_only": false
28239   },
28240   {
28241     "axioms": [
28242       "propext",
28243       "Classical.choice",
28244       "Quot.sound"
28245     ],
28246     "in_project_namespace": false,
28247     "kind": "theorem",
28248     "module": "PaperIRelease.TopologyUnconditionalBridge",
28249     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_1",
28250     "runtime_only": false
28251   },
28252   {
28253     "axioms": [
28254       "propext",
28255       "Classical.choice",
28256       "Quot.sound"
28257     ],
28258     "in_project_namespace": true,
28259     "kind": "theorem",
28260     "module": "PaperIRelease.PacketTopology",
28261     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM_toLinearMap",
28262     "runtime_only": false
28263   },
28264   {
28265     "axioms": [],
28266     "in_project_namespace": true,
28267     "kind": "definition",
28268     "module": "KomorebiVerification.KernelAudit",
28269     "name": "Komorebi.Verification.fineAddress",
28270     "runtime_only": false
28271   },
28272   {
28273     "axioms": [
28274       "propext",
28275       "Classical.choice",
28276       "Quot.sound"
28277     ],
28278     "in_project_namespace": true,
28279     "kind": "definition",
28280     "module": "KomorebiVerification.EllipticAlgorithms",
28281     "name": "Komorebi.FiniteAlgorithms.graphSpectrum",
28282     "runtime_only": false
28283   },
28284   {
28285     "axioms": [
28286       "propext",
28287       "Quot.sound"
28288     ],
28289     "in_project_namespace": true,
28290     "kind": "theorem",
28291     "module": "PaperIRelease.GrammarModules",
28292     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_11",
28293     "runtime_only": false
28294   },
28295   {
28296     "axioms": [
28297       "propext",
28298       "Quot.sound"
28299     ],
28300     "in_project_namespace": true,
28301     "kind": "theorem",
28302     "module": "KomorebiVerification.SingleOperatorGraph",
28303     "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_3",
28304     "runtime_only": false
28305   },
28306   {
28307     "axioms": [
28308       "propext",
28309       "Classical.choice",
28310       "Quot.sound"
28311     ],
28312     "in_project_namespace": false,
28313     "kind": "theorem",
28314     "module": "ReleaseBoundary",
28315     "name": "PaperIBlock08Tests.quaternion_natural_rank_one",
28316     "runtime_only": false
28317   },
28318   {
28319     "axioms": [
28320       "propext",
28321       "Quot.sound"
28322     ],
28323     "in_project_namespace": true,
28324     "kind": "theorem",
28325     "module": "KomorebiVerification.SingleOperatorGraph",
28326     "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_5",
28327     "runtime_only": false
28328   },
28329   {
28330     "axioms": [
28331       "propext",
28332       "Classical.choice",
28333       "Quot.sound"
28334     ],
28335     "in_project_namespace": true,
28336     "kind": "definition",
28337     "module": "KomorebiVerification.EllipticAlgorithms",
28338     "name": "Komorebi.EllipticCoordinates.My",
28339     "runtime_only": false
28340   },
28341   {
28342     "axioms": [
28343       "propext",
28344       "Quot.sound"
28345     ],
28346     "in_project_namespace": true,
28347     "kind": "theorem",
28348     "module": "PaperIRelease.PolynomialModule",
28349     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_3",
28350     "runtime_only": false
28351   },
28352   {
28353     "axioms": [],
28354     "in_project_namespace": true,
28355     "kind": "definition",
28356     "module": "KomorebiVerification.ProjectorCore",
28357     "name": "Komorebi.instInhabitedClaimRecord",
28358     "runtime_only": false
28359   },
28360   {
28361     "axioms": [
28362       "propext",
28363       "Classical.choice",
28364       "Quot.sound"
28365     ],
28366     "in_project_namespace": true,
28367     "kind": "definition",
28368     "module": "PaperIRelease.TopologyCategories",
28369     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ctorIdx",
28370     "runtime_only": false
28371   },
28372   {
28373     "axioms": [],
28374     "in_project_namespace": true,
28375     "kind": "definition",
28376     "module": "KomorebiVerification.ProjectorCore",
28377     "name": "Komorebi.ClaimKind.ctorIdx",
28378     "runtime_only": false
28379   },
28380   {
28381     "axioms": [
28382       "propext",
28383       "Classical.choice",
28384       "Quot.sound"
28385     ],
28386     "in_project_namespace": true,
28387     "kind": "theorem",
28388     "module": "PaperIRelease.GeneralFiniteCompletion",
28389     "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extended_packet_range",
28390     "runtime_only": false
28391   },
28392   {
28393     "axioms": [
28394       "propext",
28395       "Classical.choice",
28396       "Quot.sound"
28397     ],
28398     "in_project_namespace": true,
28399     "kind": "theorem",
28400     "module": "KomorebiVerification.PacketNaturalityCompletion",
28401     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.algebraZeroAt_iff_of_bijective",
28402     "runtime_only": false
28403   },
28404   {
28405     "axioms": [
28406       "propext",
28407       "Classical.choice",
28408       "Quot.sound"
28409     ],
28410     "in_project_namespace": true,
28411     "kind": "theorem",
28412     "module": "KomorebiVerification.TopologicalCompletion",
28413     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.topologicallyCyclic_delta",
28414     "runtime_only": false
28415   },
28416   {
28417     "axioms": [
28418       "propext",
28419       "Quot.sound"
28420     ],
28421     "in_project_namespace": true,
28422     "kind": "theorem",
28423     "module": "KomorebiVerification.SeedRankOperations",
28424     "name": "Komorebi.SeedRankOperations.productModule._proof_1",
28425     "runtime_only": false
28426   },
28427   {
28428     "axioms": [
28429       "propext",
28430       "Classical.choice",
28431       "Quot.sound"
28432     ],
28433     "in_project_namespace": true,
28434     "kind": "theorem",
28435     "module": "KomorebiVerification.SingleOperatorGraph",
28436     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_zero",
28437     "runtime_only": false
28438   },
28439   {
28440     "axioms": [
28441       "propext",
28442       "Classical.choice",
28443       "Quot.sound"
28444     ],
28445     "in_project_namespace": true,
28446     "kind": "theorem",
28447     "module": "PaperIRelease.PacketTopology",
28448     "name": "Komorebi.Foundation.LinearProjectorFamily.boundedProjector.congr_simp",
28449     "runtime_only": false
28450   },
28451   {
28452     "axioms": [
28453       "propext",
28454       "Classical.choice",
28455       "Quot.sound"
28456     ],
28457     "in_project_namespace": true,
28458     "kind": "definition",
28459     "module": "KomorebiVerification.TopologicalCompletion",
28460     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.casesOn",
28461     "runtime_only": false
28462   },
28463   {
28464     "axioms": [
28465       "propext",
28466       "Classical.choice",
28467       "Quot.sound"
28468     ],
28469     "in_project_namespace": true,
28470     "kind": "theorem",
28471     "module": "KomorebiVerification.SemisimpleCompletion",
28472     "name": "Komorebi.SemisimpleCompletion.fullMatrix_seedRank_eq_one",
28473     "runtime_only": false
28474   },
28475   {
28476     "axioms": [
28477       "propext",
28478       "Quot.sound"
28479     ],
28480     "in_project_namespace": true,
28481     "kind": "theorem",
28482     "module": "KomorebiVerification.ProjectorCore",
28483     "name": "Komorebi.Seed.seed_subset_hull",
28484     "runtime_only": false
28485   },
28486   {
28487     "axioms": [
28488       "propext",
28489       "Classical.choice",
28490       "Quot.sound"
28491     ],
28492     "in_project_namespace": true,
28493     "kind": "theorem",
28494     "module": "PaperIRelease.CategoryBoundaries",
28495     "name": "Komorebi.PaperIRelease.CategoryBoundaries.empty_vertex_algebra",
28496     "runtime_only": false
28497   },
28498   {
28499     "axioms": [
28500       "propext",
28501       "Quot.sound"
28502     ],
28503     "in_project_namespace": true,
28504     "kind": "theorem",
28505     "module": "PaperICompletion4.IntrinsicPrimary",
28506     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_3",
28507     "runtime_only": false
28508   },
28509   {
28510     "axioms": [
28511       "propext",
28512       "Classical.choice",
28513       "Quot.sound"
28514     ],
28515     "in_project_namespace": true,
28516     "kind": "theorem",
28517     "module": "PaperICompletion3.OperatorPrimaryAPI",
28518     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.injEq",
28519     "runtime_only": false
28520   },
28521   {
28522     "axioms": [
28523       "propext",
28524       "Classical.choice",
28525       "Quot.sound"
28526     ],
28527     "in_project_namespace": true,
28528     "kind": "theorem",
28529     "module": "KomorebiVerification.PaperITransport",
28530     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate_proj_apply",
28531     "runtime_only": false
28532   },
28533   {
28534     "axioms": [
28535       "propext",
28536       "Classical.choice",
28537       "Quot.sound"
28538     ],
28539     "in_project_namespace": true,
28540     "kind": "theorem",
28541     "module": "PaperICompletion4.ResidueQuotient",
28542     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap_surjective",
28543     "runtime_only": false
28544   },
28545   {
28546     "axioms": [
28547       "propext",
28548       "Classical.choice",
28549       "Quot.sound"
28550     ],
28551     "in_project_namespace": true,
28552     "kind": "theorem",
28553     "module": "PaperICompletion6.SixWayCyclicCriterion",
28554     "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_six_way",
28555     "runtime_only": false
28556   },
28557   {
28558     "axioms": [
28559       "propext",
28560       "Classical.choice",
28561       "Quot.sound"
28562     ],
28563     "in_project_namespace": true,
28564     "kind": "definition",
28565     "module": "PaperIRelease.CategoryPackets",
28566     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.noConfusion",
28567     "runtime_only": false
28568   },
28569   {
28570     "axioms": [
28571       "propext",
28572       "Classical.choice",
28573       "Quot.sound"
28574     ],
28575     "in_project_namespace": true,
28576     "kind": "theorem",
28577     "module": "KomorebiVerification.TopologicalCompletion",
28578     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.adjoint_transferBlock",
28579     "runtime_only": false
28580   },
28581   {
28582     "axioms": [],
28583     "in_project_namespace": true,
28584     "kind": "theorem",
28585     "module": "KomorebiVerification.ProjectorCore",
28586     "name": "Komorebi.Seed.OperatorExpr.atom.inj",
28587     "runtime_only": false
28588   },
28589   {
28590     "axioms": [
28591       "propext",
28592       "Classical.choice",
28593       "Quot.sound"
28594     ],
28595     "in_project_namespace": true,
28596     "kind": "theorem",
28597     "module": "PaperIRelease.PacketCorners",
28598     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_6",
28599     "runtime_only": false
28600   },
28601   {
28602     "axioms": [
28603       "propext",
28604       "Classical.choice",
28605       "Quot.sound"
28606     ],
28607     "in_project_namespace": true,
28608     "kind": "theorem",
28609     "module": "KomorebiVerification.PacketNaturalityCompletion",
28610     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB.eq_1",
28611     "runtime_only": false
28612   },
28613   {
28614     "axioms": [
28615       "propext",
28616       "Quot.sound"
28617     ],
28618     "in_project_namespace": false,
28619     "kind": "theorem",
28620     "module": "KomorebiVerification.SeedRankOperations",
28621     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_5",
28622     "runtime_only": false
28623   },
28624   {
28625     "axioms": [
28626       "propext",
28627       "Classical.choice",
28628       "Quot.sound"
28629     ],
28630     "in_project_namespace": true,
28631     "kind": "theorem",
28632     "module": "PaperIRelease.CategoryPackets",
28633     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.inj",
28634     "runtime_only": false
28635   },
28636   {
28637     "axioms": [
28638       "propext",
28639       "Classical.choice",
28640       "Quot.sound"
28641     ],
28642     "in_project_namespace": true,
28643     "kind": "theorem",
28644     "module": "PaperICompletion5.LinearPrimaryEigenspace",
28645     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap_ker",
28646     "runtime_only": false
28647   },
28648   {
28649     "axioms": [
28650       "propext",
28651       "Quot.sound"
28652     ],
28653     "in_project_namespace": true,
28654     "kind": "theorem",
28655     "module": "PaperIRelease.GrammarModules",
28656     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_6",
28657     "runtime_only": false
28658   },
28659   {
28660     "axioms": [
28661       "propext"
28662     ],
28663     "in_project_namespace": true,
28664     "kind": "theorem",
28665     "module": "KomorebiVerification.SingleOperatorGraph",
28666     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_6",
28667     "runtime_only": false
28668   },
28669   {
28670     "axioms": [
28671       "propext"
28672     ],
28673     "in_project_namespace": true,
28674     "kind": "theorem",
28675     "module": "KomorebiVerification.ProjectorCore",
28676     "name": "Komorebi.Packet.fibreProj_apply_ne",
28677     "runtime_only": false
28678   },
28679   {
28680     "axioms": [],
28681     "in_project_namespace": true,
28682     "kind": "theorem",
28683     "module": "KomorebiVerification.ProjectorCore",
28684     "name": "Komorebi.ClaimKind.corollaryClaim.sizeOf_spec",
28685     "runtime_only": false
28686   },
28687   {
28688     "axioms": [
28689       "propext",
28690       "Classical.choice",
28691       "Quot.sound"
28692     ],
28693     "in_project_namespace": true,
28694     "kind": "theorem",
28695     "module": "KomorebiVerification.SingleOperatorGraph",
28696     "name": "Komorebi.SingleOperatorGraph.cyclic_matrix_four_way_iff_of_primary_decomposition",
28697     "runtime_only": false
28698   },
28699   {
28700     "axioms": [
28701       "propext",
28702       "Classical.choice",
28703       "Quot.sound"
28704     ],
28705     "in_project_namespace": true,
28706     "kind": "theorem",
28707     "module": "KomorebiVerification.EllipticAlgorithms",
28708     "name": "Komorebi.EllipticCoordinates.quotientToNormalForm_root",
28709     "runtime_only": false
28710   },
28711   {
28712     "axioms": [
28713       "propext",
28714       "Classical.choice",
28715       "Quot.sound"
28716     ],
28717     "in_project_namespace": true,
28718     "kind": "theorem",
28719     "module": "KomorebiVerification.EllipticAlgorithms",
28720     "name": "Komorebi.EllipticCoordinates.normalFormToQuotient_y",
28721     "runtime_only": false
28722   },
28723   {
28724     "axioms": [
28725       "propext",
28726       "Classical.choice",
28727       "Quot.sound"
28728     ],
28729     "in_project_namespace": true,
28730     "kind": "theorem",
28731     "module": "PaperIRelease.BoundedStar",
28732     "name": "Komorebi.PaperIRelease.BoundedSupport.empty_pattern_boundary",
28733     "runtime_only": false
28734   },
28735   {
28736     "axioms": [],
28737     "in_project_namespace": true,
28738     "kind": "theorem",
28739     "module": "KomorebiVerification.PacketNaturalityCompletion",
28740     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_1",
28741     "runtime_only": false
28742   },
28743   {
28744     "axioms": [
28745       "propext",
28746       "Classical.choice",
28747       "Quot.sound"
28748     ],
28749     "in_project_namespace": true,
28750     "kind": "definition",
28751     "module": "KomorebiVerification.SingleOperatorGraph",
28752     "name": "Komorebi.SingleOperatorGraph.paddedBlockSum",
28753     "runtime_only": false
28754   },
28755   {
28756     "axioms": [
28757       "propext",
28758       "Classical.choice",
28759       "Quot.sound"
28760     ],
28761     "in_project_namespace": true,
28762     "kind": "definition",
28763     "module": "PaperICompletion3.OperatorPrimaryAPI",
28764     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.ctorIdx",
28765     "runtime_only": false
28766   },
28767   {
28768     "axioms": [
28769       "propext",
28770       "Classical.choice",
28771       "Quot.sound"
28772     ],
28773     "in_project_namespace": false,
28774     "kind": "theorem",
28775     "module": "PaperIRelease.TopologyCountablePackets",
28776     "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_add_le",
28777     "runtime_only": false
28778   },
28779   {
28780     "axioms": [],
28781     "in_project_namespace": true,
28782     "kind": "definition",
28783     "module": "KomorebiVerification.ProjectorCore",
28784     "name": "Komorebi.FormalizationStatus.conjectural.elim",
28785     "runtime_only": false
28786   },
28787   {
28788     "axioms": [
28789       "propext",
28790       "Classical.choice",
28791       "Quot.sound"
28792     ],
28793     "in_project_namespace": true,
28794     "kind": "theorem",
28795     "module": "PaperIRelease.CategoryPackets",
28796     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp._proof_1",
28797     "runtime_only": false
28798   },
28799   {
28800     "axioms": [
28801       "propext",
28802       "Classical.choice",
28803       "Quot.sound"
28804     ],
28805     "in_project_namespace": true,
28806     "kind": "theorem",
28807     "module": "PaperIRelease.TensorPackets",
28808     "name": "Komorebi.PaperIRelease.dualPackets._proof_2",
28809     "runtime_only": false
28810   },
28811   {
28812     "axioms": [
28813       "propext",
28814       "Classical.choice",
28815       "Quot.sound"
28816     ],
28817     "in_project_namespace": true,
28818     "kind": "theorem",
28819     "module": "KomorebiVerification.SeedRankOperations",
28820     "name": "Komorebi.SeedRankOperations.seedFinrank_isLeast_free_surjection",
28821     "runtime_only": false
28822   },
28823   {
28824     "axioms": [
28825       "propext",
28826       "Classical.choice",
28827       "Quot.sound"
28828     ],
28829     "in_project_namespace": true,
28830     "kind": "theorem",
28831     "module": "KomorebiVerification.TopologicalCompletion",
28832     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_1",
28833     "runtime_only": false
28834   },
28835   {
28836     "axioms": [
28837       "propext",
28838       "Classical.choice",
28839       "Quot.sound"
28840     ],
28841     "in_project_namespace": true,
28842     "kind": "inductive",
28843     "module": "PaperIRelease.CategoryPackets",
28844     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism",
28845     "runtime_only": false
28846   },
28847   {
28848     "axioms": [
28849       "propext",
28850       "Classical.choice",
28851       "Quot.sound"
28852     ],
28853     "in_project_namespace": true,
28854     "kind": "definition",
28855     "module": "PaperIRelease.GrammarAlgebra",
28856     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Algebra",
28857     "runtime_only": false
28858   },
28859   {
28860     "axioms": [],
28861     "in_project_namespace": true,
28862     "kind": "definition",
28863     "module": "KomorebiVerification.SemisimpleCompletion",
28864     "name": "Komorebi.SemisimpleCompletion.SplitProductAlgebra",
28865     "runtime_only": false
28866   },
28867   {
28868     "axioms": [],
28869     "in_project_namespace": true,
28870     "kind": "theorem",
28871     "module": "PaperICompletion8.ProductPresentation",
28872     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_4",
28873     "runtime_only": false
28874   },
28875   {
28876     "axioms": [],
28877     "in_project_namespace": true,
28878     "kind": "theorem",
28879     "module": "PaperICompletion8.RegularMultiplicity",
28880     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_4",
28881     "runtime_only": false
28882   },
28883   {
28884     "axioms": [
28885       "propext",
28886       "Classical.choice",
28887       "Quot.sound"
28888     ],
28889     "in_project_namespace": true,
28890     "kind": "definition",
28891     "module": "PaperIRelease.CategoryPackets",
28892     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity",
28893     "runtime_only": false
28894   },
28895   {
28896     "axioms": [
28897       "propext",
28898       "Classical.choice",
28899       "Quot.sound"
28900     ],
28901     "in_project_namespace": true,
28902     "kind": "theorem",
28903     "module": "PaperICompletion4.ResidueQuotient",
28904     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_3",
28905     "runtime_only": false
28906   },
28907   {
28908     "axioms": [
28909       "propext",
28910       "Classical.choice",
28911       "Quot.sound"
28912     ],
28913     "in_project_namespace": true,
28914     "kind": "definition",
28915     "module": "PaperIRelease.GrammarAlgebra",
28916     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.recOn",
28917     "runtime_only": false
28918   },
28919   {
28920     "axioms": [
28921       "propext",
28922       "Classical.choice",
28923       "Quot.sound"
28924     ],
28925     "in_project_namespace": true,
28926     "kind": "theorem",
28927     "module": "PaperIRelease.PacketAggregation",
28928     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_4",
28929     "runtime_only": false
28930   },
28931   {
28932     "axioms": [
28933       "propext",
28934       "Classical.choice",
28935       "Quot.sound"
28936     ],
28937     "in_project_namespace": true,
28938     "kind": "definition",
28939     "module": "PaperIRelease.GrammarEquivalence",
28940     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom._sizeOf_inst",
28941     "runtime_only": false
28942   },
28943   {
28944     "axioms": [
28945       "propext",
28946       "Classical.choice",
28947       "Quot.sound"
28948     ],
28949     "in_project_namespace": true,
28950     "kind": "theorem",
28951     "module": "PaperIRelease.PolynomialModule",
28952     "name": "Komorebi.PaperIRelease.PolynomialModule.exists_positive_primary_decomposition",
28953     "runtime_only": false
28954   },
28955   {
28956     "axioms": [
28957       "propext",
28958       "Classical.choice",
28959       "Quot.sound"
28960     ],
28961     "in_project_namespace": true,
28962     "kind": "definition",
28963     "module": "KomorebiVerification.PacketNaturalityCompletion",
28964     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockEquivToEnd",
28965     "runtime_only": false
28966   },
28967   {
28968     "axioms": [
28969       "propext",
28970       "Classical.choice",
28971       "Quot.sound"
28972     ],
28973     "in_project_namespace": true,
28974     "kind": "definition",
28975     "module": "PaperIRelease.TopologyCategories",
28976     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.comp",
28977     "runtime_only": false
28978   },
28979   {
28980     "axioms": [
28981       "propext",
28982       "Classical.choice",
28983       "Quot.sound"
28984     ],
28985     "in_project_namespace": true,
28986     "kind": "theorem",
28987     "module": "PaperIRelease.GrammarFactorization",
28988     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.span_imageAlgebra_eq",
28989     "runtime_only": false
28990   },
28991   {
28992     "axioms": [
28993       "propext",
28994       "Classical.choice",
28995       "Quot.sound"
28996     ],
28997     "in_project_namespace": true,
28998     "kind": "definition",
28999     "module": "KomorebiVerification.SeedRankBasics",
29000     "name": "Komorebi.SeedRankBasics.seedRank",
29001     "runtime_only": false
29002   },
29003   {
29004     "axioms": [
29005       "propext",
29006       "Classical.choice",
29007       "Quot.sound"
29008     ],
29009     "in_project_namespace": true,
29010     "kind": "theorem",
29011     "module": "KomorebiVerification.EllipticAlgorithms",
29012     "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_3",
29013     "runtime_only": false
29014   },
29015   {
29016     "axioms": [
29017       "propext",
29018       "Classical.choice",
29019       "Quot.sound"
29020     ],
29021     "in_project_namespace": true,
29022     "kind": "theorem",
29023     "module": "PaperIRelease.BoundedStar",
29024     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_4",
29025     "runtime_only": false
29026   },
29027   {
29028     "axioms": [
29029       "propext",
29030       "Classical.choice",
29031       "Quot.sound"
29032     ],
29033     "in_project_namespace": true,
29034     "kind": "theorem",
29035     "module": "PaperICompletion.SpectralCertificates",
29036     "name": "Komorebi.PaperICompletion.SpectralCertificates.seedNumber_isLeast_of_eigenbasis",
29037     "runtime_only": false
29038   },
29039   {
29040     "axioms": [
29041       "propext",
29042       "Classical.choice",
29043       "Quot.sound"
29044     ],
29045     "in_project_namespace": true,
29046     "kind": "theorem",
29047     "module": "PaperICompletion4.ResidueQuotient",
29048     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_4",
29049     "runtime_only": false
29050   },
29051   {
29052     "axioms": [
29053       "propext",
29054       "Quot.sound"
29055     ],
29056     "in_project_namespace": false,
29057     "kind": "theorem",
29058     "module": "KomorebiVerification.SeedRankOperations",
29059     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_2",
29060     "runtime_only": false
29061   },
29062   {
29063     "axioms": [
29064       "propext",
29065       "Classical.choice",
29066       "Quot.sound"
29067     ],
29068     "in_project_namespace": true,
29069     "kind": "definition",
29070     "module": "PaperIRelease.PacketExactSequence",
29071     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion",
29072     "runtime_only": false
29073   },
29074   {
29075     "axioms": [
29076       "propext",
29077       "Classical.choice",
29078       "Quot.sound"
29079     ],
29080     "in_project_namespace": true,
29081     "kind": "theorem",
29082     "module": "PaperIRelease.PacketTopology",
29083     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL_mk",
29084     "runtime_only": false
29085   },
29086   {
29087     "axioms": [
29088       "propext",
29089       "Classical.choice",
29090       "Quot.sound"
29091     ],
29092     "in_project_namespace": false,
29093     "kind": "theorem",
29094     "module": "PaperIRelease.TopologyDenseCompletion",
29095     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_7",
29096     "runtime_only": false
29097   },
29098   {
29099     "axioms": [],
29100     "in_project_namespace": true,
29101     "kind": "definition",
29102     "module": "KomorebiVerification.ProjectorCore",
29103     "name": "Komorebi.ClaimRecord.difficulty._default",
29104     "runtime_only": false
29105   },
29106   {
29107     "axioms": [],
29108     "in_project_namespace": true,
29109     "kind": "definition",
29110     "module": "KomorebiVerification.ProjectorCore",
29111     "name": "Komorebi.ClaimRecord.dependencySafe",
29112     "runtime_only": false
29113   },
29114   {
29115     "axioms": [
29116       "propext",
29117       "Classical.choice",
29118       "Quot.sound"
29119     ],
29120     "in_project_namespace": false,
29121     "kind": "theorem",
29122     "module": "PaperIRelease.TopologyDenseCompletion",
29123     "name": "PaperIRelease.TopologyDenseCompletion.transported_uniformConstSMul",
29124     "runtime_only": false
29125   },
29126   {
29127     "axioms": [
29128       "propext",
29129       "Quot.sound"
29130     ],
29131     "in_project_namespace": true,
29132     "kind": "theorem",
29133     "module": "PaperICompletion6.OneInvariantFactor",
29134     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_4",
29135     "runtime_only": false
29136   },
29137   {
29138     "axioms": [
29139       "propext",
29140       "Quot.sound"
29141     ],
29142     "in_project_namespace": false,
29143     "kind": "theorem",
29144     "module": "KomorebiVerification.SeedRankOperations",
29145     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.character_surjective",
29146     "runtime_only": false
29147   },
29148   {
29149     "axioms": [
29150       "propext",
29151       "Classical.choice",
29152       "Quot.sound"
29153     ],
29154     "in_project_namespace": true,
29155     "kind": "definition",
29156     "module": "PaperIRelease.GrammarTyped",
29157     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.noConfusionType",
29158     "runtime_only": false
29159   },
29160   {
29161     "axioms": [
29162       "propext",
29163       "Classical.choice",
29164       "Quot.sound"
29165     ],
29166     "in_project_namespace": true,
29167     "kind": "theorem",
29168     "module": "KomorebiVerification.SeedRankBasics",
29169     "name": "Komorebi.SeedRankBasics.seedRank_le_mk_of_familyGenerates",
29170     "runtime_only": false
29171   },
29172   {
29173     "axioms": [
29174       "propext",
29175       "Quot.sound"
29176     ],
29177     "in_project_namespace": true,
29178     "kind": "definition",
29179     "module": "KomorebiVerification.PacketNaturalityCompletion",
29180     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.sourceSeed",
29181     "runtime_only": false
29182   },
29183   {
29184     "axioms": [
29185       "propext",
29186       "Classical.choice",
29187       "Quot.sound"
29188     ],
29189     "in_project_namespace": true,
29190     "kind": "definition",
29191     "module": "PaperIRelease.GrammarAlgebra",
29192     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization._sizeOf_1",
29193     "runtime_only": false
29194   },
29195   {
29196     "axioms": [
29197       "propext",
29198       "Classical.choice",
29199       "Quot.sound"
29200     ],
29201     "in_project_namespace": true,
29202     "kind": "definition",
29203     "module": "PaperIRelease.TopologyCategories",
29204     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ctorIdx",
29205     "runtime_only": false
29206   },
29207   {
29208     "axioms": [
29209       "propext",
29210       "Classical.choice",
29211       "Quot.sound"
29212     ],
29213     "in_project_namespace": true,
29214     "kind": "theorem",
29215     "module": "PaperIRelease.CategoryPackets",
29216     "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_1",
29217     "runtime_only": false
29218   },
29219   {
29220     "axioms": [
29221       "propext",
29222       "Classical.choice",
29223       "Quot.sound"
29224     ],
29225     "in_project_namespace": true,
29226     "kind": "theorem",
29227     "module": "PaperIRelease.PacketDescent",
29228     "name": "Komorebi.Foundation.LinearProjectorFamily.descendedPacketEquivSumQuotient._proof_1",
29229     "runtime_only": false
29230   },
29231   {
29232     "axioms": [
29233       "propext",
29234       "Quot.sound"
29235     ],
29236     "in_project_namespace": true,
29237     "kind": "theorem",
29238     "module": "PaperIRelease.AlgebraClassGrouping",
29239     "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_4",
29240     "runtime_only": false
29241   },
29242   {
29243     "axioms": [
29244       "propext",
29245       "Classical.choice",
29246       "Quot.sound"
29247     ],
29248     "in_project_namespace": false,
29249     "kind": "theorem",
29250     "module": "PaperIRelease.TopologySeedRank",
29251     "name": "PaperIRelease.TopologyTransport.seedRank_mono_algebra",
29252     "runtime_only": false
29253   },
29254   {
29255     "axioms": [
29256       "propext",
29257       "Classical.choice",
29258       "Quot.sound"
29259     ],
29260     "in_project_namespace": true,
29261     "kind": "theorem",
29262     "module": "PaperICompletion5.GeometricSeedFormula",
29263     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedRank_eq_spectralSeedMaximum",
29264     "runtime_only": false
29265   },
29266   {
29267     "axioms": [
29268       "propext",
29269       "Classical.choice",
29270       "Quot.sound"
29271     ],
29272     "in_project_namespace": true,
29273     "kind": "theorem",
29274     "module": "PaperIRelease.PacketExactSequence",
29275     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_1",
29276     "runtime_only": false
29277   },
29278   {
29279     "axioms": [
29280       "propext",
29281       "Classical.choice",
29282       "Quot.sound"
29283     ],
29284     "in_project_namespace": true,
29285     "kind": "theorem",
29286     "module": "PaperICompletion8.RegularMultiplicity",
29287     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv_apply",
29288     "runtime_only": false
29289   },
29290   {
29291     "axioms": [
29292       "propext",
29293       "Quot.sound"
29294     ],
29295     "in_project_namespace": true,
29296     "kind": "definition",
29297     "module": "PaperIRelease.GrammarTyped",
29298     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.module",
29299     "runtime_only": false
29300   },
29301   {
29302     "axioms": [
29303       "propext",
29304       "Quot.sound"
29305     ],
29306     "in_project_namespace": true,
29307     "kind": "definition",
29308     "module": "PaperIRelease.PacketBoundaryTests",
29309     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.swapEnd",
29310     "runtime_only": false
29311   },
29312   {
29313     "axioms": [
29314       "propext",
29315       "Quot.sound"
29316     ],
29317     "in_project_namespace": true,
29318     "kind": "theorem",
29319     "module": "KomorebiVerification.EllipticAlgorithms",
29320     "name": "Komorebi.EllipticCoordinates.My_sq_eq_Mx_cube_sub_Mx._proof_1_2",
29321     "runtime_only": false
29322   },
29323   {
29324     "axioms": [
29325       "propext",
29326       "Classical.choice",
29327       "Quot.sound"
29328     ],
29329     "in_project_namespace": false,
29330     "kind": "theorem",
29331     "module": "PaperIRelease.TopologyUnconditional",
29332     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_7",
29333     "runtime_only": false
29334   },
29335   {
29336     "axioms": [
29337       "propext",
29338       "Classical.choice",
29339       "Quot.sound"
29340     ],
29341     "in_project_namespace": true,
29342     "kind": "theorem",
29343     "module": "PaperICompletion8.RegularMultiplicity",
29344     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.naturalDirectSum_seedRank",
29345     "runtime_only": false
29346   },
29347   {
29348     "axioms": [
29349       "propext",
29350       "Classical.choice",
29351       "Quot.sound"
29352     ],
29353     "in_project_namespace": true,
29354     "kind": "theorem",
29355     "module": "PaperICompletion5.CyclicGeometricCriterion",
29356     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff._proof_1_2",
29357     "runtime_only": false
29358   },
29359   {
29360     "axioms": [
29361       "propext"
29362     ],
29363     "in_project_namespace": true,
29364     "kind": "theorem",
29365     "module": "KomorebiVerification.ProjectorCore",
29366     "name": "Komorebi.Algebra.MatrixSupported.add",
29367     "runtime_only": false
29368   },
29369   {
29370     "axioms": [
29371       "propext",
29372       "Classical.choice",
29373       "Quot.sound"
29374     ],
29375     "in_project_namespace": true,
29376     "kind": "definition",
29377     "module": "PaperICompletion.SpectralCertificates",
29378     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity",
29379     "runtime_only": false
29380   },
29381   {
29382     "axioms": [
29383       "propext",
29384       "Classical.choice",
29385       "Quot.sound"
29386     ],
29387     "in_project_namespace": true,
29388     "kind": "theorem",
29389     "module": "PaperIRelease.AlgebraClassGrouping",
29390     "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq",
29391     "runtime_only": false
29392   },
29393   {
29394     "axioms": [
29395       "propext",
29396       "Classical.choice",
29397       "Quot.sound"
29398     ],
29399     "in_project_namespace": true,
29400     "kind": "definition",
29401     "module": "PaperICompletion4.IntrinsicPrimary",
29402     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal",
29403     "runtime_only": false
29404   },
29405   {
29406     "axioms": [
29407       "propext",
29408       "Classical.choice",
29409       "Quot.sound"
29410     ],
29411     "in_project_namespace": true,
29412     "kind": "theorem",
29413     "module": "PaperIRelease.PolynomialModule",
29414     "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_5",
29415     "runtime_only": false
29416   },
29417   {
29418     "axioms": [
29419       "propext",
29420       "Classical.choice",
29421       "Quot.sound"
29422     ],
29423     "in_project_namespace": false,
29424     "kind": "definition",
29425     "module": "PaperIRelease.TopologyUnconditional",
29426     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues",
29427     "runtime_only": false
29428   },
29429   {
29430     "axioms": [
29431       "propext",
29432       "Classical.choice",
29433       "Quot.sound"
29434     ],
29435     "in_project_namespace": true,
29436     "kind": "theorem",
29437     "module": "PaperIRelease.GrammarTyped",
29438     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_2",
29439     "runtime_only": false
29440   },
29441   {
29442     "axioms": [
29443       "propext",
29444       "Classical.choice",
29445       "Quot.sound"
29446     ],
29447     "in_project_namespace": true,
29448     "kind": "theorem",
29449     "module": "PaperIRelease.TopologyCategories",
29450     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.continuous",
29451     "runtime_only": false
29452   },
29453   {
29454     "axioms": [
29455       "propext",
29456       "Classical.choice",
29457       "Quot.sound"
29458     ],
29459     "in_project_namespace": true,
29460     "kind": "definition",
29461     "module": "KomorebiVerification.TopologicalCompletion",
29462     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation._sizeOf_inst",
29463     "runtime_only": false
29464   },
29465   {
29466     "axioms": [
29467       "propext",
29468       "Classical.choice",
29469       "Quot.sound"
29470     ],
29471     "in_project_namespace": true,
29472     "kind": "theorem",
29473     "module": "PaperIRelease.CategoryPackets",
29474     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.inj",
29475     "runtime_only": false
29476   },
29477   {
29478     "axioms": [
29479       "propext",
29480       "Classical.choice",
29481       "Quot.sound"
29482     ],
29483     "in_project_namespace": true,
29484     "kind": "theorem",
29485     "module": "PaperIRelease.GeneralNormedPackets",
29486     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv._proof_1",
29487     "runtime_only": false
29488   },
29489   {
29490     "axioms": [
29491       "propext",
29492       "Classical.choice",
29493       "Quot.sound"
29494     ],
29495     "in_project_namespace": true,
29496     "kind": "theorem",
29497     "module": "KomorebiVerification.PaperIBlockCompletion",
29498     "name": "Komorebi.Algebra.matrixSupportMulClosed_iff_transitive",
29499     "runtime_only": false
29500   },
29501   {
29502     "axioms": [
29503       "propext",
29504       "Classical.choice",
29505       "Quot.sound"
29506     ],
29507     "in_project_namespace": true,
29508     "kind": "inductive",
29509     "module": "PaperIRelease.CategoryPackets",
29510     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism",
29511     "runtime_only": false
29512   },
29513   {
29514     "axioms": [
29515       "propext",
29516       "Classical.choice",
29517       "Quot.sound"
29518     ],
29519     "in_project_namespace": true,
29520     "kind": "theorem",
29521     "module": "PaperIRelease.PacketLocalRank",
29522     "name": "Komorebi.PaperIRelease.groupedRange_preserved",
29523     "runtime_only": false
29524   },
29525   {
29526     "axioms": [],
29527     "in_project_namespace": true,
29528     "kind": "definition",
29529     "module": "KomorebiVerification.ProjectorCore",
29530     "name": "Komorebi.ClaimRecord.mk.noConfusion",
29531     "runtime_only": false
29532   },
29533   {
29534     "axioms": [
29535       "propext",
29536       "Classical.choice",
29537       "Quot.sound"
29538     ],
29539     "in_project_namespace": true,
29540     "kind": "theorem",
29541     "module": "KomorebiVerification.PacketNaturalityCompletion",
29542     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR._proof_2",
29543     "runtime_only": false
29544   },
29545   {
29546     "axioms": [
29547       "propext",
29548       "Classical.choice",
29549       "Quot.sound"
29550     ],
29551     "in_project_namespace": true,
29552     "kind": "definition",
29553     "module": "PaperIRelease.PacketPureRank",
29554     "name": "Komorebi.PaperIRelease.PureGenerates",
29555     "runtime_only": false
29556   },
29557   {
29558     "axioms": [
29559       "propext",
29560       "Classical.choice",
29561       "Quot.sound"
29562     ],
29563     "in_project_namespace": true,
29564     "kind": "theorem",
29565     "module": "PaperIRelease.AlgebraTransfer",
29566     "name": "Komorebi.PaperIRelease.target_coordinate_active_sum",
29567     "runtime_only": false
29568   },
29569   {
29570     "axioms": [
29571       "propext",
29572       "Classical.choice",
29573       "Quot.sound"
29574     ],
29575     "in_project_namespace": true,
29576     "kind": "theorem",
29577     "module": "PaperICompletion3.PrimarySeedFormula",
29578     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_primaryProduct_equiv",
29579     "runtime_only": false
29580   },
29581   {
29582     "axioms": [
29583       "propext",
29584       "Classical.choice",
29585       "Quot.sound"
29586     ],
29587     "in_project_namespace": true,
29588     "kind": "theorem",
29589     "module": "KomorebiVerification.SingleOperatorGraph",
29590     "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate.eq_1",
29591     "runtime_only": false
29592   },
29593   {
29594     "axioms": [
29595       "propext",
29596       "Classical.choice",
29597       "Quot.sound"
29598     ],
29599     "in_project_namespace": true,
29600     "kind": "theorem",
29601     "module": "PaperIRelease.AlgebraPreorder",
29602     "name": "Komorebi.PaperIRelease.strictSupport_mul_right",
29603     "runtime_only": false
29604   },
29605   {
29606     "axioms": [
29607       "propext",
29608       "Classical.choice",
29609       "Quot.sound"
29610     ],
29611     "in_project_namespace": true,
29612     "kind": "definition",
29613     "module": "KomorebiVerification.EllipticAlgorithms",
29614     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._unsafe_rec",
29615     "runtime_only": true
29616   },
29617   {
29618     "axioms": [],
29619     "in_project_namespace": true,
29620     "kind": "constructor",
29621     "module": "KomorebiVerification.ProjectorCore",
29622     "name": "Komorebi.FormalizationStatus.queued",
29623     "runtime_only": false
29624   },
29625   {
29626     "axioms": [
29627       "propext",
29628       "Quot.sound"
29629     ],
29630     "in_project_namespace": true,
29631     "kind": "theorem",
29632     "module": "KomorebiVerification.SeedRankOperations",
29633     "name": "Komorebi.SeedRankOperations.productModule._proof_4",
29634     "runtime_only": false
29635   },
29636   {
29637     "axioms": [],
29638     "in_project_namespace": true,
29639     "kind": "recursor",
29640     "module": "KomorebiVerification.ProjectorCore",
29641     "name": "Komorebi.ClaimRecord.rec",
29642     "runtime_only": false
29643   },
29644   {
29645     "axioms": [
29646       "propext",
29647       "Classical.choice",
29648       "Quot.sound"
29649     ],
29650     "in_project_namespace": true,
29651     "kind": "theorem",
29652     "module": "PaperIRelease.GraphSources",
29653     "name": "Komorebi.PaperIRelease.FiniteDigraph.exists_source_reaching",
29654     "runtime_only": false
29655   },
29656   {
29657     "axioms": [
29658       "propext",
29659       "Classical.choice",
29660       "Quot.sound"
29661     ],
29662     "in_project_namespace": false,
29663     "kind": "theorem",
29664     "module": "PaperIRelease.TopologyUnconditional",
29665     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.eq_zero_of_unconditionalNorm_eq_zero",
29666     "runtime_only": false
29667   },
29668   {
29669     "axioms": [
29670       "propext",
29671       "Classical.choice",
29672       "Quot.sound"
29673     ],
29674     "in_project_namespace": false,
29675     "kind": "theorem",
29676     "module": "PaperIRelease.TopologyDenseCompletion",
29677     "name": "PaperIRelease.TopologyDenseCompletion.transported_uniformAddGroup",
29678     "runtime_only": false
29679   },
29680   {
29681     "axioms": [],
29682     "in_project_namespace": false,
29683     "kind": "theorem",
29684     "module": "KomorebiVerification.ProjectorCore",
29685     "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.eq_2",
29686     "runtime_only": false
29687   },
29688   {
29689     "axioms": [],
29690     "in_project_namespace": true,
29691     "kind": "definition",
29692     "module": "KomorebiVerification.ProjectorCore",
29693     "name": "Komorebi.ClaimRecord.phase",
29694     "runtime_only": false
29695   },
29696   {
29697     "axioms": [
29698       "propext",
29699       "Classical.choice",
29700       "Quot.sound"
29701     ],
29702     "in_project_namespace": true,
29703     "kind": "theorem",
29704     "module": "KomorebiVerification.PacketNaturalityCompletion",
29705     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_1",
29706     "runtime_only": false
29707   },
29708   {
29709     "axioms": [
29710       "propext",
29711       "Classical.choice",
29712       "Quot.sound"
29713     ],
29714     "in_project_namespace": true,
29715     "kind": "inductive",
29716     "module": "PaperIRelease.CategoryPackets",
29717     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject",
29718     "runtime_only": false
29719   },
29720   {
29721     "axioms": [
29722       "propext",
29723       "Quot.sound"
29724     ],
29725     "in_project_namespace": true,
29726     "kind": "theorem",
29727     "module": "PaperIRelease.PacketUniversal",
29728     "name": "Komorebi.PaperIRelease.PacketUniversal.packetProjection._proof_1",
29729     "runtime_only": false
29730   },
29731   {
29732     "axioms": [
29733       "propext",
29734       "Classical.choice",
29735       "Quot.sound"
29736     ],
29737     "in_project_namespace": true,
29738     "kind": "theorem",
29739     "module": "KomorebiVerification.TopologicalCompletion",
29740     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_8",
29741     "runtime_only": false
29742   },
29743   {
29744     "axioms": [
29745       "propext",
29746       "Classical.choice",
29747       "Quot.sound"
29748     ],
29749     "in_project_namespace": true,
29750     "kind": "theorem",
29751     "module": "PaperIRelease.PacketTopology",
29752     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_1",
29753     "runtime_only": false
29754   },
29755   {
29756     "axioms": [
29757       "propext",
29758       "Classical.choice",
29759       "Quot.sound"
29760     ],
29761     "in_project_namespace": true,
29762     "kind": "theorem",
29763     "module": "PaperIRelease.TopologyCategories",
29764     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.injEq",
29765     "runtime_only": false
29766   },
29767   {
29768     "axioms": [
29769       "propext",
29770       "Classical.choice",
29771       "Quot.sound"
29772     ],
29773     "in_project_namespace": true,
29774     "kind": "definition",
29775     "module": "PaperIRelease.CategoryPackets",
29776     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ctorIdx",
29777     "runtime_only": false
29778   },
29779   {
29780     "axioms": [
29781       "propext",
29782       "Classical.choice",
29783       "Quot.sound"
29784     ],
29785     "in_project_namespace": true,
29786     "kind": "theorem",
29787     "module": "PaperIRelease.CategoryBoundaries",
29788     "name": "Komorebi.PaperIRelease.CategoryBoundaries.merge_block_naturality",
29789     "runtime_only": false
29790   },
29791   {
29792     "axioms": [
29793       "propext",
29794       "Classical.choice",
29795       "Quot.sound"
29796     ],
29797     "in_project_namespace": false,
29798     "kind": "theorem",
29799     "module": "PaperIRelease.TopologyUnconditionalBridge",
29800     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceIsometry._proof_1",
29801     "runtime_only": false
29802   },
29803   {
29804     "axioms": [
29805       "propext",
29806       "Classical.choice",
29807       "Quot.sound"
29808     ],
29809     "in_project_namespace": false,
29810     "kind": "theorem",
29811     "module": "ReleaseBoundary",
29812     "name": "PaperIBlock08Tests.zero_matrix_size_breaks_unguarded_bound",
29813     "runtime_only": false
29814   },
29815   {
29816     "axioms": [
29817       "propext",
29818       "Quot.sound"
29819     ],
29820     "in_project_namespace": true,
29821     "kind": "theorem",
29822     "module": "PaperIRelease.GrammarTyped",
29823     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.inj",
29824     "runtime_only": false
29825   },
29826   {
29827     "axioms": [
29828       "propext",
29829       "Classical.choice",
29830       "Quot.sound"
29831     ],
29832     "in_project_namespace": true,
29833     "kind": "theorem",
29834     "module": "PaperICompletion4.OperatorIntrinsicFormula",
29835     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_fiber",
29836     "runtime_only": false
29837   },
29838   {
29839     "axioms": [
29840       "propext",
29841       "Classical.choice",
29842       "Quot.sound"
29843     ],
29844     "in_project_namespace": true,
29845     "kind": "theorem",
29846     "module": "PaperICompletion.ConditionedCoordinates",
29847     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator._proof_1",
29848     "runtime_only": false
29849   },
29850   {
29851     "axioms": [
29852       "propext",
29853       "Classical.choice",
29854       "Quot.sound"
29855     ],
29856     "in_project_namespace": true,
29857     "kind": "theorem",
29858     "module": "PaperIRelease.CategoryPackets",
29859     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ext",
29860     "runtime_only": false
29861   },
29862   {
29863     "axioms": [],
29864     "in_project_namespace": true,
29865     "kind": "definition",
29866     "module": "KomorebiVerification.ProjectorCore",
29867     "name": "Komorebi.Algebra.MatrixSupported",
29868     "runtime_only": false
29869   },
29870   {
29871     "axioms": [
29872       "propext",
29873       "Classical.choice",
29874       "Quot.sound"
29875     ],
29876     "in_project_namespace": true,
29877     "kind": "theorem",
29878     "module": "PaperIRelease.GraphSources",
29879     "name": "Komorebi.PaperIRelease.FiniteDigraph.source_vertex_iff",
29880     "runtime_only": false
29881   },
29882   {
29883     "axioms": [
29884       "propext",
29885       "Quot.sound"
29886     ],
29887     "in_project_namespace": true,
29888     "kind": "theorem",
29889     "module": "PaperICompletion4.ResidueQuotient",
29890     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_1",
29891     "runtime_only": false
29892   },
29893   {
29894     "axioms": [],
29895     "in_project_namespace": true,
29896     "kind": "definition",
29897     "module": "PaperIRelease.GrammarPaths",
29898     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1",
29899     "runtime_only": false
29900   },
29901   {
29902     "axioms": [
29903       "propext",
29904       "Quot.sound"
29905     ],
29906     "in_project_namespace": true,
29907     "kind": "theorem",
29908     "module": "PaperIRelease.GraphSources",
29909     "name": "Komorebi.PaperIRelease.FiniteDigraph.component_eq_iff",
29910     "runtime_only": false
29911   },
29912   {
29913     "axioms": [
29914       "propext",
29915       "Classical.choice",
29916       "Quot.sound"
29917     ],
29918     "in_project_namespace": false,
29919     "kind": "theorem",
29920     "module": "ReleaseBoundary",
29921     "name": "PaperIBlock08Tests.absent_factor_contributes_zero",
29922     "runtime_only": false
29923   },
29924   {
29925     "axioms": [
29926       "propext",
29927       "Classical.choice",
29928       "Quot.sound"
29929     ],
29930     "in_project_namespace": true,
29931     "kind": "theorem",
29932     "module": "KomorebiVerification.TopologicalCompletion",
29933     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_9",
29934     "runtime_only": false
29935   },
29936   {
29937     "axioms": [
29938       "propext",
29939       "Classical.choice",
29940       "Quot.sound"
29941     ],
29942     "in_project_namespace": true,
29943     "kind": "theorem",
29944     "module": "PaperIRelease.AlgebraSupport",
29945     "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_4",
29946     "runtime_only": false
29947   },
29948   {
29949     "axioms": [
29950       "propext",
29951       "Classical.choice",
29952       "Quot.sound"
29953     ],
29954     "in_project_namespace": true,
29955     "kind": "theorem",
29956     "module": "PaperIRelease.PacketDescent",
29957     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_1",
29958     "runtime_only": false
29959   },
29960   {
29961     "axioms": [
29962       "propext",
29963       "Classical.choice",
29964       "Quot.sound"
29965     ],
29966     "in_project_namespace": true,
29967     "kind": "theorem",
29968     "module": "PaperICompletion8.RegularMultiplicity",
29969     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_isSimple",
29970     "runtime_only": false
29971   },
29972   {
29973     "axioms": [
29974       "propext",
29975       "Classical.choice",
29976       "Quot.sound"
29977     ],
29978     "in_project_namespace": true,
29979     "kind": "definition",
29980     "module": "PaperIRelease.GrammarIdeal",
29981     "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented",
29982     "runtime_only": false
29983   },
29984   {
29985     "axioms": [
29986       "propext",
29987       "Classical.choice",
29988       "Quot.sound"
29989     ],
29990     "in_project_namespace": true,
29991     "kind": "theorem",
29992     "module": "KomorebiVerification.TopologicalCompletion",
29993     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_apply_coe",
29994     "runtime_only": false
29995   },
29996   {
29997     "axioms": [
29998       "propext",
29999       "Classical.choice",
30000       "Quot.sound"
30001     ],
30002     "in_project_namespace": true,
30003     "kind": "theorem",
30004     "module": "PaperICompletion4.ResidueQuotient",
30005     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv.eq_1",
30006     "runtime_only": false
30007   },
30008   {
30009     "axioms": [
30010       "propext",
30011       "Classical.choice",
30012       "Quot.sound"
30013     ],
30014     "in_project_namespace": true,
30015     "kind": "definition",
30016     "module": "KomorebiVerification.PacketNaturalityCompletion",
30017     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum",
30018     "runtime_only": false
30019   },
30020   {
30021     "axioms": [
30022       "propext",
30023       "Classical.choice",
30024       "Quot.sound"
30025     ],
30026     "in_project_namespace": true,
30027     "kind": "theorem",
30028     "module": "KomorebiVerification.EllipticAlgorithms",
30029     "name": "Komorebi.EllipticCoordinates.My.eq_1",
30030     "runtime_only": false
30031   },
30032   {
30033     "axioms": [
30034       "propext",
30035       "Classical.choice",
30036       "Quot.sound"
30037     ],
30038     "in_project_namespace": true,
30039     "kind": "definition",
30040     "module": "KomorebiVerification.TopologicalCompletion",
30041     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.recOn",
30042     "runtime_only": false
30043   },
30044   {
30045     "axioms": [
30046       "propext",
30047       "Classical.choice",
30048       "Quot.sound"
30049     ],
30050     "in_project_namespace": true,
30051     "kind": "theorem",
30052     "module": "PaperIRelease.GrammarAlgebra",
30053     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_left",
30054     "runtime_only": false
30055   },
30056   {
30057     "axioms": [
30058       "propext",
30059       "Classical.choice",
30060       "Quot.sound"
30061     ],
30062     "in_project_namespace": true,
30063     "kind": "definition",
30064     "module": "KomorebiVerification.PacketNaturalityCompletion",
30065     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism._sizeOf_inst",
30066     "runtime_only": false
30067   },
30068   {
30069     "axioms": [],
30070     "in_project_namespace": true,
30071     "kind": "definition",
30072     "module": "KomorebiVerification.ProjectorCore",
30073     "name": "Komorebi.FormalizationStatus.numericalOnly.elim",
30074     "runtime_only": false
30075   },
30076   {
30077     "axioms": [
30078       "propext",
30079       "Quot.sound"
30080     ],
30081     "in_project_namespace": false,
30082     "kind": "theorem",
30083     "module": "KomorebiVerification.SeedRankOperations",
30084     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensor_familyGenerates",
30085     "runtime_only": false
30086   },
30087   {
30088     "axioms": [],
30089     "in_project_namespace": true,
30090     "kind": "definition",
30091     "module": "KomorebiVerification.ProjectorCore",
30092     "name": "Komorebi.ClaimRecord.corpus",
30093     "runtime_only": false
30094   },
30095   {
30096     "axioms": [
30097       "propext",
30098       "Quot.sound"
30099     ],
30100     "in_project_namespace": true,
30101     "kind": "theorem",
30102     "module": "PaperIRelease.ScalarExtension",
30103     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_3",
30104     "runtime_only": false
30105   },
30106   {
30107     "axioms": [
30108       "propext",
30109       "Classical.choice",
30110       "Quot.sound"
30111     ],
30112     "in_project_namespace": true,
30113     "kind": "theorem",
30114     "module": "PaperIRelease.AlgebraSupport",
30115     "name": "Komorebi.PaperIRelease.supportSubmodule._proof_5",
30116     "runtime_only": false
30117   },
30118   {
30119     "axioms": [
30120       "propext",
30121       "Classical.choice",
30122       "Quot.sound"
30123     ],
30124     "in_project_namespace": true,
30125     "kind": "theorem",
30126     "module": "PaperICompletion3.PrimarySeedFormula",
30127     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity_le_of_generates._simp_1_2",
30128     "runtime_only": false
30129   },
30130   {
30131     "axioms": [
30132       "propext",
30133       "Classical.choice",
30134       "Quot.sound"
30135     ],
30136     "in_project_namespace": true,
30137     "kind": "theorem",
30138     "module": "KomorebiVerification.ProjectorCore",
30139     "name": "Komorebi.Quantum.finiteAmplitude_zero",
30140     "runtime_only": false
30141   },
30142   {
30143     "axioms": [
30144       "propext",
30145       "Quot.sound"
30146     ],
30147     "in_project_namespace": true,
30148     "kind": "theorem",
30149     "module": "PaperICompletion6.OneInvariantFactor",
30150     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_3",
30151     "runtime_only": false
30152   },
30153   {
30154     "axioms": [
30155       "propext",
30156       "Quot.sound"
30157     ],
30158     "in_project_namespace": true,
30159     "kind": "theorem",
30160     "module": "PaperIRelease.GrammarModules",
30161     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.inj",
30162     "runtime_only": false
30163   },
30164   {
30165     "axioms": [
30166       "propext",
30167       "Quot.sound"
30168     ],
30169     "in_project_namespace": true,
30170     "kind": "theorem",
30171     "module": "PaperIRelease.GrammarModules",
30172     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_2",
30173     "runtime_only": false
30174   },
30175   {
30176     "axioms": [
30177       "propext",
30178       "Classical.choice",
30179       "Quot.sound"
30180     ],
30181     "in_project_namespace": true,
30182     "kind": "definition",
30183     "module": "PaperIRelease.PolynomialMonic",
30184     "name": "Komorebi.PaperIRelease.PolynomialModule.monicSpectrumEquiv",
30185     "runtime_only": false
30186   },
30187   {
30188     "axioms": [
30189       "propext"
30190     ],
30191     "in_project_namespace": true,
30192     "kind": "theorem",
30193     "module": "PaperIRelease.CategoryExport",
30194     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.injEq",
30195     "runtime_only": false
30196   },
30197   {
30198     "axioms": [
30199       "propext",
30200       "Classical.choice",
30201       "Quot.sound"
30202     ],
30203     "in_project_namespace": false,
30204     "kind": "definition",
30205     "module": "PaperIRelease.TopologyCountablePackets",
30206     "name": "PaperIRelease.TopologyCountablePackets.Projectors._sizeOf_1",
30207     "runtime_only": false
30208   },
30209   {
30210     "axioms": [
30211       "propext",
30212       "Classical.choice",
30213       "Quot.sound"
30214     ],
30215     "in_project_namespace": true,
30216     "kind": "theorem",
30217     "module": "PaperICompletion.SpectralCertificates",
30218     "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedIndex_eigenvalue",
30219     "runtime_only": false
30220   },
30221   {
30222     "axioms": [
30223       "propext",
30224       "Classical.choice",
30225       "Quot.sound"
30226     ],
30227     "in_project_namespace": false,
30228     "kind": "theorem",
30229     "module": "PaperIRelease.TopologyFiniteCompletion",
30230     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_2",
30231     "runtime_only": false
30232   },
30233   {
30234     "axioms": [
30235       "propext",
30236       "Classical.choice",
30237       "Quot.sound"
30238     ],
30239     "in_project_namespace": true,
30240     "kind": "theorem",
30241     "module": "PaperIRelease.PacketAggregation",
30242     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_1",
30243     "runtime_only": false
30244   },
30245   {
30246     "axioms": [
30247       "propext",
30248       "Quot.sound"
30249     ],
30250     "in_project_namespace": true,
30251     "kind": "theorem",
30252     "module": "PaperIRelease.SeedOperations",
30253     "name": "Komorebi.PaperIRelease.SeedOperations.cyclic_annihilator_eq_module_iff",
30254     "runtime_only": false
30255   },
30256   {
30257     "axioms": [
30258       "propext",
30259       "Classical.choice",
30260       "Quot.sound"
30261     ],
30262     "in_project_namespace": false,
30263     "kind": "theorem",
30264     "module": "PaperIRelease.TopologyCountablePackets",
30265     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv._proof_1",
30266     "runtime_only": false
30267   },
30268   {
30269     "axioms": [
30270       "propext",
30271       "Classical.choice",
30272       "Quot.sound"
30273     ],
30274     "in_project_namespace": true,
30275     "kind": "theorem",
30276     "module": "PaperIRelease.AlgebraPreorder",
30277     "name": "Komorebi.PaperIRelease.nonzero_word_block_strictPath",
30278     "runtime_only": false
30279   },
30280   {
30281     "axioms": [
30282       "propext",
30283       "Classical.choice",
30284       "Quot.sound"
30285     ],
30286     "in_project_namespace": false,
30287     "kind": "theorem",
30288     "module": "PaperIRelease.TopologyUnconditionalBridge",
30289     "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_1",
30290     "runtime_only": false
30291   },
30292   {
30293     "axioms": [
30294       "propext",
30295       "Classical.choice",
30296       "Quot.sound"
30297     ],
30298     "in_project_namespace": false,
30299     "kind": "definition",
30300     "module": "PaperIRelease.TopologyCountablePackets",
30301     "name": "PaperIRelease.TopologyCountablePackets.Projectors.ctorIdx",
30302     "runtime_only": false
30303   },
30304   {
30305     "axioms": [
30306       "propext",
30307       "Classical.choice",
30308       "Quot.sound"
30309     ],
30310     "in_project_namespace": true,
30311     "kind": "theorem",
30312     "module": "PaperIRelease.AlgebraTransfer",
30313     "name": "Komorebi.PaperIRelease.packetPure_iff_zero_or_range",
30314     "runtime_only": false
30315   },
30316   {
30317     "axioms": [
30318       "propext",
30319       "Classical.choice",
30320       "Quot.sound"
30321     ],
30322     "in_project_namespace": true,
30323     "kind": "definition",
30324     "module": "PaperIRelease.CategoryPackets",
30325     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.ctorIdx",
30326     "runtime_only": false
30327   },
30328   {
30329     "axioms": [
30330       "propext",
30331       "Classical.choice",
30332       "Quot.sound"
30333     ],
30334     "in_project_namespace": true,
30335     "kind": "definition",
30336     "module": "PaperIRelease.CategoryPackets",
30337     "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector",
30338     "runtime_only": false
30339   },
30340   {
30341     "axioms": [
30342       "propext",
30343       "Classical.choice",
30344       "Quot.sound"
30345     ],
30346     "in_project_namespace": true,
30347     "kind": "theorem",
30348     "module": "PaperICompletion3.OperatorPrimaryAPI",
30349     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.cyclic_of_label_injective",
30350     "runtime_only": false
30351   },
30352   {
30353     "axioms": [
30354       "propext",
30355       "Classical.choice",
30356       "Quot.sound"
30357     ],
30358     "in_project_namespace": true,
30359     "kind": "theorem",
30360     "module": "PaperICompletion3.PrimarySeedFormula",
30361     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primaryProduct_seedNumber_isLeast",
30362     "runtime_only": false
30363   },
30364   {
30365     "axioms": [
30366       "propext",
30367       "Classical.choice",
30368       "Quot.sound"
30369     ],
30370     "in_project_namespace": true,
30371     "kind": "theorem",
30372     "module": "PaperIRelease.ExactSequences",
30373     "name": "Komorebi.PaperIRelease.seedRank_le_add_of_exact",
30374     "runtime_only": false
30375   },
30376   {
30377     "axioms": [
30378       "propext",
30379       "Classical.choice",
30380       "Quot.sound"
30381     ],
30382     "in_project_namespace": true,
30383     "kind": "constructor",
30384     "module": "PaperIRelease.CategoryPackets",
30385     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk",
30386     "runtime_only": false
30387   },
30388   {
30389     "axioms": [
30390       "propext",
30391       "Classical.choice",
30392       "Quot.sound"
30393     ],
30394     "in_project_namespace": true,
30395     "kind": "definition",
30396     "module": "KomorebiVerification.EllipticAlgorithms",
30397     "name": "Komorebi.FiniteAlgorithms.transferGraph",
30398     "runtime_only": false
30399   },
30400   {
30401     "axioms": [
30402       "propext",
30403       "Classical.choice",
30404       "Quot.sound"
30405     ],
30406     "in_project_namespace": true,
30407     "kind": "theorem",
30408     "module": "PaperICompletion8.DivisionProduct",
30409     "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_seedRank_eq_maxCeilDiv",
30410     "runtime_only": false
30411   },
30412   {
30413     "axioms": [
30414       "propext",
30415       "Classical.choice",
30416       "Quot.sound"
30417     ],
30418     "in_project_namespace": true,
30419     "kind": "theorem",
30420     "module": "PaperICompletion7.Nakayama",
30421     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_2",
30422     "runtime_only": false
30423   },
30424   {
30425     "axioms": [],
30426     "in_project_namespace": true,
30427     "kind": "constructor",
30428     "module": "PaperIRelease.CategoryExport",
30429     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar",
30430     "runtime_only": false
30431   },
30432   {
30433     "axioms": [
30434       "propext"
30435     ],
30436     "in_project_namespace": true,
30437     "kind": "theorem",
30438     "module": "KomorebiVerification.ProjectorCore",
30439     "name": "Komorebi.FiniteDifference.forwardDiff_neg",
30440     "runtime_only": false
30441   },
30442   {
30443     "axioms": [],
30444     "in_project_namespace": true,
30445     "kind": "definition",
30446     "module": "PaperIRelease.CategoryExport",
30447     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.noConfusion",
30448     "runtime_only": false
30449   },
30450   {
30451     "axioms": [
30452       "propext",
30453       "Classical.choice",
30454       "Quot.sound"
30455     ],
30456     "in_project_namespace": true,
30457     "kind": "theorem",
30458     "module": "PaperICompletion8.RegularMultiplicity",
30459     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_3",
30460     "runtime_only": false
30461   },
30462   {
30463     "axioms": [
30464       "propext",
30465       "Classical.choice",
30466       "Quot.sound"
30467     ],
30468     "in_project_namespace": true,
30469     "kind": "theorem",
30470     "module": "PaperICompletion.SpectralCertificates",
30471     "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList.eq_1",
30472     "runtime_only": false
30473   },
30474   {
30475     "axioms": [
30476       "propext",
30477       "Classical.choice",
30478       "Quot.sound"
30479     ],
30480     "in_project_namespace": false,
30481     "kind": "definition",
30482     "module": "PaperIRelease.TopologyDenseCompletion",
30483     "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv",
30484     "runtime_only": false
30485   },
30486   {
30487     "axioms": [
30488       "propext",
30489       "Quot.sound"
30490     ],
30491     "in_project_namespace": true,
30492     "kind": "theorem",
30493     "module": "KomorebiVerification.SingleOperatorGraph",
30494     "name": "Komorebi.SingleOperatorGraph.seedPresentation._proof_1",
30495     "runtime_only": false
30496   },
30497   {
30498     "axioms": [
30499       "propext",
30500       "Classical.choice",
30501       "Quot.sound"
30502     ],
30503     "in_project_namespace": true,
30504     "kind": "theorem",
30505     "module": "PaperIRelease.AlgebraQuotient",
30506     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_10",
30507     "runtime_only": false
30508   },
30509   {
30510     "axioms": [
30511       "propext"
30512     ],
30513     "in_project_namespace": true,
30514     "kind": "theorem",
30515     "module": "PaperICompletion4.IntrinsicPrimary",
30516     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_3",
30517     "runtime_only": false
30518   },
30519   {
30520     "axioms": [
30521       "propext",
30522       "Classical.choice",
30523       "Quot.sound"
30524     ],
30525     "in_project_namespace": true,
30526     "kind": "theorem",
30527     "module": "PaperICompletion8.RegularMultiplicity",
30528     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv._proof_2",
30529     "runtime_only": false
30530   },
30531   {
30532     "axioms": [
30533       "propext",
30534       "Classical.choice",
30535       "Quot.sound"
30536     ],
30537     "in_project_namespace": true,
30538     "kind": "recursor",
30539     "module": "KomorebiVerification.ProjectorCore",
30540     "name": "Komorebi.Foundation.LinearProjectorFamily.rec",
30541     "runtime_only": false
30542   },
30543   {
30544     "axioms": [
30545       "propext",
30546       "Quot.sound"
30547     ],
30548     "in_project_namespace": true,
30549     "kind": "theorem",
30550     "module": "KomorebiVerification.EllipticAlgorithms",
30551     "name": "Komorebi.FiniteAlgorithms.orbitClosureStep._proof_1",
30552     "runtime_only": false
30553   },
30554   {
30555     "axioms": [],
30556     "in_project_namespace": true,
30557     "kind": "recursor",
30558     "module": "KomorebiVerification.ProjectorCore",
30559     "name": "Komorebi.FormalizationStatus.rec",
30560     "runtime_only": false
30561   },
30562   {
30563     "axioms": [
30564       "propext",
30565       "Classical.choice",
30566       "Quot.sound"
30567     ],
30568     "in_project_namespace": false,
30569     "kind": "theorem",
30570     "module": "ReleaseBoundary",
30571     "name": "PaperIBlock08Tests.dualLinearEquiv._proof_2",
30572     "runtime_only": false
30573   },
30574   {
30575     "axioms": [
30576       "propext",
30577       "Classical.choice",
30578       "Quot.sound"
30579     ],
30580     "in_project_namespace": true,
30581     "kind": "recursor",
30582     "module": "KomorebiVerification.TopologicalCompletion",
30583     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.rec",
30584     "runtime_only": false
30585   },
30586   {
30587     "axioms": [
30588       "propext",
30589       "Classical.choice",
30590       "Quot.sound"
30591     ],
30592     "in_project_namespace": true,
30593     "kind": "theorem",
30594     "module": "PaperIRelease.GeneralNormedPackets",
30595     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.idempotentRange_eq_closure_map",
30596     "runtime_only": false
30597   },
30598   {
30599     "axioms": [
30600       "propext",
30601       "Classical.choice",
30602       "Quot.sound"
30603     ],
30604     "in_project_namespace": true,
30605     "kind": "theorem",
30606     "module": "PaperICompletion4.GroupedPrimary",
30607     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryProduct_mem_iff",
30608     "runtime_only": false
30609   },
30610   {
30611     "axioms": [],
30612     "in_project_namespace": true,
30613     "kind": "theorem",
30614     "module": "PaperICompletion7.Nakayama",
30615     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_1",
30616     "runtime_only": false
30617   },
30618   {
30619     "axioms": [
30620       "propext",
30621       "Classical.choice",
30622       "Quot.sound"
30623     ],
30624     "in_project_namespace": true,
30625     "kind": "theorem",
30626     "module": "PaperIRelease.GrammarEquivalence",
30627     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_8",
30628     "runtime_only": false
30629   },
30630   {
30631     "axioms": [],
30632     "in_project_namespace": true,
30633     "kind": "definition",
30634     "module": "KomorebiVerification.ProjectorCore",
30635     "name": "Komorebi.ClaimKind.classicalInput.elim",
30636     "runtime_only": false
30637   },
30638   {
30639     "axioms": [
30640       "propext",
30641       "Classical.choice",
30642       "Quot.sound"
30643     ],
30644     "in_project_namespace": false,
30645     "kind": "theorem",
30646     "module": "PaperIRelease.TopologyDenseCompletion",
30647     "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv_apply_mk",
30648     "runtime_only": false
30649   },
30650   {
30651     "axioms": [
30652       "propext",
30653       "Classical.choice",
30654       "Quot.sound"
30655     ],
30656     "in_project_namespace": true,
30657     "kind": "theorem",
30658     "module": "PaperIRelease.GrammarPaths",
30659     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_def",
30660     "runtime_only": false
30661   },
30662   {
30663     "axioms": [
30664       "propext",
30665       "Classical.choice",
30666       "Quot.sound"
30667     ],
30668     "in_project_namespace": true,
30669     "kind": "theorem",
30670     "module": "PaperIRelease.BoundedStar",
30671     "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_3",
30672     "runtime_only": false
30673   },
30674   {
30675     "axioms": [
30676       "propext",
30677       "Classical.choice",
30678       "Quot.sound"
30679     ],
30680     "in_project_namespace": true,
30681     "kind": "theorem",
30682     "module": "KomorebiVerification.PacketNaturalityCompletion",
30683     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.mappedGeneratedHull_eq_top",
30684     "runtime_only": false
30685   },
30686   {
30687     "axioms": [
30688       "propext",
30689       "Classical.choice",
30690       "Quot.sound"
30691     ],
30692     "in_project_namespace": false,
30693     "kind": "theorem",
30694     "module": "PaperIRelease.TopologySeedRank",
30695     "name": "PaperIRelease.TopologyTransport.seedRank_le_of_surjective",
30696     "runtime_only": false
30697   },
30698   {
30699     "axioms": [
30700       "propext",
30701       "Quot.sound"
30702     ],
30703     "in_project_namespace": true,
30704     "kind": "theorem",
30705     "module": "PaperIRelease.GrammarEquivalence",
30706     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_1",
30707     "runtime_only": false
30708   },
30709   {
30710     "axioms": [
30711       "propext",
30712       "Quot.sound"
30713     ],
30714     "in_project_namespace": true,
30715     "kind": "theorem",
30716     "module": "PaperIRelease.GrammarModules",
30717     "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_1",
30718     "runtime_only": false
30719   },
30720   {
30721     "axioms": [
30722       "propext",
30723       "Classical.choice",
30724       "Quot.sound"
30725     ],
30726     "in_project_namespace": true,
30727     "kind": "theorem",
30728     "module": "KomorebiVerification.TopologicalCompletion",
30729     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower_apply",
30730     "runtime_only": false
30731   },
30732   {
30733     "axioms": [
30734       "propext",
30735       "Quot.sound"
30736     ],
30737     "in_project_namespace": true,
30738     "kind": "definition",
30739     "module": "PaperIRelease.GrammarAlgebra",
30740     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Free",
30741     "runtime_only": false
30742   },
30743   {
30744     "axioms": [
30745       "propext",
30746       "Classical.choice",
30747       "Quot.sound"
30748     ],
30749     "in_project_namespace": true,
30750     "kind": "definition",
30751     "module": "KomorebiVerification.PacketNaturalityCompletion",
30752     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.recOn",
30753     "runtime_only": false
30754   },
30755   {
30756     "axioms": [
30757       "propext",
30758       "Quot.sound"
30759     ],
30760     "in_project_namespace": true,
30761     "kind": "definition",
30762     "module": "PaperIRelease.AlgebraTransfer",
30763     "name": "Komorebi.PaperIRelease.packetWordSum.match_1",
30764     "runtime_only": false
30765   },
30766   {
30767     "axioms": [
30768       "propext",
30769       "Classical.choice",
30770       "Quot.sound"
30771     ],
30772     "in_project_namespace": true,
30773     "kind": "theorem",
30774     "module": "PaperICompletion.CyclicClassification",
30775     "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_minpoly_eq_charpoly",
30776     "runtime_only": false
30777   },
30778   {
30779     "axioms": [
30780       "propext",
30781       "Classical.choice",
30782       "Quot.sound"
30783     ],
30784     "in_project_namespace": true,
30785     "kind": "theorem",
30786     "module": "PaperIRelease.AlgebraClassGrouping",
30787     "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_1",
30788     "runtime_only": false
30789   },
30790   {
30791     "axioms": [
30792       "propext",
30793       "Quot.sound"
30794     ],
30795     "in_project_namespace": true,
30796     "kind": "theorem",
30797     "module": "PaperICompletion8.RegularMultiplicity",
30798     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_1",
30799     "runtime_only": false
30800   },
30801   {
30802     "axioms": [],
30803     "in_project_namespace": true,
30804     "kind": "constructor",
30805     "module": "KomorebiVerification.ProjectorCore",
30806     "name": "Komorebi.Seed.OperatorExpr.comp",
30807     "runtime_only": false
30808   },
30809   {
30810     "axioms": [
30811       "propext",
30812       "Classical.choice",
30813       "Quot.sound"
30814     ],
30815     "in_project_namespace": true,
30816     "kind": "theorem",
30817     "module": "PaperIRelease.PacketExactSequence",
30818     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_3",
30819     "runtime_only": false
30820   },
30821   {
30822     "axioms": [
30823       "propext",
30824       "Quot.sound"
30825     ],
30826     "in_project_namespace": true,
30827     "kind": "theorem",
30828     "module": "KomorebiVerification.SeedRankOperations",
30829     "name": "Komorebi.SeedRankOperations.tensorLeftTower",
30830     "runtime_only": false
30831   },
30832   {
30833     "axioms": [
30834       "propext",
30835       "Classical.choice",
30836       "Quot.sound"
30837     ],
30838     "in_project_namespace": true,
30839     "kind": "theorem",
30840     "module": "PaperIRelease.GrammarTyped",
30841     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_orthogonal",
30842     "runtime_only": false
30843   },
30844   {
30845     "axioms": [
30846       "propext",
30847       "Classical.choice",
30848       "Quot.sound"
30849     ],
30850     "in_project_namespace": true,
30851     "kind": "definition",
30852     "module": "PaperIRelease.GeneralNormedPackets",
30853     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis",
30854     "runtime_only": false
30855   },
30856   {
30857     "axioms": [
30858       "propext",
30859       "Classical.choice",
30860       "Quot.sound"
30861     ],
30862     "in_project_namespace": true,
30863     "kind": "definition",
30864     "module": "PaperIRelease.GrammarPaths",
30865     "name": "Komorebi.PaperIRelease.GrammarAlgebra.grammarFromPathRelations",
30866     "runtime_only": false
30867   },
30868   {
30869     "axioms": [
30870       "propext",
30871       "Classical.choice",
30872       "Quot.sound"
30873     ],
30874     "in_project_namespace": true,
30875     "kind": "theorem",
30876     "module": "PaperICompletion4.OperatorIntrinsicFormula",
30877     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_4",
30878     "runtime_only": false
30879   },
30880   {
30881     "axioms": [
30882       "propext",
30883       "Quot.sound"
30884     ],
30885     "in_project_namespace": true,
30886     "kind": "theorem",
30887     "module": "PaperIRelease.GraphPropagation",
30888     "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_1",
30889     "runtime_only": false
30890   },
30891   {
30892     "axioms": [
30893       "propext",
30894       "Classical.choice",
30895       "Quot.sound"
30896     ],
30897     "in_project_namespace": true,
30898     "kind": "definition",
30899     "module": "PaperIRelease.CategoryPackets",
30900     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.algebra",
30901     "runtime_only": false
30902   },
30903   {
30904     "axioms": [
30905       "propext",
30906       "Classical.choice",
30907       "Quot.sound"
30908     ],
30909     "in_project_namespace": true,
30910     "kind": "theorem",
30911     "module": "PaperIRelease.GrammarEquivalence",
30912     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_10",
30913     "runtime_only": false
30914   },
30915   {
30916     "axioms": [],
30917     "in_project_namespace": true,
30918     "kind": "definition",
30919     "module": "KomorebiVerification.ProjectorCore",
30920     "name": "Komorebi.ClaimRecord.notes._default",
30921     "runtime_only": false
30922   },
30923   {
30924     "axioms": [
30925       "propext",
30926       "Classical.choice",
30927       "Quot.sound"
30928     ],
30929     "in_project_namespace": true,
30930     "kind": "definition",
30931     "module": "PaperIRelease.PacketDescent",
30932     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv",
30933     "runtime_only": false
30934   },
30935   {
30936     "axioms": [
30937       "propext",
30938       "Classical.choice",
30939       "Quot.sound"
30940     ],
30941     "in_project_namespace": true,
30942     "kind": "definition",
30943     "module": "PaperICompletion4.IntrinsicPrimary",
30944     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal",
30945     "runtime_only": false
30946   },
30947   {
30948     "axioms": [
30949       "propext",
30950       "Classical.choice",
30951       "Quot.sound"
30952     ],
30953     "in_project_namespace": true,
30954     "kind": "definition",
30955     "module": "KomorebiVerification.TopologicalCompletion",
30956     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.ctorIdx",
30957     "runtime_only": false
30958   },
30959   {
30960     "axioms": [],
30961     "in_project_namespace": true,
30962     "kind": "definition",
30963     "module": "KomorebiVerification.ProjectorCore",
30964     "name": "Komorebi.Seed.instReprOperatorExpr.repr._sunfold",
30965     "runtime_only": false
30966   },
30967   {
30968     "axioms": [],
30969     "in_project_namespace": true,
30970     "kind": "theorem",
30971     "module": "KomorebiVerification.PacketNaturalityCompletion",
30972     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_2",
30973     "runtime_only": false
30974   },
30975   {
30976     "axioms": [
30977       "propext",
30978       "Classical.choice",
30979       "Quot.sound"
30980     ],
30981     "in_project_namespace": false,
30982     "kind": "definition",
30983     "module": "PaperIRelease.TopologyCountablePackets",
30984     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup",
30985     "runtime_only": false
30986   },
30987   {
30988     "axioms": [
30989       "propext",
30990       "Classical.choice",
30991       "Quot.sound"
30992     ],
30993     "in_project_namespace": true,
30994     "kind": "theorem",
30995     "module": "PaperICompletion6.ScalarExtension",
30996     "name": "Komorebi.PaperICompletion6.ScalarExtension.linearIndependent_baseChange_powers",
30997     "runtime_only": false
30998   },
30999   {
31000     "axioms": [
31001       "propext",
31002       "Quot.sound"
31003     ],
31004     "in_project_namespace": true,
31005     "kind": "theorem",
31006     "module": "KomorebiVerification.PacketNaturalityCompletion",
31007     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.sourceSeed.eq_1",
31008     "runtime_only": false
31009   },
31010   {
31011     "axioms": [
31012       "propext",
31013       "Classical.choice",
31014       "Quot.sound"
31015     ],
31016     "in_project_namespace": true,
31017     "kind": "theorem",
31018     "module": "KomorebiVerification.PacketNaturalityCompletion",
31019     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverWord_preserves_uReachable",
31020     "runtime_only": false
31021   },
31022   {
31023     "axioms": [
31024       "propext",
31025       "Classical.choice",
31026       "Quot.sound"
31027     ],
31028     "in_project_namespace": true,
31029     "kind": "theorem",
31030     "module": "KomorebiVerification.PacketNaturalityCompletion",
31031     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.u_supported_hull_le_uReachable",
31032     "runtime_only": false
31033   },
31034   {
31035     "axioms": [],
31036     "in_project_namespace": false,
31037     "kind": "theorem",
31038     "module": "PaperIRelease.GrammarPaths",
31039     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.eq_2",
31040     "runtime_only": false
31041   },
31042   {
31043     "axioms": [
31044       "propext",
31045       "Classical.choice",
31046       "Quot.sound"
31047     ],
31048     "in_project_namespace": true,
31049     "kind": "definition",
31050     "module": "PaperIRelease.GrammarIdeal",
31051     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedIdealModuleEquivalence",
31052     "runtime_only": false
31053   },
31054   {
31055     "axioms": [
31056       "propext",
31057       "Quot.sound"
31058     ],
31059     "in_project_namespace": true,
31060     "kind": "definition",
31061     "module": "PaperIRelease.GrammarAlgebra",
31062     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.ctorIdx",
31063     "runtime_only": false
31064   },
31065   {
31066     "axioms": [
31067       "propext",
31068       "Quot.sound"
31069     ],
31070     "in_project_namespace": true,
31071     "kind": "definition",
31072     "module": "KomorebiVerification.SeedRankOperations",
31073     "name": "Komorebi.SeedRankOperations.prodFstSemilinear",
31074     "runtime_only": false
31075   },
31076   {
31077     "axioms": [
31078       "propext",
31079       "Classical.choice",
31080       "Quot.sound"
31081     ],
31082     "in_project_namespace": true,
31083     "kind": "theorem",
31084     "module": "PaperIRelease.CategoryPackets",
31085     "name": "Komorebi.PaperIRelease.CategoryPackets.seeded_surjection_generates",
31086     "runtime_only": false
31087   },
31088   {
31089     "axioms": [
31090       "propext",
31091       "Quot.sound"
31092     ],
31093     "in_project_namespace": true,
31094     "kind": "theorem",
31095     "module": "PaperIRelease.GrammarModules",
31096     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.sizeOf_spec",
31097     "runtime_only": false
31098   },
31099   {
31100     "axioms": [
31101       "propext",
31102       "Classical.choice",
31103       "Quot.sound"
31104     ],
31105     "in_project_namespace": true,
31106     "kind": "constructor",
31107     "module": "PaperIRelease.GrammarAlgebra",
31108     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_complete",
31109     "runtime_only": false
31110   },
31111   {
31112     "axioms": [
31113       "propext",
31114       "Classical.choice",
31115       "Quot.sound"
31116     ],
31117     "in_project_namespace": true,
31118     "kind": "theorem",
31119     "module": "PaperIRelease.TopologyCategories",
31120     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.injEq",
31121     "runtime_only": false
31122   },
31123   {
31124     "axioms": [
31125       "propext",
31126       "Classical.choice",
31127       "Quot.sound"
31128     ],
31129     "in_project_namespace": false,
31130     "kind": "theorem",
31131     "module": "PaperIRelease.TopologyCountablePackets",
31132     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_23",
31133     "runtime_only": false
31134   },
31135   {
31136     "axioms": [
31137       "propext",
31138       "Classical.choice",
31139       "Quot.sound"
31140     ],
31141     "in_project_namespace": true,
31142     "kind": "theorem",
31143     "module": "PaperIRelease.PacketUniversal",
31144     "name": "Komorebi.PaperIRelease.PacketUniversal.packet_assembleIn",
31145     "runtime_only": false
31146   },
31147   {
31148     "axioms": [
31149       "propext",
31150       "Quot.sound"
31151     ],
31152     "in_project_namespace": true,
31153     "kind": "theorem",
31154     "module": "PaperIRelease.PacketSourceLower",
31155     "name": "Komorebi.PaperIRelease.localNonzeroSeeds._proof_1",
31156     "runtime_only": false
31157   },
31158   {
31159     "axioms": [
31160       "propext",
31161       "Classical.choice",
31162       "Quot.sound"
31163     ],
31164     "in_project_namespace": true,
31165     "kind": "theorem",
31166     "module": "KomorebiVerification.SingleOperatorGraph",
31167     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow_map_adjacency",
31168     "runtime_only": false
31169   },
31170   {
31171     "axioms": [
31172       "propext",
31173       "Classical.choice",
31174       "Quot.sound"
31175     ],
31176     "in_project_namespace": true,
31177     "kind": "theorem",
31178     "module": "PaperICompletion8.SemisimpleFormula",
31179     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.semisimple_seedRank_of_decompositions",
31180     "runtime_only": false
31181   },
31182   {
31183     "axioms": [
31184       "propext",
31185       "Classical.choice",
31186       "Quot.sound"
31187     ],
31188     "in_project_namespace": true,
31189     "kind": "definition",
31190     "module": "PaperIRelease.TopologyCategories",
31191     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.toPacketMorphism",
31192     "runtime_only": false
31193   },
31194   {
31195     "axioms": [
31196       "propext",
31197       "Classical.choice",
31198       "Quot.sound"
31199     ],
31200     "in_project_namespace": true,
31201     "kind": "theorem",
31202     "module": "PaperIRelease.GeneralPacketBounds",
31203     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.equivalent_norm_packet_bounds",
31204     "runtime_only": false
31205   },
31206   {
31207     "axioms": [
31208       "propext",
31209       "Classical.choice",
31210       "Quot.sound"
31211     ],
31212     "in_project_namespace": true,
31213     "kind": "theorem",
31214     "module": "PaperIRelease.AlgebraSupport",
31215     "name": "Komorebi.PaperIRelease.supportSubmodule._proof_3",
31216     "runtime_only": false
31217   },
31218   {
31219     "axioms": [
31220       "propext"
31221     ],
31222     "in_project_namespace": true,
31223     "kind": "theorem",
31224     "module": "PaperIRelease.CategoryExport",
31225     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_6",
31226     "runtime_only": false
31227   },
31228   {
31229     "axioms": [
31230       "propext",
31231       "Classical.choice",
31232       "Quot.sound"
31233     ],
31234     "in_project_namespace": true,
31235     "kind": "theorem",
31236     "module": "PaperIRelease.GeneralPacketBounds",
31237     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.exists_uniform_bound",
31238     "runtime_only": false
31239   },
31240   {
31241     "axioms": [
31242       "propext",
31243       "Classical.choice",
31244       "Quot.sound"
31245     ],
31246     "in_project_namespace": true,
31247     "kind": "theorem",
31248     "module": "PaperIRelease.PolynomialModule",
31249     "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction._proof_2",
31250     "runtime_only": false
31251   },
31252   {
31253     "axioms": [
31254       "propext",
31255       "Classical.choice",
31256       "Quot.sound"
31257     ],
31258     "in_project_namespace": true,
31259     "kind": "theorem",
31260     "module": "PaperIRelease.TensorPackets",
31261     "name": "Komorebi.PaperIRelease.tensorPackets._simp_1",
31262     "runtime_only": false
31263   },
31264   {
31265     "axioms": [
31266       "propext"
31267     ],
31268     "in_project_namespace": true,
31269     "kind": "theorem",
31270     "module": "PaperIRelease.CategoryExport",
31271     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_4",
31272     "runtime_only": false
31273   },
31274   {
31275     "axioms": [
31276       "propext",
31277       "Classical.choice",
31278       "Quot.sound"
31279     ],
31280     "in_project_namespace": true,
31281     "kind": "constructor",
31282     "module": "PaperIRelease.GrammarAlgebra",
31283     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_idempotent",
31284     "runtime_only": false
31285   },
31286   {
31287     "axioms": [
31288       "propext",
31289       "Classical.choice",
31290       "Quot.sound"
31291     ],
31292     "in_project_namespace": true,
31293     "kind": "constructor",
31294     "module": "PaperIRelease.GrammarEquivalence",
31295     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk",
31296     "runtime_only": false
31297   },
31298   {
31299     "axioms": [
31300       "propext",
31301       "Classical.choice",
31302       "Quot.sound"
31303     ],
31304     "in_project_namespace": true,
31305     "kind": "definition",
31306     "module": "KomorebiVerification.SingleOperatorGraph",
31307     "name": "Komorebi.SingleOperatorGraph.SeedNumberLE",
31308     "runtime_only": false
31309   },
31310   {
31311     "axioms": [
31312       "propext",
31313       "Classical.choice",
31314       "Quot.sound"
31315     ],
31316     "in_project_namespace": false,
31317     "kind": "definition",
31318     "module": "PaperIRelease.TopologyUnconditional",
31319     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_1",
31320     "runtime_only": false
31321   },
31322   {
31323     "axioms": [
31324       "propext",
31325       "Classical.choice",
31326       "Quot.sound"
31327     ],
31328     "in_project_namespace": true,
31329     "kind": "theorem",
31330     "module": "PaperIRelease.PacketDescent",
31331     "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_2",
31332     "runtime_only": false
31333   },
31334   {
31335     "axioms": [
31336       "propext",
31337       "Classical.choice",
31338       "Quot.sound"
31339     ],
31340     "in_project_namespace": true,
31341     "kind": "theorem",
31342     "module": "KomorebiVerification.PacketNaturalityCompletion",
31343     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_blocks_eq_sum_products",
31344     "runtime_only": false
31345   },
31346   {
31347     "axioms": [
31348       "propext",
31349       "Classical.choice",
31350       "Quot.sound"
31351     ],
31352     "in_project_namespace": true,
31353     "kind": "theorem",
31354     "module": "PaperICompletion.ConditionedCoordinates",
31355     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber_eq",
31356     "runtime_only": false
31357   },
31358   {
31359     "axioms": [
31360       "propext",
31361       "Quot.sound"
31362     ],
31363     "in_project_namespace": true,
31364     "kind": "definition",
31365     "module": "PaperIRelease.GrammarAlgebra",
31366     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.source",
31367     "runtime_only": false
31368   },
31369   {
31370     "axioms": [
31371       "propext",
31372       "Quot.sound"
31373     ],
31374     "in_project_namespace": true,
31375     "kind": "theorem",
31376     "module": "PaperICompletion5.LinearPrimaryEigenspace",
31377     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_3",
31378     "runtime_only": false
31379   },
31380   {
31381     "axioms": [
31382       "propext"
31383     ],
31384     "in_project_namespace": true,
31385     "kind": "theorem",
31386     "module": "KomorebiVerification.SingleOperatorGraph",
31387     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_6",
31388     "runtime_only": false
31389   },
31390   {
31391     "axioms": [
31392       "propext",
31393       "Classical.choice",
31394       "Quot.sound"
31395     ],
31396     "in_project_namespace": true,
31397     "kind": "theorem",
31398     "module": "PaperIRelease.PacketDescent",
31399     "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros_proj_ne_zero",
31400     "runtime_only": false
31401   },
31402   {
31403     "axioms": [
31404       "propext",
31405       "Classical.choice",
31406       "Quot.sound"
31407     ],
31408     "in_project_namespace": true,
31409     "kind": "theorem",
31410     "module": "PaperIRelease.CategoryUniversal",
31411     "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal_map",
31412     "runtime_only": false
31413   },
31414   {
31415     "axioms": [
31416       "propext",
31417       "Classical.choice",
31418       "Quot.sound"
31419     ],
31420     "in_project_namespace": true,
31421     "kind": "definition",
31422     "module": "PaperIRelease.TopologyCategories",
31423     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.toContinuousPacketObject",
31424     "runtime_only": false
31425   },
31426   {
31427     "axioms": [
31428       "propext",
31429       "Classical.choice",
31430       "Quot.sound"
31431     ],
31432     "in_project_namespace": true,
31433     "kind": "definition",
31434     "module": "PaperIRelease.PacketTopology",
31435     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientMapCLM",
31436     "runtime_only": false
31437   },
31438   {
31439     "axioms": [
31440       "propext",
31441       "Classical.choice",
31442       "Quot.sound"
31443     ],
31444     "in_project_namespace": true,
31445     "kind": "theorem",
31446     "module": "KomorebiVerification.PacketNaturalityCompletion",
31447     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_1",
31448     "runtime_only": false
31449   },
31450   {
31451     "axioms": [
31452       "propext",
31453       "Quot.sound"
31454     ],
31455     "in_project_namespace": true,
31456     "kind": "theorem",
31457     "module": "PaperIRelease.GraphReachability",
31458     "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra._proof_2",
31459     "runtime_only": false
31460   },
31461   {
31462     "axioms": [],
31463     "in_project_namespace": true,
31464     "kind": "definition",
31465     "module": "PaperIRelease.GrammarPaths",
31466     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorElimType",
31467     "runtime_only": false
31468   },
31469   {
31470     "axioms": [
31471       "propext",
31472       "Classical.choice",
31473       "Quot.sound"
31474     ],
31475     "in_project_namespace": true,
31476     "kind": "theorem",
31477     "module": "PaperIRelease.TensorPackets",
31478     "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_4",
31479     "runtime_only": false
31480   },
31481   {
31482     "axioms": [
31483       "propext",
31484       "Quot.sound"
31485     ],
31486     "in_project_namespace": true,
31487     "kind": "theorem",
31488     "module": "PaperIRelease.GrammarAlgebra",
31489     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertexWord.eq_1",
31490     "runtime_only": false
31491   },
31492   {
31493     "axioms": [
31494       "propext",
31495       "Classical.choice",
31496       "Quot.sound"
31497     ],
31498     "in_project_namespace": true,
31499     "kind": "theorem",
31500     "module": "PaperIRelease.GrammarIdeal",
31501     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv._proof_1",
31502     "runtime_only": false
31503   },
31504   {
31505     "axioms": [
31506       "propext",
31507       "Quot.sound"
31508     ],
31509     "in_project_namespace": true,
31510     "kind": "definition",
31511     "module": "PaperIRelease.AlgebraTransfer",
31512     "name": "Komorebi.PaperIRelease.operatorWord.match_1",
31513     "runtime_only": false
31514   },
31515   {
31516     "axioms": [],
31517     "in_project_namespace": true,
31518     "kind": "definition",
31519     "module": "PaperICompletion8.DivisionBlock",
31520     "name": "Komorebi.PaperICompletion8.DivisionBlock.BlockAlgebra",
31521     "runtime_only": false
31522   },
31523   {
31524     "axioms": [
31525       "propext",
31526       "Classical.choice",
31527       "Quot.sound"
31528     ],
31529     "in_project_namespace": true,
31530     "kind": "theorem",
31531     "module": "PaperIRelease.PacketAggregation",
31532     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_1",
31533     "runtime_only": false
31534   },
31535   {
31536     "axioms": [],
31537     "in_project_namespace": true,
31538     "kind": "theorem",
31539     "module": "PaperIRelease.SeedOperations",
31540     "name": "Komorebi.SeedRankBasics.oneSeedMap.eq_1",
31541     "runtime_only": false
31542   },
31543   {
31544     "axioms": [
31545       "propext",
31546       "Quot.sound"
31547     ],
31548     "in_project_namespace": true,
31549     "kind": "theorem",
31550     "module": "PaperIRelease.PacketAggregation",
31551     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_1",
31552     "runtime_only": false
31553   },
31554   {
31555     "axioms": [
31556       "propext",
31557       "Classical.choice",
31558       "Quot.sound"
31559     ],
31560     "in_project_namespace": true,
31561     "kind": "theorem",
31562     "module": "PaperIRelease.CategoryBoundaries",
31563     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_3",
31564     "runtime_only": false
31565   },
31566   {
31567     "axioms": [
31568       "propext",
31569       "Classical.choice",
31570       "Quot.sound"
31571     ],
31572     "in_project_namespace": true,
31573     "kind": "theorem",
31574     "module": "KomorebiVerification.EllipticAlgorithms",
31575     "name": "Komorebi.EllipticCoordinates.P0_apply",
31576     "runtime_only": false
31577   },
31578   {
31579     "axioms": [
31580       "propext",
31581       "Classical.choice",
31582       "Quot.sound"
31583     ],
31584     "in_project_namespace": false,
31585     "kind": "theorem",
31586     "module": "PaperIRelease.TopologyPresentations",
31587     "name": "PaperIRelease.TopologyDenseCompletion.dense_free_evaluation",
31588     "runtime_only": false
31589   },
31590   {
31591     "axioms": [],
31592     "in_project_namespace": false,
31593     "kind": "theorem",
31594     "module": "PaperIRelease.CategoryExport",
31595     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_4",
31596     "runtime_only": false
31597   },
31598   {
31599     "axioms": [
31600       "propext",
31601       "Classical.choice",
31602       "Quot.sound"
31603     ],
31604     "in_project_namespace": true,
31605     "kind": "theorem",
31606     "module": "PaperICompletion3.OperatorPrimaryAPI",
31607     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.irreducible",
31608     "runtime_only": false
31609   },
31610   {
31611     "axioms": [
31612       "propext",
31613       "Quot.sound"
31614     ],
31615     "in_project_namespace": false,
31616     "kind": "definition",
31617     "module": "PaperIRelease.AlgebraTransfer",
31618     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.splitter",
31619     "runtime_only": false
31620   },
31621   {
31622     "axioms": [
31623       "propext",
31624       "Classical.choice",
31625       "Quot.sound"
31626     ],
31627     "in_project_namespace": true,
31628     "kind": "theorem",
31629     "module": "KomorebiVerification.TopologicalCompletion",
31630     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2._proof_1",
31631     "runtime_only": false
31632   },
31633   {
31634     "axioms": [
31635       "propext",
31636       "Classical.choice",
31637       "Quot.sound"
31638     ],
31639     "in_project_namespace": true,
31640     "kind": "theorem",
31641     "module": "PaperICompletion.CyclicClassification",
31642     "name": "Komorebi.PaperICompletion.CyclicClassification.orbit_finrank_eq_minpoly_degree",
31643     "runtime_only": false
31644   },
31645   {
31646     "axioms": [
31647       "propext",
31648       "Classical.choice",
31649       "Quot.sound"
31650     ],
31651     "in_project_namespace": true,
31652     "kind": "definition",
31653     "module": "PaperIRelease.AlgebraClassGrouping",
31654     "name": "Komorebi.PaperIRelease.preorderDiagonalHom",
31655     "runtime_only": false
31656   },
31657   {
31658     "axioms": [
31659       "propext",
31660       "Quot.sound"
31661     ],
31662     "in_project_namespace": true,
31663     "kind": "theorem",
31664     "module": "PaperIRelease.AlgebraTransfer",
31665     "name": "Komorebi.PaperIRelease.operatorWord.eq_2",
31666     "runtime_only": false
31667   },
31668   {
31669     "axioms": [
31670       "propext",
31671       "Quot.sound"
31672     ],
31673     "in_project_namespace": true,
31674     "kind": "theorem",
31675     "module": "KomorebiVerification.SingleOperatorGraph",
31676     "name": "Komorebi.SingleOperatorGraph.seedNumber_one_isLeast_of_cyclic._proof_1_1",
31677     "runtime_only": false
31678   },
31679   {
31680     "axioms": [
31681       "propext",
31682       "Classical.choice",
31683       "Quot.sound"
31684     ],
31685     "in_project_namespace": true,
31686     "kind": "theorem",
31687     "module": "PaperICompletion7.LocalResidue",
31688     "name": "Komorebi.PaperICompletion7.LocalResidue.proper_sup_ne_top",
31689     "runtime_only": false
31690   },
31691   {
31692     "axioms": [],
31693     "in_project_namespace": true,
31694     "kind": "definition",
31695     "module": "KomorebiVerification.ProjectorCore",
31696     "name": "Komorebi.ClaimKind.algorithmClaim.elim",
31697     "runtime_only": false
31698   },
31699   {
31700     "axioms": [
31701       "propext",
31702       "Classical.choice",
31703       "Quot.sound"
31704     ],
31705     "in_project_namespace": true,
31706     "kind": "theorem",
31707     "module": "PaperIRelease.TensorPackets",
31708     "name": "Komorebi.PaperIRelease.tensor_packet_range",
31709     "runtime_only": false
31710   },
31711   {
31712     "axioms": [
31713       "propext",
31714       "Classical.choice",
31715       "Quot.sound"
31716     ],
31717     "in_project_namespace": true,
31718     "kind": "definition",
31719     "module": "KomorebiVerification.TopologicalCompletion",
31720     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.ctorIdx",
31721     "runtime_only": false
31722   },
31723   {
31724     "axioms": [
31725       "propext",
31726       "Classical.choice",
31727       "Quot.sound"
31728     ],
31729     "in_project_namespace": true,
31730     "kind": "definition",
31731     "module": "KomorebiVerification.PacketNaturalityCompletion",
31732     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear",
31733     "runtime_only": false
31734   },
31735   {
31736     "axioms": [
31737       "propext",
31738       "Classical.choice",
31739       "Quot.sound"
31740     ],
31741     "in_project_namespace": true,
31742     "kind": "theorem",
31743     "module": "PaperICompletion8.DivisionProduct",
31744     "name": "Komorebi.PaperICompletion8.DivisionProduct.exists_divisionProduct_generators_iff_maxCeilDiv_le",
31745     "runtime_only": false
31746   },
31747   {
31748     "axioms": [
31749       "propext",
31750       "Classical.choice",
31751       "Quot.sound"
31752     ],
31753     "in_project_namespace": true,
31754     "kind": "theorem",
31755     "module": "KomorebiVerification.SingleOperatorGraph",
31756     "name": "Komorebi.SingleOperatorGraph.complex_cycle_seedNumber_isLeast_two",
31757     "runtime_only": false
31758   },
31759   {
31760     "axioms": [
31761       "propext",
31762       "Classical.choice",
31763       "Quot.sound"
31764     ],
31765     "in_project_namespace": true,
31766     "kind": "theorem",
31767     "module": "KomorebiVerification.SeedRankBasics",
31768     "name": "Komorebi.SeedRankBasics.seedRank_lt_aleph0_iff",
31769     "runtime_only": false
31770   },
31771   {
31772     "axioms": [
31773       "propext",
31774       "Classical.choice",
31775       "Quot.sound"
31776     ],
31777     "in_project_namespace": false,
31778     "kind": "theorem",
31779     "module": "ReleaseBoundary",
31780     "name": "PaperIBlock08Tests.wrong_factor_acts_zero",
31781     "runtime_only": false
31782   },
31783   {
31784     "axioms": [],
31785     "in_project_namespace": true,
31786     "kind": "definition",
31787     "module": "KomorebiVerification.ProjectorCore",
31788     "name": "Komorebi.ClaimRecord.status",
31789     "runtime_only": false
31790   },
31791   {
31792     "axioms": [
31793       "propext",
31794       "Classical.choice",
31795       "Quot.sound"
31796     ],
31797     "in_project_namespace": false,
31798     "kind": "theorem",
31799     "module": "PaperIRelease.TopologySeedRank",
31800     "name": "PaperIRelease.TopologyTransport.exists_generating_set_card_eq_seedRank",
31801     "runtime_only": false
31802   },
31803   {
31804     "axioms": [
31805       "propext",
31806       "Classical.choice",
31807       "Quot.sound"
31808     ],
31809     "in_project_namespace": true,
31810     "kind": "theorem",
31811     "module": "PaperICompletion8.RegularMultiplicity",
31812     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_1",
31813     "runtime_only": false
31814   },
31815   {
31816     "axioms": [
31817       "propext",
31818       "Classical.choice",
31819       "Quot.sound"
31820     ],
31821     "in_project_namespace": false,
31822     "kind": "theorem",
31823     "module": "PaperIRelease.TopologyDenseCompletion",
31824     "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_2",
31825     "runtime_only": false
31826   },
31827   {
31828     "axioms": [
31829       "propext",
31830       "Classical.choice",
31831       "Quot.sound"
31832     ],
31833     "in_project_namespace": true,
31834     "kind": "theorem",
31835     "module": "KomorebiVerification.PacketNaturalityCompletion",
31836     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.inj",
31837     "runtime_only": false
31838   },
31839   {
31840     "axioms": [
31841       "propext",
31842       "Classical.choice",
31843       "Quot.sound"
31844     ],
31845     "in_project_namespace": false,
31846     "kind": "definition",
31847     "module": "PaperIRelease.TopologyUnconditional",
31848     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.noConfusionType",
31849     "runtime_only": false
31850   },
31851   {
31852     "axioms": [],
31853     "in_project_namespace": true,
31854     "kind": "definition",
31855     "module": "KomorebiVerification.ProjectorCore",
31856     "name": "Komorebi.FormalizationStatus.proofTermPresent.elim",
31857     "runtime_only": false
31858   },
31859   {
31860     "axioms": [
31861       "propext",
31862       "Classical.choice",
31863       "Quot.sound"
31864     ],
31865     "in_project_namespace": true,
31866     "kind": "theorem",
31867     "module": "PaperIRelease.PacketTopology",
31868     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_4",
31869     "runtime_only": false
31870   },
31871   {
31872     "axioms": [
31873       "propext",
31874       "Classical.choice",
31875       "Quot.sound"
31876     ],
31877     "in_project_namespace": true,
31878     "kind": "theorem",
31879     "module": "KomorebiVerification.TopologicalCompletion",
31880     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv_apply",
31881     "runtime_only": false
31882   },
31883   {
31884     "axioms": [
31885       "propext",
31886       "Classical.choice",
31887       "Quot.sound"
31888     ],
31889     "in_project_namespace": false,
31890     "kind": "definition",
31891     "module": "PaperIRelease.TopologySeedRank",
31892     "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates",
31893     "runtime_only": false
31894   },
31895   {
31896     "axioms": [],
31897     "in_project_namespace": true,
31898     "kind": "definition",
31899     "module": "KomorebiVerification.SemisimpleCompletion",
31900     "name": "Komorebi.SemisimpleCompletion.SplitProductModule",
31901     "runtime_only": false
31902   },
31903   {
31904     "axioms": [
31905       "propext",
31906       "Quot.sound"
31907     ],
31908     "in_project_namespace": true,
31909     "kind": "definition",
31910     "module": "PaperIRelease.GrammarModules",
31911     "name": "Komorebi.PaperIRelease.GrammarModules.toModules",
31912     "runtime_only": false
31913   },
31914   {
31915     "axioms": [
31916       "propext",
31917       "Classical.choice",
31918       "Quot.sound"
31919     ],
31920     "in_project_namespace": true,
31921     "kind": "definition",
31922     "module": "KomorebiVerification.EllipticAlgorithms",
31923     "name": "Komorebi.EllipticCoordinates.P1",
31924     "runtime_only": false
31925   },
31926   {
31927     "axioms": [
31928       "propext",
31929       "Classical.choice",
31930       "Quot.sound"
31931     ],
31932     "in_project_namespace": true,
31933     "kind": "theorem",
31934     "module": "PaperIRelease.PacketSourceUpper",
31935     "name": "Komorebi.PaperIRelease.localPureSeedRank.eq_1",
31936     "runtime_only": false
31937   },
31938   {
31939     "axioms": [
31940       "propext",
31941       "Quot.sound"
31942     ],
31943     "in_project_namespace": true,
31944     "kind": "constructor",
31945     "module": "PaperIRelease.GrammarTyped",
31946     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk",
31947     "runtime_only": false
31948   },
31949   {
31950     "axioms": [
31951       "propext",
31952       "Classical.choice",
31953       "Quot.sound"
31954     ],
31955     "in_project_namespace": true,
31956     "kind": "theorem",
31957     "module": "PaperIRelease.GrammarPaths",
31958     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_2",
31959     "runtime_only": false
31960   },
31961   {
31962     "axioms": [],
31963     "in_project_namespace": true,
31964     "kind": "theorem",
31965     "module": "KomorebiVerification.ProjectorCore",
31966     "name": "Komorebi.Seed.OperatorRelation.satisfied_symm",
31967     "runtime_only": false
31968   },
31969   {
31970     "axioms": [
31971       "propext",
31972       "Quot.sound"
31973     ],
31974     "in_project_namespace": true,
31975     "kind": "definition",
31976     "module": "KomorebiVerification.ProjectorCore",
31977     "name": "Komorebi.Seed.algebraicHull",
31978     "runtime_only": false
31979   },
31980   {
31981     "axioms": [
31982       "propext",
31983       "Classical.choice",
31984       "Quot.sound"
31985     ],
31986     "in_project_namespace": true,
31987     "kind": "theorem",
31988     "module": "PaperIRelease.PacketTopology",
31989     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_3",
31990     "runtime_only": false
31991   },
31992   {
31993     "axioms": [
31994       "propext",
31995       "Classical.choice",
31996       "Quot.sound"
31997     ],
31998     "in_project_namespace": false,
31999     "kind": "definition",
32000     "module": "PaperIRelease.TopologyDenseCompletion",
32001     "name": "PaperIRelease.TopologyDenseCompletion.completedAction",
32002     "runtime_only": false
32003   },
32004   {
32005     "axioms": [
32006       "propext",
32007       "Classical.choice",
32008       "Quot.sound"
32009     ],
32010     "in_project_namespace": true,
32011     "kind": "theorem",
32012     "module": "KomorebiVerification.PacketNaturalityCompletion",
32013     "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_reachableFrom_iff",
32014     "runtime_only": false
32015   },
32016   {
32017     "axioms": [],
32018     "in_project_namespace": true,
32019     "kind": "theorem",
32020     "module": "KomorebiVerification.ProjectorCore",
32021     "name": "Komorebi.FormalizationStatus.ofNat_ctorIdx",
32022     "runtime_only": false
32023   },
32024   {
32025     "axioms": [],
32026     "in_project_namespace": true,
32027     "kind": "theorem",
32028     "module": "PaperIRelease.CategoryExport",
32029     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn.eq",
32030     "runtime_only": false
32031   },
32032   {
32033     "axioms": [
32034       "propext",
32035       "Classical.choice",
32036       "Quot.sound"
32037     ],
32038     "in_project_namespace": true,
32039     "kind": "definition",
32040     "module": "KomorebiVerification.TopologicalCompletion",
32041     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.noConfusion",
32042     "runtime_only": false
32043   },
32044   {
32045     "axioms": [
32046       "propext"
32047     ],
32048     "in_project_namespace": true,
32049     "kind": "theorem",
32050     "module": "KomorebiVerification.SingleOperatorGraph",
32051     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor._proof_1",
32052     "runtime_only": false
32053   },
32054   {
32055     "axioms": [
32056       "propext",
32057       "Classical.choice",
32058       "Quot.sound"
32059     ],
32060     "in_project_namespace": true,
32061     "kind": "definition",
32062     "module": "PaperIRelease.CategoryPackets",
32063     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism._sizeOf_1",
32064     "runtime_only": false
32065   },
32066   {
32067     "axioms": [
32068       "propext",
32069       "Classical.choice",
32070       "Quot.sound"
32071     ],
32072     "in_project_namespace": true,
32073     "kind": "theorem",
32074     "module": "PaperIRelease.PacketPureRank",
32075     "name": "Komorebi.PaperIRelease.packetPureSeedRank_bounds",
32076     "runtime_only": false
32077   },
32078   {
32079     "axioms": [
32080       "propext",
32081       "Classical.choice",
32082       "Quot.sound"
32083     ],
32084     "in_project_namespace": true,
32085     "kind": "theorem",
32086     "module": "PaperICompletion5.GeometricSeedFormula",
32087     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues_bddAbove",
32088     "runtime_only": false
32089   },
32090   {
32091     "axioms": [
32092       "propext",
32093       "Quot.sound"
32094     ],
32095     "in_project_namespace": true,
32096     "kind": "definition",
32097     "module": "KomorebiVerification.EllipticAlgorithms",
32098     "name": "Komorebi.FiniteAlgorithms.InvariantUnder",
32099     "runtime_only": false
32100   },
32101   {
32102     "axioms": [
32103       "propext",
32104       "Quot.sound"
32105     ],
32106     "in_project_namespace": true,
32107     "kind": "theorem",
32108     "module": "KomorebiVerification.PacketNaturalityCompletion",
32109     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2082.eq_1",
32110     "runtime_only": false
32111   },
32112   {
32113     "axioms": [
32114       "propext",
32115       "Classical.choice",
32116       "Quot.sound"
32117     ],
32118     "in_project_namespace": true,
32119     "kind": "theorem",
32120     "module": "PaperIRelease.AlgebraPreorder",
32121     "name": "Komorebi.PaperIRelease.strictPath_le_maximal",
32122     "runtime_only": false
32123   },
32124   {
32125     "axioms": [
32126       "propext",
32127       "Classical.choice",
32128       "Quot.sound"
32129     ],
32130     "in_project_namespace": true,
32131     "kind": "definition",
32132     "module": "PaperIRelease.CategoryPackets",
32133     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.toPacketObject",
32134     "runtime_only": false
32135   },
32136   {
32137     "axioms": [
32138       "propext",
32139       "Classical.choice",
32140       "Quot.sound"
32141     ],
32142     "in_project_namespace": true,
32143     "kind": "theorem",
32144     "module": "PaperIRelease.TopologyCategories",
32145     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ext_iff",
32146     "runtime_only": false
32147   },
32148   {
32149     "axioms": [
32150       "propext",
32151       "Classical.choice",
32152       "Quot.sound"
32153     ],
32154     "in_project_namespace": true,
32155     "kind": "definition",
32156     "module": "PaperIRelease.CategoryPackets",
32157     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject._sizeOf_inst",
32158     "runtime_only": false
32159   },
32160   {
32161     "axioms": [],
32162     "in_project_namespace": true,
32163     "kind": "theorem",
32164     "module": "PaperICompletion3.PrimarySeedFormula",
32165     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor._proof_1",
32166     "runtime_only": false
32167   },
32168   {
32169     "axioms": [
32170       "propext",
32171       "Quot.sound"
32172     ],
32173     "in_project_namespace": true,
32174     "kind": "theorem",
32175     "module": "PaperIRelease.ScalarExtension",
32176     "name": "Komorebi.PaperIRelease.ScalarExtension.one_tmul_generates",
32177     "runtime_only": false
32178   },
32179   {
32180     "axioms": [
32181       "propext",
32182       "Quot.sound"
32183     ],
32184     "in_project_namespace": true,
32185     "kind": "definition",
32186     "module": "KomorebiVerification.SeedRankBasics",
32187     "name": "Komorebi.SeedRankBasics.FamilyGenerates",
32188     "runtime_only": false
32189   },
32190   {
32191     "axioms": [
32192       "propext",
32193       "Classical.choice",
32194       "Quot.sound"
32195     ],
32196     "in_project_namespace": true,
32197     "kind": "theorem",
32198     "module": "PaperIRelease.AlgebraTransfer",
32199     "name": "Komorebi.PaperIRelease.packetSupport_image_eq_of_noncancellation",
32200     "runtime_only": false
32201   },
32202   {
32203     "axioms": [
32204       "propext",
32205       "Quot.sound"
32206     ],
32207     "in_project_namespace": true,
32208     "kind": "theorem",
32209     "module": "PaperIRelease.ScalarExtension",
32210     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRight_smul_tmul",
32211     "runtime_only": false
32212   },
32213   {
32214     "axioms": [
32215       "propext",
32216       "Classical.choice",
32217       "Quot.sound"
32218     ],
32219     "in_project_namespace": true,
32220     "kind": "theorem",
32221     "module": "PaperIRelease.TopologyCategories",
32222     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.identity._proof_1",
32223     "runtime_only": false
32224   },
32225   {
32226     "axioms": [
32227       "propext",
32228       "Quot.sound"
32229     ],
32230     "in_project_namespace": true,
32231     "kind": "definition",
32232     "module": "PaperIRelease.GrammarModules",
32233     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ctorIdx",
32234     "runtime_only": false
32235   },
32236   {
32237     "axioms": [],
32238     "in_project_namespace": true,
32239     "kind": "definition",
32240     "module": "PaperIRelease.CategoryExport",
32241     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.noConfusionType",
32242     "runtime_only": false
32243   },
32244   {
32245     "axioms": [],
32246     "in_project_namespace": true,
32247     "kind": "theorem",
32248     "module": "KomorebiVerification.ProjectorCore",
32249     "name": "Komorebi.FormalizationStatus.contextOnly.sizeOf_spec",
32250     "runtime_only": false
32251   },
32252   {
32253     "axioms": [
32254       "propext",
32255       "Classical.choice",
32256       "Quot.sound"
32257     ],
32258     "in_project_namespace": false,
32259     "kind": "theorem",
32260     "module": "PaperIRelease.TopologyUnconditional",
32261     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_10",
32262     "runtime_only": false
32263   },
32264   {
32265     "axioms": [
32266       "propext",
32267       "Classical.choice",
32268       "Quot.sound"
32269     ],
32270     "in_project_namespace": true,
32271     "kind": "definition",
32272     "module": "KomorebiVerification.PacketNaturalityCompletion",
32273     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA",
32274     "runtime_only": false
32275   },
32276   {
32277     "axioms": [
32278       "propext",
32279       "Classical.choice",
32280       "Quot.sound"
32281     ],
32282     "in_project_namespace": true,
32283     "kind": "definition",
32284     "module": "PaperICompletion8.DivisionProduct",
32285     "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv",
32286     "runtime_only": false
32287   },
32288   {
32289     "axioms": [],
32290     "in_project_namespace": true,
32291     "kind": "constructor",
32292     "module": "KomorebiVerification.ProjectorCore",
32293     "name": "Komorebi.ClaimKind.theoremClaim",
32294     "runtime_only": false
32295   },
32296   {
32297     "axioms": [
32298       "propext"
32299     ],
32300     "in_project_namespace": true,
32301     "kind": "theorem",
32302     "module": "PaperIRelease.CategoryExport",
32303     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_5",
32304     "runtime_only": false
32305   },
32306   {
32307     "axioms": [
32308       "propext",
32309       "Quot.sound"
32310     ],
32311     "in_project_namespace": true,
32312     "kind": "theorem",
32313     "module": "PaperIRelease.GrammarModules",
32314     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_12",
32315     "runtime_only": false
32316   },
32317   {
32318     "axioms": [
32319       "propext",
32320       "Quot.sound"
32321     ],
32322     "in_project_namespace": true,
32323     "kind": "definition",
32324     "module": "PaperIRelease.GrammarPaths",
32325     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unsafe_rec",
32326     "runtime_only": true
32327   },
32328   {
32329     "axioms": [
32330       "propext",
32331       "Classical.choice",
32332       "Quot.sound"
32333     ],
32334     "in_project_namespace": true,
32335     "kind": "theorem",
32336     "module": "PaperIRelease.PacketTopologyGeneral",
32337     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM._proof_2",
32338     "runtime_only": false
32339   },
32340   {
32341     "axioms": [
32342       "propext",
32343       "Classical.choice",
32344       "Quot.sound"
32345     ],
32346     "in_project_namespace": false,
32347     "kind": "theorem",
32348     "module": "ReleaseBoundary",
32349     "name": "PaperIBlock08Tests.nonsplit_finite_algebra_api",
32350     "runtime_only": false
32351   },
32352   {
32353     "axioms": [
32354       "propext",
32355       "Quot.sound"
32356     ],
32357     "in_project_namespace": true,
32358     "kind": "theorem",
32359     "module": "PaperICompletion5.LinearPrimaryEigenspace",
32360     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_3",
32361     "runtime_only": false
32362   },
32363   {
32364     "axioms": [
32365       "propext",
32366       "Classical.choice",
32367       "Quot.sound"
32368     ],
32369     "in_project_namespace": true,
32370     "kind": "definition",
32371     "module": "KomorebiVerification.SeedRankBasics",
32372     "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquivRange",
32373     "runtime_only": false
32374   },
32375   {
32376     "axioms": [
32377       "propext",
32378       "Classical.choice",
32379       "Quot.sound"
32380     ],
32381     "in_project_namespace": true,
32382     "kind": "theorem",
32383     "module": "PaperIRelease.AlgebraClassGrouping",
32384     "name": "Komorebi.PaperIRelease.class_strict_path_lengths",
32385     "runtime_only": false
32386   },
32387   {
32388     "axioms": [],
32389     "in_project_namespace": true,
32390     "kind": "definition",
32391     "module": "KomorebiVerification.ProjectorCore",
32392     "name": "Komorebi.ClaimRecord._sizeOf_inst",
32393     "runtime_only": false
32394   },
32395   {
32396     "axioms": [
32397       "propext",
32398       "Classical.choice",
32399       "Quot.sound"
32400     ],
32401     "in_project_namespace": true,
32402     "kind": "definition",
32403     "module": "PaperICompletion8.DivisionRows",
32404     "name": "Komorebi.PaperICompletion8.DivisionRows.LeftGenerates",
32405     "runtime_only": false
32406   },
32407   {
32408     "axioms": [
32409       "propext",
32410       "Classical.choice",
32411       "Quot.sound"
32412     ],
32413     "in_project_namespace": false,
32414     "kind": "theorem",
32415     "module": "PaperIRelease.TopologyUnconditional",
32416     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_23",
32417     "runtime_only": false
32418   },
32419   {
32420     "axioms": [
32421       "propext",
32422       "Classical.choice",
32423       "Quot.sound"
32424     ],
32425     "in_project_namespace": false,
32426     "kind": "theorem",
32427     "module": "ReleaseBoundary",
32428     "name": "PaperIBlock08Tests.qi.eq_1",
32429     "runtime_only": false
32430   },
32431   {
32432     "axioms": [
32433       "propext",
32434       "Quot.sound"
32435     ],
32436     "in_project_namespace": true,
32437     "kind": "theorem",
32438     "module": "PaperICompletion5.CyclicGeometricCriterion",
32439     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_2",
32440     "runtime_only": false
32441   },
32442   {
32443     "axioms": [
32444       "propext",
32445       "Quot.sound"
32446     ],
32447     "in_project_namespace": true,
32448     "kind": "theorem",
32449     "module": "PaperIRelease.SeedOperations",
32450     "name": "Komorebi.PaperIRelease.SeedOperations.annihilator_isTwoSided_iff",
32451     "runtime_only": false
32452   },
32453   {
32454     "axioms": [
32455       "propext",
32456       "Quot.sound"
32457     ],
32458     "in_project_namespace": false,
32459     "kind": "theorem",
32460     "module": "PaperIRelease.AlgebraTransfer",
32461     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.eq_1",
32462     "runtime_only": false
32463   },
32464   {
32465     "axioms": [
32466       "propext",
32467       "Classical.choice",
32468       "Quot.sound"
32469     ],
32470     "in_project_namespace": true,
32471     "kind": "theorem",
32472     "module": "KomorebiVerification.TopologicalCompletion",
32473     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.map_packetRange_eq",
32474     "runtime_only": false
32475   },
32476   {
32477     "axioms": [],
32478     "in_project_namespace": true,
32479     "kind": "theorem",
32480     "module": "PaperIRelease.AlgebraClassGrouping",
32481     "name": "Komorebi.PaperIRelease.packetClass.eq_1",
32482     "runtime_only": false
32483   },
32484   {
32485     "axioms": [
32486       "propext",
32487       "Classical.choice",
32488       "Quot.sound"
32489     ],
32490     "in_project_namespace": true,
32491     "kind": "theorem",
32492     "module": "PaperICompletion6.PrimaryCyclicCriterion",
32493     "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.cyclic_of_subsingleton",
32494     "runtime_only": false
32495   },
32496   {
32497     "axioms": [
32498       "propext",
32499       "Classical.choice",
32500       "Quot.sound"
32501     ],
32502     "in_project_namespace": true,
32503     "kind": "definition",
32504     "module": "PaperIRelease.CategoryPackets",
32505     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.toPacketMorphism",
32506     "runtime_only": false
32507   },
32508   {
32509     "axioms": [
32510       "propext",
32511       "Classical.choice",
32512       "Quot.sound"
32513     ],
32514     "in_project_namespace": true,
32515     "kind": "theorem",
32516     "module": "PaperIRelease.GrammarPaths",
32517     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathCombination_action",
32518     "runtime_only": false
32519   },
32520   {
32521     "axioms": [
32522       "propext",
32523       "Classical.choice",
32524       "Quot.sound"
32525     ],
32526     "in_project_namespace": true,
32527     "kind": "definition",
32528     "module": "PaperIRelease.TopologyCategories",
32529     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.noConfusion",
32530     "runtime_only": false
32531   },
32532   {
32533     "axioms": [
32534       "propext",
32535       "Quot.sound"
32536     ],
32537     "in_project_namespace": false,
32538     "kind": "theorem",
32539     "module": "PaperIRelease.TopologyPresentations",
32540     "name": "PaperIRelease.TopologyDenseCompletion.restricted_kernel",
32541     "runtime_only": false
32542   },
32543   {
32544     "axioms": [
32545       "propext",
32546       "Classical.choice",
32547       "Quot.sound"
32548     ],
32549     "in_project_namespace": true,
32550     "kind": "definition",
32551     "module": "PaperIRelease.GeneralConditionedCoordinates",
32552     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packetSynthesis",
32553     "runtime_only": false
32554   },
32555   {
32556     "axioms": [
32557       "propext",
32558       "Classical.choice",
32559       "Quot.sound"
32560     ],
32561     "in_project_namespace": true,
32562     "kind": "theorem",
32563     "module": "PaperICompletion7.ModuleTop",
32564     "name": "Komorebi.PaperICompletion7.ModuleTop.quotient_basis_lifts_generate",
32565     "runtime_only": false
32566   },
32567   {
32568     "axioms": [
32569       "propext",
32570       "Classical.choice",
32571       "Quot.sound"
32572     ],
32573     "in_project_namespace": true,
32574     "kind": "theorem",
32575     "module": "PaperIRelease.AlgebraTransfer",
32576     "name": "Komorebi.PaperIRelease.packetSupport_image_subset",
32577     "runtime_only": false
32578   },
32579   {
32580     "axioms": [],
32581     "in_project_namespace": true,
32582     "kind": "definition",
32583     "module": "KomorebiVerification.ProjectorCore",
32584     "name": "Komorebi.Seed.OperatorExpr.ctorElimType",
32585     "runtime_only": false
32586   },
32587   {
32588     "axioms": [
32589       "propext"
32590     ],
32591     "in_project_namespace": true,
32592     "kind": "theorem",
32593     "module": "KomorebiVerification.PathGraphKrylov",
32594     "name": "Komorebi.PathGraphKrylov.leftTerm.eq_1",
32595     "runtime_only": false
32596   },
32597   {
32598     "axioms": [
32599       "propext",
32600       "Classical.choice",
32601       "Quot.sound"
32602     ],
32603     "in_project_namespace": true,
32604     "kind": "theorem",
32605     "module": "PaperICompletion5.LinearPrimaryEigenspace",
32606     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_5",
32607     "runtime_only": false
32608   },
32609   {
32610     "axioms": [],
32611     "in_project_namespace": true,
32612     "kind": "definition",
32613     "module": "KomorebiVerification.ProjectorCore",
32614     "name": "Komorebi.ClaimKind.casesOn",
32615     "runtime_only": false
32616   },
32617   {
32618     "axioms": [
32619       "propext",
32620       "Classical.choice",
32621       "Quot.sound"
32622     ],
32623     "in_project_namespace": true,
32624     "kind": "theorem",
32625     "module": "PaperIRelease.BoundedStar",
32626     "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_2",
32627     "runtime_only": false
32628   },
32629   {
32630     "axioms": [
32631       "propext",
32632       "Classical.choice",
32633       "Quot.sound"
32634     ],
32635     "in_project_namespace": true,
32636     "kind": "theorem",
32637     "module": "PaperIRelease.PacketPureBoundaryTests",
32638     "name": "Komorebi.PaperIRelease.PureBoundaryTests.singleton_packet_rank",
32639     "runtime_only": false
32640   },
32641   {
32642     "axioms": [
32643       "propext",
32644       "Classical.choice",
32645       "Quot.sound"
32646     ],
32647     "in_project_namespace": true,
32648     "kind": "definition",
32649     "module": "PaperIRelease.GrammarTyped",
32650     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.recOn",
32651     "runtime_only": false
32652   },
32653   {
32654     "axioms": [
32655       "propext",
32656       "Quot.sound"
32657     ],
32658     "in_project_namespace": true,
32659     "kind": "theorem",
32660     "module": "PaperICompletion4.GroupedPrimary",
32661     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_3",
32662     "runtime_only": false
32663   },
32664   {
32665     "axioms": [
32666       "propext",
32667       "Classical.choice",
32668       "Quot.sound"
32669     ],
32670     "in_project_namespace": true,
32671     "kind": "definition",
32672     "module": "PaperICompletion.ConditionedCoordinates",
32673     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber",
32674     "runtime_only": false
32675   },
32676   {
32677     "axioms": [],
32678     "in_project_namespace": true,
32679     "kind": "definition",
32680     "module": "KomorebiVerification.ProjectorCore",
32681     "name": "Komorebi.ClaimRecord.volume",
32682     "runtime_only": false
32683   },
32684   {
32685     "axioms": [],
32686     "in_project_namespace": true,
32687     "kind": "theorem",
32688     "module": "KomorebiVerification.PacketNaturalityCompletion",
32689     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraAlgebra._proof_1",
32690     "runtime_only": false
32691   },
32692   {
32693     "axioms": [
32694       "propext",
32695       "Classical.choice",
32696       "Quot.sound"
32697     ],
32698     "in_project_namespace": false,
32699     "kind": "theorem",
32700     "module": "ReleaseBoundary",
32701     "name": "PaperIBlock08Tests.quaternion_noncommutes",
32702     "runtime_only": false
32703   },
32704   {
32705     "axioms": [
32706       "propext",
32707       "Classical.choice",
32708       "Quot.sound"
32709     ],
32710     "in_project_namespace": true,
32711     "kind": "theorem",
32712     "module": "PaperICompletion6.OneInvariantFactor",
32713     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv_intertwines",
32714     "runtime_only": false
32715   },
32716   {
32717     "axioms": [
32718       "propext",
32719       "Classical.choice",
32720       "Quot.sound"
32721     ],
32722     "in_project_namespace": true,
32723     "kind": "theorem",
32724     "module": "PaperIRelease.PolynomialModule",
32725     "name": "Komorebi.PaperIRelease.PolynomialModule.finitely_many_primary_components",
32726     "runtime_only": false
32727   },
32728   {
32729     "axioms": [
32730       "propext",
32731       "Quot.sound"
32732     ],
32733     "in_project_namespace": true,
32734     "kind": "theorem",
32735     "module": "PaperIRelease.GrammarModules",
32736     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_5",
32737     "runtime_only": false
32738   },
32739   {
32740     "axioms": [
32741       "propext",
32742       "Classical.choice",
32743       "Quot.sound"
32744     ],
32745     "in_project_namespace": true,
32746     "kind": "theorem",
32747     "module": "PaperIRelease.GrammarEquivalence",
32748     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_2",
32749     "runtime_only": false
32750   },
32751   {
32752     "axioms": [
32753       "propext",
32754       "Quot.sound"
32755     ],
32756     "in_project_namespace": true,
32757     "kind": "theorem",
32758     "module": "PaperICompletion3.PrimarySeedFormula",
32759     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_2",
32760     "runtime_only": false
32761   },
32762   {
32763     "axioms": [
32764       "propext",
32765       "Classical.choice",
32766       "Quot.sound"
32767     ],
32768     "in_project_namespace": true,
32769     "kind": "definition",
32770     "module": "PaperIRelease.GrammarEquivalence",
32771     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ctorIdx",
32772     "runtime_only": false
32773   },
32774   {
32775     "axioms": [
32776       "propext",
32777       "Quot.sound"
32778     ],
32779     "in_project_namespace": true,
32780     "kind": "definition",
32781     "module": "PaperIRelease.GrammarTyped",
32782     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.noConfusion",
32783     "runtime_only": false
32784   },
32785   {
32786     "axioms": [
32787       "propext",
32788       "Classical.choice",
32789       "Quot.sound"
32790     ],
32791     "in_project_namespace": false,
32792     "kind": "theorem",
32793     "module": "PaperIRelease.TopologyCountablePackets",
32794     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_5",
32795     "runtime_only": false
32796   },
32797   {
32798     "axioms": [
32799       "propext",
32800       "Classical.choice",
32801       "Quot.sound"
32802     ],
32803     "in_project_namespace": true,
32804     "kind": "theorem",
32805     "module": "PaperIRelease.CategoryPackets",
32806     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.sizeOf_spec",
32807     "runtime_only": false
32808   },
32809   {
32810     "axioms": [
32811       "propext",
32812       "Classical.choice",
32813       "Quot.sound"
32814     ],
32815     "in_project_namespace": true,
32816     "kind": "theorem",
32817     "module": "PaperIRelease.TopologyCategories",
32818     "name": "Komorebi.PaperIRelease.TopologyCategories.operator_mem_closedHull",
32819     "runtime_only": false
32820   },
32821   {
32822     "axioms": [
32823       "propext",
32824       "Classical.choice",
32825       "Quot.sound"
32826     ],
32827     "in_project_namespace": true,
32828     "kind": "theorem",
32829     "module": "PaperIRelease.SeedOperations",
32830     "name": "Komorebi.PaperIRelease.SeedOperations.shared_direct_sum_bounds",
32831     "runtime_only": false
32832   },
32833   {
32834     "axioms": [
32835       "propext",
32836       "Classical.choice",
32837       "Quot.sound"
32838     ],
32839     "in_project_namespace": true,
32840     "kind": "theorem",
32841     "module": "PaperIRelease.AlgebraPreorder",
32842     "name": "Komorebi.PaperIRelease.no_strictPath_after_maximal",
32843     "runtime_only": false
32844   },
32845   {
32846     "axioms": [
32847       "propext",
32848       "Quot.sound"
32849     ],
32850     "in_project_namespace": true,
32851     "kind": "theorem",
32852     "module": "KomorebiVerification.SingleOperatorGraph",
32853     "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_3",
32854     "runtime_only": false
32855   },
32856   {
32857     "axioms": [
32858       "propext",
32859       "Classical.choice",
32860       "Quot.sound"
32861     ],
32862     "in_project_namespace": true,
32863     "kind": "theorem",
32864     "module": "PaperIRelease.PacketEquivalentNorm",
32865     "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_4",
32866     "runtime_only": false
32867   },
32868   {
32869     "axioms": [],
32870     "in_project_namespace": true,
32871     "kind": "theorem",
32872     "module": "KomorebiVerification.ProjectorCore",
32873     "name": "Komorebi.FormalizationStatus.kernelChecked.sizeOf_spec",
32874     "runtime_only": false
32875   },
32876   {
32877     "axioms": [],
32878     "in_project_namespace": true,
32879     "kind": "theorem",
32880     "module": "PaperIRelease.GrammarAlgebra",
32881     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_left._simp_1_1",
32882     "runtime_only": false
32883   },
32884   {
32885     "axioms": [
32886       "propext",
32887       "Classical.choice",
32888       "Quot.sound"
32889     ],
32890     "in_project_namespace": false,
32891     "kind": "theorem",
32892     "module": "PaperIRelease.TopologySemilinearRank",
32893     "name": "PaperIRelease.TopologySemilinearRank.rank_le_card",
32894     "runtime_only": false
32895   },
32896   {
32897     "axioms": [],
32898     "in_project_namespace": true,
32899     "kind": "definition",
32900     "module": "KomorebiVerification.ProjectorCore",
32901     "name": "Komorebi.instReprFormalizationStatus",
32902     "runtime_only": false
32903   },
32904   {
32905     "axioms": [
32906       "propext",
32907       "Classical.choice",
32908       "Quot.sound"
32909     ],
32910     "in_project_namespace": true,
32911     "kind": "definition",
32912     "module": "KomorebiVerification.SemisimpleSeedRank",
32913     "name": "Komorebi.SemisimpleSeedRank.LeftGenerates",
32914     "runtime_only": false
32915   },
32916   {
32917     "axioms": [],
32918     "in_project_namespace": true,
32919     "kind": "definition",
32920     "module": "KomorebiVerification.ProjectorCore",
32921     "name": "Komorebi.Seed.OperatorExpr.casesOn",
32922     "runtime_only": false
32923   },
32924   {
32925     "axioms": [
32926       "propext",
32927       "Classical.choice",
32928       "Quot.sound"
32929     ],
32930     "in_project_namespace": true,
32931     "kind": "theorem",
32932     "module": "PaperIRelease.CategoryPackets",
32933     "name": "Komorebi.PaperIRelease.CategoryPackets.sum_fibers",
32934     "runtime_only": false
32935   },
32936   {
32937     "axioms": [
32938       "propext",
32939       "Classical.choice",
32940       "Quot.sound"
32941     ],
32942     "in_project_namespace": true,
32943     "kind": "theorem",
32944     "module": "PaperICompletion4.OperatorIntrinsicFormula",
32945     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_primary_membership",
32946     "runtime_only": false
32947   },
32948   {
32949     "axioms": [],
32950     "in_project_namespace": true,
32951     "kind": "definition",
32952     "module": "KomorebiVerification.PacketNaturalityCompletion",
32953     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply",
32954     "runtime_only": false
32955   },
32956   {
32957     "axioms": [
32958       "propext",
32959       "Classical.choice",
32960       "Quot.sound"
32961     ],
32962     "in_project_namespace": true,
32963     "kind": "theorem",
32964     "module": "PaperIRelease.GrammarEquivalence",
32965     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.freeAction_natural",
32966     "runtime_only": false
32967   },
32968   {
32969     "axioms": [
32970       "propext",
32971       "Classical.choice",
32972       "Quot.sound"
32973     ],
32974     "in_project_namespace": true,
32975     "kind": "theorem",
32976     "module": "KomorebiVerification.ProjectorCore",
32977     "name": "Komorebi.Operator.blockApply.eq_1",
32978     "runtime_only": false
32979   },
32980   {
32981     "axioms": [
32982       "propext",
32983       "Classical.choice",
32984       "Quot.sound"
32985     ],
32986     "in_project_namespace": true,
32987     "kind": "theorem",
32988     "module": "PaperICompletion3.PrimarySeedFormula",
32989     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds_generate",
32990     "runtime_only": false
32991   },
32992   {
32993     "axioms": [
32994       "propext",
32995       "Classical.choice",
32996       "Quot.sound"
32997     ],
32998     "in_project_namespace": true,
32999     "kind": "theorem",
33000     "module": "KomorebiVerification.TopologicalCompletion",
33001     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.injEq",
33002     "runtime_only": false
33003   },
33004   {
33005     "axioms": [
33006       "propext",
33007       "Classical.choice",
33008       "Quot.sound"
33009     ],
33010     "in_project_namespace": true,
33011     "kind": "theorem",
33012     "module": "PaperIRelease.AlgebraClassGrouping",
33013     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection.congr_simp",
33014     "runtime_only": false
33015   },
33016   {
33017     "axioms": [
33018       "propext",
33019       "Classical.choice",
33020       "Quot.sound"
33021     ],
33022     "in_project_namespace": true,
33023     "kind": "theorem",
33024     "module": "KomorebiVerification.ResidueProjectors",
33025     "name": "Komorebi.Residue.residueProj_refinement",
33026     "runtime_only": false
33027   },
33028   {
33029     "axioms": [
33030       "propext",
33031       "Classical.choice",
33032       "Quot.sound"
33033     ],
33034     "in_project_namespace": true,
33035     "kind": "theorem",
33036     "module": "PaperICompletion.ConditionedCoordinates",
33037     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_symm",
33038     "runtime_only": false
33039   },
33040   {
33041     "axioms": [
33042       "propext",
33043       "Classical.choice",
33044       "Quot.sound"
33045     ],
33046     "in_project_namespace": true,
33047     "kind": "theorem",
33048     "module": "PaperICompletion4.OperatorIntrinsicFormula",
33049     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.primary_fiber_presentation_invariant",
33050     "runtime_only": false
33051   },
33052   {
33053     "axioms": [
33054       "propext",
33055       "Classical.choice",
33056       "Quot.sound"
33057     ],
33058     "in_project_namespace": true,
33059     "kind": "theorem",
33060     "module": "KomorebiVerification.SeedRankBasics",
33061     "name": "Komorebi.SeedRankBasics.generates_singleton_iff_surjective",
33062     "runtime_only": false
33063   },
33064   {
33065     "axioms": [
33066       "propext",
33067       "Quot.sound"
33068     ],
33069     "in_project_namespace": true,
33070     "kind": "theorem",
33071     "module": "KomorebiVerification.PacketNaturalityCompletion",
33072     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.map_mem_span_image_of_intertwining",
33073     "runtime_only": false
33074   },
33075   {
33076     "axioms": [
33077       "propext",
33078       "Classical.choice",
33079       "Quot.sound"
33080     ],
33081     "in_project_namespace": true,
33082     "kind": "theorem",
33083     "module": "KomorebiVerification.PacketNaturalityCompletion",
33084     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.end_finrank_eq_packet_sum_eq_square",
33085     "runtime_only": false
33086   },
33087   {
33088     "axioms": [
33089       "propext",
33090       "Classical.choice",
33091       "Quot.sound"
33092     ],
33093     "in_project_namespace": true,
33094     "kind": "definition",
33095     "module": "PaperIRelease.PacketCorners",
33096     "name": "Komorebi.PaperIRelease.packetCornerAlgebra",
33097     "runtime_only": false
33098   },
33099   {
33100     "axioms": [
33101       "propext",
33102       "Classical.choice",
33103       "Quot.sound"
33104     ],
33105     "in_project_namespace": true,
33106     "kind": "definition",
33107     "module": "PaperICompletion3.OperatorPrimaryAPI",
33108     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.noConfusion",
33109     "runtime_only": false
33110   },
33111   {
33112     "axioms": [
33113       "propext",
33114       "Classical.choice",
33115       "Quot.sound"
33116     ],
33117     "in_project_namespace": true,
33118     "kind": "theorem",
33119     "module": "KomorebiVerification.PacketNaturalityCompletion",
33120     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packet_natural",
33121     "runtime_only": false
33122   },
33123   {
33124     "axioms": [
33125       "propext",
33126       "Classical.choice",
33127       "Quot.sound"
33128     ],
33129     "in_project_namespace": true,
33130     "kind": "theorem",
33131     "module": "KomorebiVerification.SingleOperatorGraph",
33132     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_8",
33133     "runtime_only": false
33134   },
33135   {
33136     "axioms": [
33137       "propext",
33138       "Classical.choice",
33139       "Quot.sound"
33140     ],
33141     "in_project_namespace": true,
33142     "kind": "theorem",
33143     "module": "PaperICompletion6.OneInvariantFactor",
33144     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.exists_companion_basis_of_cyclic",
33145     "runtime_only": false
33146   },
33147   {
33148     "axioms": [
33149       "propext",
33150       "Classical.choice",
33151       "Quot.sound"
33152     ],
33153     "in_project_namespace": true,
33154     "kind": "theorem",
33155     "module": "KomorebiVerification.EllipticAlgorithms",
33156     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_My",
33157     "runtime_only": false
33158   },
33159   {
33160     "axioms": [
33161       "propext",
33162       "Classical.choice",
33163       "Quot.sound"
33164     ],
33165     "in_project_namespace": true,
33166     "kind": "theorem",
33167     "module": "KomorebiVerification.SingleOperatorGraph",
33168     "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_2",
33169     "runtime_only": false
33170   },
33171   {
33172     "axioms": [],
33173     "in_project_namespace": true,
33174     "kind": "definition",
33175     "module": "KomorebiVerification.EllipticAlgorithms",
33176     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.match_1",
33177     "runtime_only": false
33178   },
33179   {
33180     "axioms": [
33181       "propext",
33182       "Classical.choice",
33183       "Quot.sound"
33184     ],
33185     "in_project_namespace": true,
33186     "kind": "theorem",
33187     "module": "KomorebiVerification.FibreRefinement",
33188     "name": "Komorebi.Packet.fibreProj_refinement",
33189     "runtime_only": false
33190   },
33191   {
33192     "axioms": [
33193       "propext",
33194       "Quot.sound"
33195     ],
33196     "in_project_namespace": true,
33197     "kind": "theorem",
33198     "module": "PaperIRelease.GrammarModules",
33199     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.module_smul",
33200     "runtime_only": false
33201   },
33202   {
33203     "axioms": [
33204       "propext",
33205       "Classical.choice",
33206       "Quot.sound"
33207     ],
33208     "in_project_namespace": true,
33209     "kind": "definition",
33210     "module": "PaperIRelease.GraphSources",
33211     "name": "Komorebi.PaperIRelease.FiniteDigraph.sourcesFintype",
33212     "runtime_only": false
33213   },
33214   {
33215     "axioms": [],
33216     "in_project_namespace": true,
33217     "kind": "theorem",
33218     "module": "KomorebiVerification.ProjectorCore",
33219     "name": "Komorebi.FiniteDifference.iteratedDiff.eq_1",
33220     "runtime_only": false
33221   },
33222   {
33223     "axioms": [],
33224     "in_project_namespace": true,
33225     "kind": "definition",
33226     "module": "PaperIRelease.AlgebraPreorder",
33227     "name": "Komorebi.PaperIRelease.StrictPath._unsafe_rec",
33228     "runtime_only": true
33229   },
33230   {
33231     "axioms": [],
33232     "in_project_namespace": true,
33233     "kind": "theorem",
33234     "module": "KomorebiVerification.ResidueProjectors",
33235     "name": "Komorebi.Residue.mergeAddress._proof_1",
33236     "runtime_only": false
33237   },
33238   {
33239     "axioms": [
33240       "propext",
33241       "Classical.choice",
33242       "Quot.sound"
33243     ],
33244     "in_project_namespace": false,
33245     "kind": "theorem",
33246     "module": "PaperIRelease.TopologySeedRank",
33247     "name": "PaperIRelease.TopologyTransport.seedRank_le_card",
33248     "runtime_only": false
33249   },
33250   {
33251     "axioms": [
33252       "propext",
33253       "Classical.choice",
33254       "Quot.sound"
33255     ],
33256     "in_project_namespace": true,
33257     "kind": "theorem",
33258     "module": "PaperIRelease.GrammarEquivalence",
33259     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_9",
33260     "runtime_only": false
33261   },
33262   {
33263     "axioms": [
33264       "propext",
33265       "Classical.choice",
33266       "Quot.sound"
33267     ],
33268     "in_project_namespace": true,
33269     "kind": "definition",
33270     "module": "PaperIRelease.GrammarIdeal",
33271     "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealQuotientMap",
33272     "runtime_only": false
33273   },
33274   {
33275     "axioms": [
33276       "propext",
33277       "Classical.choice",
33278       "Quot.sound"
33279     ],
33280     "in_project_namespace": true,
33281     "kind": "theorem",
33282     "module": "PaperIRelease.TopologyCategories",
33283     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.sizeOf_spec",
33284     "runtime_only": false
33285   },
33286   {
33287     "axioms": [
33288       "propext",
33289       "Classical.choice",
33290       "Quot.sound"
33291     ],
33292     "in_project_namespace": true,
33293     "kind": "definition",
33294     "module": "KomorebiVerification.TopologicalCompletion",
33295     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv",
33296     "runtime_only": false
33297   },
33298   {
33299     "axioms": [
33300       "propext",
33301       "Classical.choice",
33302       "Quot.sound"
33303     ],
33304     "in_project_namespace": true,
33305     "kind": "theorem",
33306     "module": "PaperICompletion4.OperatorIntrinsicFormula",
33307     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_1",
33308     "runtime_only": false
33309   },
33310   {
33311     "axioms": [
33312       "propext",
33313       "Classical.choice",
33314       "Quot.sound"
33315     ],
33316     "in_project_namespace": true,
33317     "kind": "theorem",
33318     "module": "PaperICompletion5.LinearPrimaryEigenspace",
33319     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.intrinsicMultiplicity_X_sub_C_eq_eigenspace",
33320     "runtime_only": false
33321   },
33322   {
33323     "axioms": [
33324       "propext",
33325       "Classical.choice",
33326       "Quot.sound"
33327     ],
33328     "in_project_namespace": true,
33329     "kind": "definition",
33330     "module": "PaperIRelease.GrammarEquivalence",
33331     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.noConfusion",
33332     "runtime_only": false
33333   },
33334   {
33335     "axioms": [
33336       "propext",
33337       "Classical.choice",
33338       "Quot.sound"
33339     ],
33340     "in_project_namespace": true,
33341     "kind": "theorem",
33342     "module": "KomorebiVerification.EllipticAlgorithms",
33343     "name": "Komorebi.EllipticCoordinates.curveWeight.eq_1",
33344     "runtime_only": false
33345   },
33346   {
33347     "axioms": [
33348       "propext",
33349       "Classical.choice",
33350       "Quot.sound"
33351     ],
33352     "in_project_namespace": false,
33353     "kind": "theorem",
33354     "module": "PaperIRelease.TopologyDenseCompletion",
33355     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_4",
33356     "runtime_only": false
33357   },
33358   {
33359     "axioms": [],
33360     "in_project_namespace": true,
33361     "kind": "definition",
33362     "module": "KomorebiVerification.ProjectorCore",
33363     "name": "Komorebi.instBEqFormalizationStatus.beq",
33364     "runtime_only": false
33365   },
33366   {
33367     "axioms": [
33368       "propext"
33369     ],
33370     "in_project_namespace": true,
33371     "kind": "theorem",
33372     "module": "KomorebiVerification.ProjectorCore",
33373     "name": "Komorebi.Packet.fibreProj_apply_same",
33374     "runtime_only": false
33375   },
33376   {
33377     "axioms": [
33378       "propext",
33379       "Classical.choice",
33380       "Quot.sound"
33381     ],
33382     "in_project_namespace": true,
33383     "kind": "definition",
33384     "module": "PaperIRelease.CategoryBoundaries",
33385     "name": "Komorebi.PaperIRelease.CategoryBoundaries.onePacket",
33386     "runtime_only": false
33387   },
33388   {
33389     "axioms": [
33390       "propext",
33391       "Quot.sound"
33392     ],
33393     "in_project_namespace": true,
33394     "kind": "theorem",
33395     "module": "PaperIRelease.GrammarAlgebra",
33396     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction._proof_1",
33397     "runtime_only": false
33398   },
33399   {
33400     "axioms": [
33401       "propext"
33402     ],
33403     "in_project_namespace": true,
33404     "kind": "definition",
33405     "module": "PaperIRelease.CategoryExport",
33406     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._unsafe_rec",
33407     "runtime_only": true
33408   },
33409   {
33410     "axioms": [
33411       "propext",
33412       "Classical.choice",
33413       "Quot.sound"
33414     ],
33415     "in_project_namespace": true,
33416     "kind": "theorem",
33417     "module": "KomorebiVerification.PacketNaturalityCompletion",
33418     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesized_restricted_block",
33419     "runtime_only": false
33420   },
33421   {
33422     "axioms": [
33423       "propext",
33424       "Classical.choice",
33425       "Quot.sound"
33426     ],
33427     "in_project_namespace": true,
33428     "kind": "theorem",
33429     "module": "PaperIRelease.PacketTopology",
33430     "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_quotient_packet",
33431     "runtime_only": false
33432   },
33433   {
33434     "axioms": [
33435       "propext",
33436       "Classical.choice",
33437       "Quot.sound"
33438     ],
33439     "in_project_namespace": true,
33440     "kind": "definition",
33441     "module": "PaperIRelease.GrammarPaths",
33442     "name": "Komorebi.PaperIRelease.GrammarAlgebra.pathCombinationWord",
33443     "runtime_only": false
33444   },
33445   {
33446     "axioms": [
33447       "propext",
33448       "Classical.choice",
33449       "Quot.sound"
33450     ],
33451     "in_project_namespace": true,
33452     "kind": "theorem",
33453     "module": "PaperIRelease.PacketTopology",
33454     "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_range_of_bounded",
33455     "runtime_only": false
33456   },
33457   {
33458     "axioms": [
33459       "propext",
33460       "Classical.choice",
33461       "Quot.sound"
33462     ],
33463     "in_project_namespace": true,
33464     "kind": "theorem",
33465     "module": "KomorebiVerification.EllipticAlgorithms",
33466     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_4",
33467     "runtime_only": false
33468   },
33469   {
33470     "axioms": [
33471       "propext",
33472       "Quot.sound"
33473     ],
33474     "in_project_namespace": true,
33475     "kind": "theorem",
33476     "module": "PaperIRelease.GrammarModules",
33477     "name": "Komorebi.PaperIRelease.GrammarModules.toModules_isEquivalence",
33478     "runtime_only": false
33479   },
33480   {
33481     "axioms": [
33482       "propext",
33483       "Classical.choice",
33484       "Quot.sound"
33485     ],
33486     "in_project_namespace": true,
33487     "kind": "definition",
33488     "module": "PaperICompletion.SpectralCertificates",
33489     "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList",
33490     "runtime_only": false
33491   },
33492   {
33493     "axioms": [
33494       "propext",
33495       "Classical.choice",
33496       "Quot.sound"
33497     ],
33498     "in_project_namespace": true,
33499     "kind": "recursor",
33500     "module": "PaperIRelease.CategoryPackets",
33501     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.rec",
33502     "runtime_only": false
33503   },
33504   {
33505     "axioms": [
33506       "propext",
33507       "Classical.choice",
33508       "Quot.sound"
33509     ],
33510     "in_project_namespace": true,
33511     "kind": "definition",
33512     "module": "KomorebiVerification.SingleOperatorGraph",
33513     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor",
33514     "runtime_only": false
33515   },
33516   {
33517     "axioms": [
33518       "propext",
33519       "Quot.sound"
33520     ],
33521     "in_project_namespace": true,
33522     "kind": "theorem",
33523     "module": "KomorebiVerification.PathGraphKrylov",
33524     "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_4",
33525     "runtime_only": false
33526   },
33527   {
33528     "axioms": [
33529       "propext",
33530       "Classical.choice",
33531       "Quot.sound"
33532     ],
33533     "in_project_namespace": true,
33534     "kind": "theorem",
33535     "module": "PaperIRelease.PacketExactSequence",
33536     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion_natural",
33537     "runtime_only": false
33538   },
33539   {
33540     "axioms": [
33541       "propext",
33542       "Classical.choice",
33543       "Quot.sound"
33544     ],
33545     "in_project_namespace": false,
33546     "kind": "theorem",
33547     "module": "PaperIRelease.TopologyUnconditional",
33548     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_add_val",
33549     "runtime_only": false
33550   },
33551   {
33552     "axioms": [
33553       "propext",
33554       "Classical.choice",
33555       "Quot.sound"
33556     ],
33557     "in_project_namespace": true,
33558     "kind": "constructor",
33559     "module": "PaperICompletion3.OperatorPrimaryAPI",
33560     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk",
33561     "runtime_only": false
33562   },
33563   {
33564     "axioms": [
33565       "propext",
33566       "Classical.choice",
33567       "Quot.sound"
33568     ],
33569     "in_project_namespace": true,
33570     "kind": "theorem",
33571     "module": "PaperIRelease.PacketTopology",
33572     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM_toLinearMap",
33573     "runtime_only": false
33574   },
33575   {
33576     "axioms": [
33577       "propext",
33578       "Classical.choice",
33579       "Quot.sound"
33580     ],
33581     "in_project_namespace": true,
33582     "kind": "theorem",
33583     "module": "KomorebiVerification.SemisimpleCompletion",
33584     "name": "Komorebi.SemisimpleCompletion.splitProduct_familyGenerates_iff",
33585     "runtime_only": false
33586   },
33587   {
33588     "axioms": [
33589       "propext",
33590       "Classical.choice",
33591       "Quot.sound"
33592     ],
33593     "in_project_namespace": true,
33594     "kind": "theorem",
33595     "module": "PaperIRelease.PacketUniversal",
33596     "name": "Komorebi.PaperIRelease.PacketUniversal.transferBlock_ext",
33597     "runtime_only": false
33598   },
33599   {
33600     "axioms": [
33601       "propext",
33602       "Classical.choice",
33603       "Quot.sound"
33604     ],
33605     "in_project_namespace": true,
33606     "kind": "theorem",
33607     "module": "PaperICompletion3.OperatorPrimaryAPI",
33608     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedFinrank_eq",
33609     "runtime_only": false
33610   },
33611   {
33612     "axioms": [
33613       "propext",
33614       "Classical.choice",
33615       "Quot.sound"
33616     ],
33617     "in_project_namespace": true,
33618     "kind": "theorem",
33619     "module": "PaperIRelease.PolynomialModule",
33620     "name": "Komorebi.PaperIRelease.PolynomialModule.exists_grouped_primary_decomposition",
33621     "runtime_only": false
33622   },
33623   {
33624     "axioms": [
33625       "propext",
33626       "Classical.choice",
33627       "Quot.sound"
33628     ],
33629     "in_project_namespace": true,
33630     "kind": "theorem",
33631     "module": "KomorebiVerification.SemisimpleCompletion",
33632     "name": "Komorebi.SemisimpleCompletion.maxCeilDiv_isLeast_product_generatorCount",
33633     "runtime_only": false
33634   },
33635   {
33636     "axioms": [
33637       "propext",
33638       "Classical.choice",
33639       "Quot.sound"
33640     ],
33641     "in_project_namespace": true,
33642     "kind": "definition",
33643     "module": "PaperICompletion3.OperatorPrimaryAPI",
33644     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.maxCount",
33645     "runtime_only": false
33646   },
33647   {
33648     "axioms": [
33649       "propext",
33650       "Classical.choice",
33651       "Quot.sound"
33652     ],
33653     "in_project_namespace": true,
33654     "kind": "theorem",
33655     "module": "PaperIRelease.TopologyCategories",
33656     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ext",
33657     "runtime_only": false
33658   },
33659   {
33660     "axioms": [
33661       "propext",
33662       "Quot.sound"
33663     ],
33664     "in_project_namespace": true,
33665     "kind": "theorem",
33666     "module": "PaperIRelease.GraphReachability",
33667     "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra._proof_1",
33668     "runtime_only": false
33669   },
33670   {
33671     "axioms": [
33672       "propext",
33673       "Classical.choice",
33674       "Quot.sound"
33675     ],
33676     "in_project_namespace": true,
33677     "kind": "theorem",
33678     "module": "PaperIRelease.GrammarEquivalence",
33679     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_4",
33680     "runtime_only": false
33681   },
33682   {
33683     "axioms": [
33684       "propext",
33685       "Classical.choice",
33686       "Quot.sound"
33687     ],
33688     "in_project_namespace": false,
33689     "kind": "theorem",
33690     "module": "PaperIRelease.TopologySeedRank",
33691     "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates._proof_1",
33692     "runtime_only": false
33693   },
33694   {
33695     "axioms": [
33696       "propext",
33697       "Classical.choice",
33698       "Quot.sound"
33699     ],
33700     "in_project_namespace": true,
33701     "kind": "definition",
33702     "module": "PaperICompletion4.ResidueQuotient",
33703     "name": "Komorebi.PaperICompletion4.ResidueQuotient.ScalarQuotient",
33704     "runtime_only": false
33705   },
33706   {
33707     "axioms": [
33708       "propext",
33709       "Classical.choice",
33710       "Quot.sound"
33711     ],
33712     "in_project_namespace": false,
33713     "kind": "theorem",
33714     "module": "PaperIRelease.TopologyTransport",
33715     "name": "PaperIRelease.TopologyTransport.quotientEquiv_apply_mk",
33716     "runtime_only": false
33717   },
33718   {
33719     "axioms": [
33720       "propext",
33721       "Classical.choice",
33722       "Quot.sound"
33723     ],
33724     "in_project_namespace": true,
33725     "kind": "theorem",
33726     "module": "KomorebiVerification.TopologicalCompletion",
33727     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.HasTopologicalSeedRankOne.cardinality_one_and_not_zero",
33728     "runtime_only": false
33729   },
33730   {
33731     "axioms": [
33732       "propext",
33733       "Classical.choice",
33734       "Quot.sound"
33735     ],
33736     "in_project_namespace": true,
33737     "kind": "theorem",
33738     "module": "KomorebiVerification.SeedRankBasics",
33739     "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv._proof_1",
33740     "runtime_only": false
33741   },
33742   {
33743     "axioms": [
33744       "propext",
33745       "Quot.sound"
33746     ],
33747     "in_project_namespace": true,
33748     "kind": "definition",
33749     "module": "PaperIRelease.GrammarPaths",
33750     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unsafe_rec",
33751     "runtime_only": true
33752   },
33753   {
33754     "axioms": [
33755       "propext",
33756       "Classical.choice",
33757       "Quot.sound"
33758     ],
33759     "in_project_namespace": true,
33760     "kind": "theorem",
33761     "module": "PaperICompletion3.OperatorPrimaryAPI",
33762     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.cyclic_iff_label_injective",
33763     "runtime_only": false
33764   },
33765   {
33766     "axioms": [
33767       "propext",
33768       "Classical.choice",
33769       "Quot.sound"
33770     ],
33771     "in_project_namespace": true,
33772     "kind": "theorem",
33773     "module": "PaperIRelease.PacketTopology",
33774     "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjector_norm_apply_le",
33775     "runtime_only": false
33776   },
33777   {
33778     "axioms": [
33779       "propext",
33780       "Classical.choice",
33781       "Quot.sound"
33782     ],
33783     "in_project_namespace": true,
33784     "kind": "theorem",
33785     "module": "PaperIRelease.CategoryPackets",
33786     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packet_apply",
33787     "runtime_only": false
33788   },
33789   {
33790     "axioms": [
33791       "propext",
33792       "Classical.choice",
33793       "Quot.sound"
33794     ],
33795     "in_project_namespace": true,
33796     "kind": "theorem",
33797     "module": "PaperICompletion4.OperatorIntrinsicFormula",
33798     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_2",
33799     "runtime_only": false
33800   },
33801   {
33802     "axioms": [],
33803     "in_project_namespace": true,
33804     "kind": "constructor",
33805     "module": "PaperIRelease.CategoryExport",
33806     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg",
33807     "runtime_only": false
33808   },
33809   {
33810     "axioms": [
33811       "propext",
33812       "Classical.choice",
33813       "Quot.sound"
33814     ],
33815     "in_project_namespace": true,
33816     "kind": "theorem",
33817     "module": "PaperIRelease.PacketTopology",
33818     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientLiftCLM._proof_1",
33819     "runtime_only": false
33820   },
33821   {
33822     "axioms": [
33823       "propext",
33824       "Classical.choice",
33825       "Quot.sound"
33826     ],
33827     "in_project_namespace": true,
33828     "kind": "definition",
33829     "module": "KomorebiVerification.FibreRefinement",
33830     "name": "Komorebi.Packet.fibreLinearProjectorFamily",
33831     "runtime_only": false
33832   },
33833   {
33834     "axioms": [
33835       "propext",
33836       "Classical.choice",
33837       "Quot.sound"
33838     ],
33839     "in_project_namespace": true,
33840     "kind": "theorem",
33841     "module": "PaperIRelease.GrammarPaths",
33842     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary.eq_def",
33843     "runtime_only": false
33844   },
33845   {
33846     "axioms": [
33847       "propext",
33848       "Classical.choice",
33849       "Quot.sound"
33850     ],
33851     "in_project_namespace": true,
33852     "kind": "definition",
33853     "module": "PaperIRelease.AlgebraDiagonal",
33854     "name": "Komorebi.PaperIRelease.diagonalProjection",
33855     "runtime_only": false
33856   },
33857   {
33858     "axioms": [
33859       "propext",
33860       "Classical.choice",
33861       "Quot.sound"
33862     ],
33863     "in_project_namespace": true,
33864     "kind": "theorem",
33865     "module": "PaperICompletion8.DivisionRows",
33866     "name": "Komorebi.PaperICompletion8.DivisionRows.ceilDiv_isLeast_generatorCount",
33867     "runtime_only": false
33868   },
33869   {
33870     "axioms": [
33871       "propext",
33872       "Classical.choice",
33873       "Quot.sound"
33874     ],
33875     "in_project_namespace": true,
33876     "kind": "theorem",
33877     "module": "KomorebiVerification.ProjectorCore",
33878     "name": "Komorebi.Quantum.finiteAmplitude.eq_1",
33879     "runtime_only": false
33880   },
33881   {
33882     "axioms": [
33883       "propext",
33884       "Classical.choice",
33885       "Quot.sound"
33886     ],
33887     "in_project_namespace": true,
33888     "kind": "definition",
33889     "module": "KomorebiVerification.ExactCoordinates",
33890     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis",
33891     "runtime_only": false
33892   },
33893   {
33894     "axioms": [],
33895     "in_project_namespace": true,
33896     "kind": "theorem",
33897     "module": "PaperIRelease.CategoryExport",
33898     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.inj",
33899     "runtime_only": false
33900   },
33901   {
33902     "axioms": [
33903       "propext",
33904       "Classical.choice",
33905       "Quot.sound"
33906     ],
33907     "in_project_namespace": true,
33908     "kind": "theorem",
33909     "module": "PaperICompletion6.ScalarExtension",
33910     "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_baseChange",
33911     "runtime_only": false
33912   },
33913   {
33914     "axioms": [
33915       "propext",
33916       "Quot.sound"
33917     ],
33918     "in_project_namespace": true,
33919     "kind": "theorem",
33920     "module": "KomorebiVerification.SingleOperatorGraph",
33921     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._proof_1_1",
33922     "runtime_only": false
33923   },
33924   {
33925     "axioms": [
33926       "propext",
33927       "Classical.choice",
33928       "Quot.sound"
33929     ],
33930     "in_project_namespace": false,
33931     "kind": "constructor",
33932     "module": "PaperIRelease.TopologyUnconditional",
33933     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk",
33934     "runtime_only": false
33935   },
33936   {
33937     "axioms": [
33938       "propext",
33939       "Classical.choice",
33940       "Quot.sound"
33941     ],
33942     "in_project_namespace": true,
33943     "kind": "theorem",
33944     "module": "ReleaseBoundary",
33945     "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv.eq_1",
33946     "runtime_only": false
33947   },
33948   {
33949     "axioms": [
33950       "propext",
33951       "Classical.choice",
33952       "Quot.sound"
33953     ],
33954     "in_project_namespace": true,
33955     "kind": "theorem",
33956     "module": "PaperICompletion8.RegularMultiplicity",
33957     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.natural_nonzero_generates",
33958     "runtime_only": false
33959   },
33960   {
33961     "axioms": [
33962       "propext",
33963       "Classical.choice",
33964       "Quot.sound"
33965     ],
33966     "in_project_namespace": true,
33967     "kind": "theorem",
33968     "module": "KomorebiVerification.SingleOperatorGraph",
33969     "name": "Komorebi.SingleOperatorGraph.aeval_apply_of_eigenvector",
33970     "runtime_only": false
33971   },
33972   {
33973     "axioms": [
33974       "propext",
33975       "Classical.choice",
33976       "Quot.sound"
33977     ],
33978     "in_project_namespace": true,
33979     "kind": "inductive",
33980     "module": "PaperIRelease.TopologyCategories",
33981     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism",
33982     "runtime_only": false
33983   },
33984   {
33985     "axioms": [
33986       "propext",
33987       "Classical.choice",
33988       "Quot.sound"
33989     ],
33990     "in_project_namespace": false,
33991     "kind": "theorem",
33992     "module": "PaperIRelease.TopologyTransport",
33993     "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_6",
33994     "runtime_only": false
33995   },
33996   {
33997     "axioms": [],
33998     "in_project_namespace": true,
33999     "kind": "definition",
34000     "module": "PaperIRelease.CategoryExport",
34001     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.elim",
34002     "runtime_only": false
34003   },
34004   {
34005     "axioms": [
34006       "propext",
34007       "Classical.choice",
34008       "Quot.sound"
34009     ],
34010     "in_project_namespace": true,
34011     "kind": "recursor",
34012     "module": "PaperIRelease.CategoryPackets",
34013     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.rec",
34014     "runtime_only": false
34015   },
34016   {
34017     "axioms": [
34018       "propext",
34019       "Classical.choice",
34020       "Quot.sound"
34021     ],
34022     "in_project_namespace": true,
34023     "kind": "theorem",
34024     "module": "PaperICompletion4.GroupedPrimary",
34025     "name": "Komorebi.PaperICompletion4.GroupedPrimary.eq_zero_of_coprime_smul",
34026     "runtime_only": false
34027   },
34028   {
34029     "axioms": [
34030       "propext",
34031       "Quot.sound"
34032     ],
34033     "in_project_namespace": true,
34034     "kind": "theorem",
34035     "module": "KomorebiVerification.SeedRankOperations",
34036     "name": "Komorebi.SeedRankOperations.tensorOperator_smul_tmul",
34037     "runtime_only": false
34038   },
34039   {
34040     "axioms": [
34041       "propext",
34042       "Classical.choice",
34043       "Quot.sound"
34044     ],
34045     "in_project_namespace": true,
34046     "kind": "definition",
34047     "module": "PaperICompletion8.RegularMultiplicity",
34048     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv",
34049     "runtime_only": false
34050   },
34051   {
34052     "axioms": [
34053       "propext",
34054       "Quot.sound"
34055     ],
34056     "in_project_namespace": true,
34057     "kind": "theorem",
34058     "module": "PaperIRelease.GrammarPaths",
34059     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_3",
34060     "runtime_only": false
34061   },
34062   {
34063     "axioms": [
34064       "propext",
34065       "Classical.choice",
34066       "Quot.sound"
34067     ],
34068     "in_project_namespace": true,
34069     "kind": "theorem",
34070     "module": "KomorebiVerification.ProjectorCore",
34071     "name": "Komorebi.Foundation.LinearProjectorFamily.complete",
34072     "runtime_only": false
34073   },
34074   {
34075     "axioms": [
34076       "propext",
34077       "Classical.choice",
34078       "Quot.sound"
34079     ],
34080     "in_project_namespace": true,
34081     "kind": "theorem",
34082     "module": "PaperIRelease.TensorPackets",
34083     "name": "Komorebi.PaperIRelease.tensor_transfer_blocks",
34084     "runtime_only": false
34085   },
34086   {
34087     "axioms": [
34088       "propext",
34089       "Classical.choice",
34090       "Quot.sound"
34091     ],
34092     "in_project_namespace": true,
34093     "kind": "theorem",
34094     "module": "PaperIRelease.CategoryPackets",
34095     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packet_natural",
34096     "runtime_only": false
34097   },
34098   {
34099     "axioms": [
34100       "propext",
34101       "Classical.choice",
34102       "Quot.sound"
34103     ],
34104     "in_project_namespace": false,
34105     "kind": "theorem",
34106     "module": "PaperIRelease.TopologyUnconditionalBridge",
34107     "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_2",
34108     "runtime_only": false
34109   },
34110   {
34111     "axioms": [
34112       "propext",
34113       "Quot.sound"
34114     ],
34115     "in_project_namespace": false,
34116     "kind": "theorem",
34117     "module": "PaperIRelease.AlgebraTransfer",
34118     "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.eq_2",
34119     "runtime_only": false
34120   },
34121   {
34122     "axioms": [
34123       "propext",
34124       "Classical.choice",
34125       "Quot.sound"
34126     ],
34127     "in_project_namespace": true,
34128     "kind": "theorem",
34129     "module": "KomorebiVerification.ProjectorCore",
34130     "name": "Komorebi.Operator.lowRankApply.eq_1",
34131     "runtime_only": false
34132   },
34133   {
34134     "axioms": [
34135       "propext",
34136       "Classical.choice",
34137       "Quot.sound"
34138     ],
34139     "in_project_namespace": true,
34140     "kind": "theorem",
34141     "module": "PaperIRelease.PacketCorners",
34142     "name": "Komorebi.PaperIRelease.cornerCompression.eq_1",
34143     "runtime_only": false
34144   },
34145   {
34146     "axioms": [
34147       "propext",
34148       "Classical.choice",
34149       "Quot.sound"
34150     ],
34151     "in_project_namespace": true,
34152     "kind": "theorem",
34153     "module": "KomorebiVerification.TopologicalCompletion",
34154     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_topologicallyCyclic",
34155     "runtime_only": false
34156   },
34157   {
34158     "axioms": [
34159       "propext",
34160       "Classical.choice",
34161       "Quot.sound"
34162     ],
34163     "in_project_namespace": true,
34164     "kind": "theorem",
34165     "module": "PaperICompletion4.OperatorIntrinsicFormula",
34166     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsic_primary_max",
34167     "runtime_only": false
34168   },
34169   {
34170     "axioms": [
34171       "propext",
34172       "Classical.choice",
34173       "Quot.sound"
34174     ],
34175     "in_project_namespace": true,
34176     "kind": "theorem",
34177     "module": "PaperIRelease.PacketTopologyGeneral",
34178     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.isClosed_packet",
34179     "runtime_only": false
34180   },
34181   {
34182     "axioms": [
34183       "propext",
34184       "Classical.choice",
34185       "Quot.sound"
34186     ],
34187     "in_project_namespace": true,
34188     "kind": "definition",
34189     "module": "PaperIRelease.BoundedStar",
34190     "name": "Komorebi.PaperIRelease.BoundedSupport.Supported",
34191     "runtime_only": false
34192   },
34193   {
34194     "axioms": [
34195       "propext",
34196       "Classical.choice",
34197       "Quot.sound"
34198     ],
34199     "in_project_namespace": false,
34200     "kind": "theorem",
34201     "module": "PaperIRelease.TopologyUnconditional",
34202     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_norm_eq",
34203     "runtime_only": false
34204   },
34205   {
34206     "axioms": [
34207       "propext",
34208       "Quot.sound"
34209     ],
34210     "in_project_namespace": false,
34211     "kind": "theorem",
34212     "module": "PaperIRelease.GrammarPaths",
34213     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.eq_2",
34214     "runtime_only": false
34215   },
34216   {
34217     "axioms": [
34218       "propext",
34219       "Classical.choice",
34220       "Quot.sound"
34221     ],
34222     "in_project_namespace": true,
34223     "kind": "definition",
34224     "module": "PaperIRelease.CategoryPackets",
34225     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.addCommGroup",
34226     "runtime_only": false
34227   },
34228   {
34229     "axioms": [
34230       "propext",
34231       "Classical.choice",
34232       "Quot.sound"
34233     ],
34234     "in_project_namespace": true,
34235     "kind": "theorem",
34236     "module": "PaperIRelease.BoundedStar",
34237     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_5",
34238     "runtime_only": false
34239   },
34240   {
34241     "axioms": [],
34242     "in_project_namespace": true,
34243     "kind": "definition",
34244     "module": "KomorebiVerification.ProjectorCore",
34245     "name": "Komorebi.Seed.OperatorExpr.noConfusion",
34246     "runtime_only": false
34247   },
34248   {
34249     "axioms": [
34250       "propext",
34251       "Quot.sound"
34252     ],
34253     "in_project_namespace": true,
34254     "kind": "theorem",
34255     "module": "KomorebiVerification.SingleOperatorGraph",
34256     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_2",
34257     "runtime_only": false
34258   },
34259   {
34260     "axioms": [
34261       "propext",
34262       "Classical.choice",
34263       "Quot.sound"
34264     ],
34265     "in_project_namespace": true,
34266     "kind": "definition",
34267     "module": "PaperIRelease.GrammarAlgebra",
34268     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.casesOn",
34269     "runtime_only": false
34270   },
34271   {
34272     "axioms": [
34273       "propext",
34274       "Quot.sound"
34275     ],
34276     "in_project_namespace": false,
34277     "kind": "theorem",
34278     "module": "KomorebiVerification.SeedRankOperations",
34279     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.product_familyGenerates",
34280     "runtime_only": false
34281   },
34282   {
34283     "axioms": [],
34284     "in_project_namespace": true,
34285     "kind": "definition",
34286     "module": "KomorebiVerification.ProjectorCore",
34287     "name": "Komorebi.FormalizationStatus.casesOn",
34288     "runtime_only": false
34289   },
34290   {
34291     "axioms": [
34292       "propext",
34293       "Quot.sound"
34294     ],
34295     "in_project_namespace": true,
34296     "kind": "definition",
34297     "module": "KomorebiVerification.PacketNaturalityCompletion",
34298     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraGeneratedHull",
34299     "runtime_only": false
34300   },
34301   {
34302     "axioms": [
34303       "propext",
34304       "Classical.choice",
34305       "Quot.sound"
34306     ],
34307     "in_project_namespace": true,
34308     "kind": "theorem",
34309     "module": "PaperIRelease.GeneralPacketBounds",
34310     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_isBounded",
34311     "runtime_only": false
34312   },
34313   {
34314     "axioms": [
34315       "propext",
34316       "Classical.choice",
34317       "Quot.sound"
34318     ],
34319     "in_project_namespace": true,
34320     "kind": "theorem",
34321     "module": "KomorebiVerification.PacketNaturalityCompletion",
34322     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMul.eq_1",
34323     "runtime_only": false
34324   },
34325   {
34326     "axioms": [
34327       "propext",
34328       "Quot.sound"
34329     ],
34330     "in_project_namespace": true,
34331     "kind": "theorem",
34332     "module": "PaperIRelease.GrammarModules",
34333     "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_8",
34334     "runtime_only": false
34335   },
34336   {
34337     "axioms": [
34338       "propext",
34339       "Classical.choice",
34340       "Quot.sound"
34341     ],
34342     "in_project_namespace": true,
34343     "kind": "theorem",
34344     "module": "KomorebiVerification.TopologicalCompletion",
34345     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis_analysis",
34346     "runtime_only": false
34347   },
34348   {
34349     "axioms": [],
34350     "in_project_namespace": true,
34351     "kind": "definition",
34352     "module": "KomorebiVerification.ProjectorCore",
34353     "name": "Komorebi.ClaimRecord.phase._default",
34354     "runtime_only": false
34355   },
34356   {
34357     "axioms": [
34358       "propext",
34359       "Classical.choice",
34360       "Quot.sound"
34361     ],
34362     "in_project_namespace": false,
34363     "kind": "theorem",
34364     "module": "ReleaseBoundary",
34365     "name": "PaperIBlock08Tests.mixed_product_rank_max_not_sum",
34366     "runtime_only": false
34367   },
34368   {
34369     "axioms": [
34370       "propext",
34371       "Classical.choice",
34372       "Quot.sound"
34373     ],
34374     "in_project_namespace": false,
34375     "kind": "definition",
34376     "module": "PaperIRelease.TopologyUnconditional",
34377     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk._flat_ctor",
34378     "runtime_only": false
34379   },
34380   {
34381     "axioms": [
34382       "propext",
34383       "Classical.choice",
34384       "Quot.sound"
34385     ],
34386     "in_project_namespace": false,
34387     "kind": "definition",
34388     "module": "ReleaseBoundary",
34389     "name": "PaperIBlock08Tests.mixedDivision",
34390     "runtime_only": false
34391   },
34392   {
34393     "axioms": [
34394       "propext",
34395       "Classical.choice",
34396       "Quot.sound"
34397     ],
34398     "in_project_namespace": true,
34399     "kind": "definition",
34400     "module": "KomorebiVerification.ProjectorCore",
34401     "name": "Komorebi.Foundation.LinearProjectorFamily._sizeOf_inst",
34402     "runtime_only": false
34403   },
34404   {
34405     "axioms": [],
34406     "in_project_namespace": true,
34407     "kind": "theorem",
34408     "module": "KomorebiVerification.ProjectorCore",
34409     "name": "Komorebi.FormalizationStatus.conjectural.sizeOf_spec",
34410     "runtime_only": false
34411   },
34412   {
34413     "axioms": [
34414       "propext",
34415       "Quot.sound"
34416     ],
34417     "in_project_namespace": true,
34418     "kind": "theorem",
34419     "module": "KomorebiVerification.ProjectorCore",
34420     "name": "Komorebi.FiniteDifference.iteratedWeightedDiff_geometric",
34421     "runtime_only": false
34422   },
34423   {
34424     "axioms": [
34425       "propext",
34426       "Quot.sound"
34427     ],
34428     "in_project_namespace": true,
34429     "kind": "theorem",
34430     "module": "PaperIRelease.GrammarEquivalence",
34431     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_2",
34432     "runtime_only": false
34433   },
34434   {
34435     "axioms": [
34436       "propext",
34437       "Classical.choice",
34438       "Quot.sound"
34439     ],
34440     "in_project_namespace": true,
34441     "kind": "theorem",
34442     "module": "PaperICompletion8.DivisionProduct",
34443     "name": "Komorebi.PaperICompletion8.DivisionProduct.seedRank_eq_maxCeilDiv_of_divisionProduct_decomposition",
34444     "runtime_only": false
34445   },
34446   {
34447     "axioms": [
34448       "propext",
34449       "Classical.choice",
34450       "Quot.sound"
34451     ],
34452     "in_project_namespace": true,
34453     "kind": "theorem",
34454     "module": "PaperIRelease.TopologyCategories",
34455     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.comp._proof_1",
34456     "runtime_only": false
34457   },
34458   {
34459     "axioms": [
34460       "propext",
34461       "Quot.sound"
34462     ],
34463     "in_project_namespace": true,
34464     "kind": "definition",
34465     "module": "PaperIRelease.GrammarTyped",
34466     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData._sizeOf_inst",
34467     "runtime_only": false
34468   },
34469   {
34470     "axioms": [
34471       "propext",
34472       "Classical.choice",
34473       "Quot.sound"
34474     ],
34475     "in_project_namespace": true,
34476     "kind": "theorem",
34477     "module": "PaperIRelease.BoundedStar",
34478     "name": "Komorebi.PaperIRelease.BoundedSupport.transitive_of_mul_closed",
34479     "runtime_only": false
34480   },
34481   {
34482     "axioms": [
34483       "propext",
34484       "Quot.sound"
34485     ],
34486     "in_project_namespace": true,
34487     "kind": "theorem",
34488     "module": "PaperIRelease.ScalarExtension",
34489     "name": "Komorebi.PaperIRelease.ScalarExtension.instIsScalarTowerTensorProduct_paperIRelease",
34490     "runtime_only": false
34491   },
34492   {
34493     "axioms": [],
34494     "in_project_namespace": true,
34495     "kind": "definition",
34496     "module": "KomorebiVerification.ProjectorCore",
34497     "name": "Komorebi.Seed.OperatorExpr.brecOn.go",
34498     "runtime_only": false
34499   },
34500   {
34501     "axioms": [
34502       "propext",
34503       "Classical.choice",
34504       "Quot.sound"
34505     ],
34506     "in_project_namespace": true,
34507     "kind": "theorem",
34508     "module": "KomorebiVerification.EllipticAlgorithms",
34509     "name": "Komorebi.EllipticCoordinates.unitSeed_generates",
34510     "runtime_only": false
34511   },
34512   {
34513     "axioms": [
34514       "propext",
34515       "Classical.choice",
34516       "Quot.sound"
34517     ],
34518     "in_project_namespace": true,
34519     "kind": "theorem",
34520     "module": "PaperIRelease.TopologyCategories",
34521     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.injEq",
34522     "runtime_only": false
34523   },
34524   {
34525     "axioms": [
34526       "propext",
34527       "Classical.choice",
34528       "Quot.sound"
34529     ],
34530     "in_project_namespace": true,
34531     "kind": "theorem",
34532     "module": "PaperIRelease.PolynomialModule",
34533     "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction._proof_1",
34534     "runtime_only": false
34535   },
34536   {
34537     "axioms": [
34538       "propext",
34539       "Classical.choice",
34540       "Quot.sound"
34541     ],
34542     "in_project_namespace": true,
34543     "kind": "theorem",
34544     "module": "KomorebiVerification.ProjectorCore",
34545     "name": "Komorebi.Seed.hull_empty",
34546     "runtime_only": false
34547   },
34548   {
34549     "axioms": [
34550       "propext",
34551       "Classical.choice",
34552       "Quot.sound"
34553     ],
34554     "in_project_namespace": true,
34555     "kind": "theorem",
34556     "module": "PaperIRelease.PacketDescent",
34557     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_4",
34558     "runtime_only": false
34559   },
34560   {
34561     "axioms": [
34562       "propext",
34563       "Classical.choice",
34564       "Quot.sound"
34565     ],
34566     "in_project_namespace": true,
34567     "kind": "definition",
34568     "module": "PaperIRelease.GraphPropagation",
34569     "name": "Komorebi.PaperIRelease.EdgeSurjective",
34570     "runtime_only": false
34571   },
34572   {
34573     "axioms": [
34574       "propext",
34575       "Classical.choice",
34576       "Quot.sound"
34577     ],
34578     "in_project_namespace": true,
34579     "kind": "theorem",
34580     "module": "PaperIRelease.GrammarAlgebra",
34581     "name": "Komorebi.PaperIRelease.GrammarAlgebra.quotient.eq_1",
34582     "runtime_only": false
34583   },
34584   {
34585     "axioms": [
34586       "propext",
34587       "Classical.choice",
34588       "Quot.sound"
34589     ],
34590     "in_project_namespace": true,
34591     "kind": "theorem",
34592     "module": "KomorebiVerification.TopologicalCompletion",
34593     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_neg_comp",
34594     "runtime_only": false
34595   },
34596   {
34597     "axioms": [
34598       "propext",
34599       "Quot.sound"
34600     ],
34601     "in_project_namespace": true,
34602     "kind": "theorem",
34603     "module": "KomorebiVerification.SeedRankBasics",
34604     "name": "Komorebi.SeedRankBasics.Cyclic.eq_1",
34605     "runtime_only": false
34606   },
34607   {
34608     "axioms": [
34609       "propext",
34610       "Classical.choice",
34611       "Quot.sound"
34612     ],
34613     "in_project_namespace": true,
34614     "kind": "definition",
34615     "module": "PaperICompletion4.GroupedPrimary",
34616     "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv",
34617     "runtime_only": false
34618   },
34619   {
34620     "axioms": [
34621       "propext",
34622       "Classical.choice",
34623       "Quot.sound"
34624     ],
34625     "in_project_namespace": true,
34626     "kind": "definition",
34627     "module": "PaperIRelease.GrammarAlgebra",
34628     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ctorIdx",
34629     "runtime_only": false
34630   },
34631   {
34632     "axioms": [
34633       "propext",
34634       "Classical.choice",
34635       "Quot.sound"
34636     ],
34637     "in_project_namespace": false,
34638     "kind": "definition",
34639     "module": "PaperIRelease.TopologyCountablePackets",
34640     "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis",
34641     "runtime_only": false
34642   },
34643   {
34644     "axioms": [
34645       "propext",
34646       "Classical.choice",
34647       "Quot.sound"
34648     ],
34649     "in_project_namespace": true,
34650     "kind": "theorem",
34651     "module": "PaperIRelease.GrammarEquivalence",
34652     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.action_natural",
34653     "runtime_only": false
34654   },
34655   {
34656     "axioms": [
34657       "propext",
34658       "Classical.choice",
34659       "Quot.sound"
34660     ],
34661     "in_project_namespace": false,
34662     "kind": "theorem",
34663     "module": "ReleaseBoundary",
34664     "name": "PaperIBlock08Tests.quaternion_zero_multiplicity",
34665     "runtime_only": false
34666   },
34667   {
34668     "axioms": [
34669       "Quot.sound"
34670     ],
34671     "in_project_namespace": true,
34672     "kind": "theorem",
34673     "module": "KomorebiVerification.ProjectorCore",
34674     "name": "Komorebi.Packet.fibreProj.congr_simp",
34675     "runtime_only": false
34676   },
34677   {
34678     "axioms": [
34679       "propext",
34680       "Classical.choice",
34681       "Quot.sound"
34682     ],
34683     "in_project_namespace": true,
34684     "kind": "theorem",
34685     "module": "PaperICompletion4.ResidueQuotient",
34686     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr_mk",
34687     "runtime_only": false
34688   },
34689   {
34690     "axioms": [
34691       "propext",
34692       "Classical.choice",
34693       "Quot.sound"
34694     ],
34695     "in_project_namespace": true,
34696     "kind": "definition",
34697     "module": "PaperIRelease.GeneralNormedPackets",
34698     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.recOn",
34699     "runtime_only": false
34700   },
34701   {
34702     "axioms": [
34703       "propext",
34704       "Classical.choice",
34705       "Quot.sound"
34706     ],
34707     "in_project_namespace": true,
34708     "kind": "theorem",
34709     "module": "PaperIRelease.PacketTopologyGeneral",
34710     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM._proof_1",
34711     "runtime_only": false
34712   },
34713   {
34714     "axioms": [],
34715     "in_project_namespace": true,
34716     "kind": "definition",
34717     "module": "PaperIRelease.CategoryBoundaries",
34718     "name": "Komorebi.PaperIRelease.CategoryBoundaries.emptySource",
34719     "runtime_only": false
34720   },
34721   {
34722     "axioms": [
34723       "propext",
34724       "Classical.choice",
34725       "Quot.sound"
34726     ],
34727     "in_project_namespace": true,
34728     "kind": "theorem",
34729     "module": "PaperIRelease.TopologyCategories",
34730     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ext",
34731     "runtime_only": false
34732   },
34733   {
34734     "axioms": [
34735       "propext",
34736       "Classical.choice",
34737       "Quot.sound"
34738     ],
34739     "in_project_namespace": true,
34740     "kind": "definition",
34741     "module": "PaperIRelease.TopologyCategories",
34742     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.recOn",
34743     "runtime_only": false
34744   },
34745   {
34746     "axioms": [
34747       "propext",
34748       "Classical.choice",
34749       "Quot.sound"
34750     ],
34751     "in_project_namespace": true,
34752     "kind": "theorem",
34753     "module": "PaperICompletion4.ResidueQuotient",
34754     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_5",
34755     "runtime_only": false
34756   },
34757   {
34758     "axioms": [
34759       "propext"
34760     ],
34761     "in_project_namespace": true,
34762     "kind": "theorem",
34763     "module": "KomorebiVerification.PacketNaturalityCompletion",
34764     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable._simp_1_2",
34765     "runtime_only": false
34766   },
34767   {
34768     "axioms": [
34769       "propext",
34770       "Classical.choice",
34771       "Quot.sound"
34772     ],
34773     "in_project_namespace": true,
34774     "kind": "definition",
34775     "module": "PaperIRelease.CategoryBoundaries",
34776     "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets",
34777     "runtime_only": false
34778   },
34779   {
34780     "axioms": [
34781       "propext",
34782       "Classical.choice",
34783       "Quot.sound"
34784     ],
34785     "in_project_namespace": true,
34786     "kind": "theorem",
34787     "module": "PaperICompletion4.ResidueQuotient",
34788     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_10",
34789     "runtime_only": false
34790   },
34791   {
34792     "axioms": [],
34793     "in_project_namespace": true,
34794     "kind": "definition",
34795     "module": "KomorebiVerification.ProjectorCore",
34796     "name": "Komorebi.Quantum.diagonalApply",
34797     "runtime_only": false
34798   },
34799   {
34800     "axioms": [
34801       "propext",
34802       "Classical.choice",
34803       "Quot.sound"
34804     ],
34805     "in_project_namespace": true,
34806     "kind": "theorem",
34807     "module": "PaperIRelease.PacketTopology",
34808     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL._proof_1",
34809     "runtime_only": false
34810   },
34811   {
34812     "axioms": [
34813       "propext",
34814       "Classical.choice",
34815       "Quot.sound"
34816     ],
34817     "in_project_namespace": true,
34818     "kind": "theorem",
34819     "module": "PaperIRelease.AlgebraDiagonal",
34820     "name": "Komorebi.PaperIRelease.proj_diagonalProjection",
34821     "runtime_only": false
34822   },
34823   {
34824     "axioms": [
34825       "propext",
34826       "Classical.choice",
34827       "Quot.sound"
34828     ],
34829     "in_project_namespace": true,
34830     "kind": "theorem",
34831     "module": "PaperIRelease.GraphSourceCount",
34832     "name": "Komorebi.PaperIRelease.packetPureSeedRank_eq_source_card",
34833     "runtime_only": false
34834   },
34835   {
34836     "axioms": [
34837       "propext",
34838       "Quot.sound"
34839     ],
34840     "in_project_namespace": true,
34841     "kind": "theorem",
34842     "module": "PaperIRelease.SeedOperations",
34843     "name": "Komorebi.PaperIRelease.SeedOperations.cyclic_annihilator_two_sided_iff",
34844     "runtime_only": false
34845   },
34846   {
34847     "axioms": [
34848       "propext",
34849       "Classical.choice",
34850       "Quot.sound"
34851     ],
34852     "in_project_namespace": false,
34853     "kind": "theorem",
34854     "module": "PaperIRelease.AlgebraPreorder",
34855     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_height._proof_1_1",
34856     "runtime_only": false
34857   },
34858   {
34859     "axioms": [
34860       "propext",
34861       "Classical.choice",
34862       "Quot.sound"
34863     ],
34864     "in_project_namespace": true,
34865     "kind": "theorem",
34866     "module": "KomorebiVerification.EllipticAlgorithms",
34867     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_le_succ",
34868     "runtime_only": false
34869   },
34870   {
34871     "axioms": [
34872       "propext",
34873       "Classical.choice",
34874       "Quot.sound"
34875     ],
34876     "in_project_namespace": true,
34877     "kind": "theorem",
34878     "module": "PaperIRelease.CategoryBoundaries",
34879     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_5",
34880     "runtime_only": false
34881   },
34882   {
34883     "axioms": [
34884       "propext",
34885       "Quot.sound"
34886     ],
34887     "in_project_namespace": true,
34888     "kind": "theorem",
34889     "module": "PaperIRelease.PacketPureRank",
34890     "name": "Komorebi.PaperIRelease.PureGenerates._proof_2",
34891     "runtime_only": false
34892   },
34893   {
34894     "axioms": [],
34895     "in_project_namespace": true,
34896     "kind": "definition",
34897     "module": "KomorebiVerification.ProjectorCore",
34898     "name": "Komorebi.ClaimKind.remarkClaim.elim",
34899     "runtime_only": false
34900   },
34901   {
34902     "axioms": [],
34903     "in_project_namespace": true,
34904     "kind": "theorem",
34905     "module": "PaperIRelease.GraphSourceBoundary",
34906     "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_no_reverse",
34907     "runtime_only": false
34908   },
34909   {
34910     "axioms": [
34911       "propext",
34912       "Classical.choice",
34913       "Quot.sound"
34914     ],
34915     "in_project_namespace": true,
34916     "kind": "definition",
34917     "module": "PaperIRelease.CategoryUniversal",
34918     "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal",
34919     "runtime_only": false
34920   },
34921   {
34922     "axioms": [
34923       "propext",
34924       "Quot.sound"
34925     ],
34926     "in_project_namespace": true,
34927     "kind": "theorem",
34928     "module": "PaperIRelease.TensorPackets",
34929     "name": "Komorebi.PaperIRelease.tensor_transfer_blocks._simp_1_2",
34930     "runtime_only": false
34931   },
34932   {
34933     "axioms": [
34934       "propext",
34935       "Classical.choice",
34936       "Quot.sound"
34937     ],
34938     "in_project_namespace": true,
34939     "kind": "theorem",
34940     "module": "PaperIRelease.PacketTopology",
34941     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_2",
34942     "runtime_only": false
34943   },
34944   {
34945     "axioms": [
34946       "propext",
34947       "Classical.choice",
34948       "Quot.sound"
34949     ],
34950     "in_project_namespace": true,
34951     "kind": "theorem",
34952     "module": "PaperIRelease.GrammarPaths",
34953     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unary._proof_1",
34954     "runtime_only": false
34955   },
34956   {
34957     "axioms": [
34958       "propext",
34959       "Classical.choice",
34960       "Quot.sound"
34961     ],
34962     "in_project_namespace": true,
34963     "kind": "theorem",
34964     "module": "PaperIRelease.CoordinateTransport",
34965     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_7",
34966     "runtime_only": false
34967   },
34968   {
34969     "axioms": [
34970       "propext",
34971       "Classical.choice",
34972       "Quot.sound"
34973     ],
34974     "in_project_namespace": true,
34975     "kind": "theorem",
34976     "module": "PaperIRelease.GrammarTyped",
34977     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_4",
34978     "runtime_only": false
34979   },
34980   {
34981     "axioms": [
34982       "propext",
34983       "Classical.choice",
34984       "Quot.sound"
34985     ],
34986     "in_project_namespace": true,
34987     "kind": "definition",
34988     "module": "PaperIRelease.CategoryPackets",
34989     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject._sizeOf_1",
34990     "runtime_only": false
34991   },
34992   {
34993     "axioms": [
34994       "propext",
34995       "Classical.choice",
34996       "Quot.sound"
34997     ],
34998     "in_project_namespace": true,
34999     "kind": "definition",
35000     "module": "PaperIRelease.GrammarAlgebra",
35001     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapsedActionEquiv",
35002     "runtime_only": false
35003   },
35004   {
35005     "axioms": [
35006       "propext",
35007       "Classical.choice",
35008       "Quot.sound"
35009     ],
35010     "in_project_namespace": true,
35011     "kind": "definition",
35012     "module": "KomorebiVerification.ProjectorCore",
35013     "name": "Komorebi.Foundation.LinearProjectorFamily.mk.noConfusion",
35014     "runtime_only": false
35015   },
35016   {
35017     "axioms": [
35018       "propext",
35019       "Classical.choice",
35020       "Quot.sound"
35021     ],
35022     "in_project_namespace": true,
35023     "kind": "definition",
35024     "module": "PaperIRelease.GeneralNormedPackets",
35025     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.noConfusion",
35026     "runtime_only": false
35027   },
35028   {
35029     "axioms": [
35030       "propext",
35031       "Classical.choice",
35032       "Quot.sound"
35033     ],
35034     "in_project_namespace": true,
35035     "kind": "theorem",
35036     "module": "PaperICompletion4.ResidueQuotient",
35037     "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_6",
35038     "runtime_only": false
35039   },
35040   {
35041     "axioms": [
35042       "propext",
35043       "Classical.choice",
35044       "Quot.sound"
35045     ],
35046     "in_project_namespace": true,
35047     "kind": "theorem",
35048     "module": "PaperIRelease.AlgebraTransfer",
35049     "name": "Komorebi.PaperIRelease.transferBlock_word",
35050     "runtime_only": false
35051   },
35052   {
35053     "axioms": [],
35054     "in_project_namespace": true,
35055     "kind": "definition",
35056     "module": "KomorebiVerification.ProjectorCore",
35057     "name": "Komorebi.FormalizationStatus.boundaryOnly.elim",
35058     "runtime_only": false
35059   },
35060   {
35061     "axioms": [
35062       "propext",
35063       "Classical.choice",
35064       "Quot.sound"
35065     ],
35066     "in_project_namespace": true,
35067     "kind": "theorem",
35068     "module": "PaperIRelease.GraphPropagation",
35069     "name": "Komorebi.PaperIRelease.source_block_zero",
35070     "runtime_only": false
35071   },
35072   {
35073     "axioms": [
35074       "propext",
35075       "Classical.choice",
35076       "Quot.sound"
35077     ],
35078     "in_project_namespace": true,
35079     "kind": "definition",
35080     "module": "PaperIRelease.TensorPackets",
35081     "name": "Komorebi.PaperIRelease.tensorFactorCoordinates",
35082     "runtime_only": false
35083   },
35084   {
35085     "axioms": [],
35086     "in_project_namespace": true,
35087     "kind": "definition",
35088     "module": "KomorebiVerification.ProjectorCore",
35089     "name": "Komorebi.FormalizationStatus.recOn",
35090     "runtime_only": false
35091   },
35092   {
35093     "axioms": [
35094       "propext",
35095       "Classical.choice",
35096       "Quot.sound"
35097     ],
35098     "in_project_namespace": true,
35099     "kind": "inductive",
35100     "module": "KomorebiVerification.TopologicalCompletion",
35101     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily",
35102     "runtime_only": false
35103   },
35104   {
35105     "axioms": [
35106       "propext",
35107       "Classical.choice",
35108       "Quot.sound"
35109     ],
35110     "in_project_namespace": true,
35111     "kind": "definition",
35112     "module": "PaperIRelease.CategoryPackets",
35113     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject._sizeOf_1",
35114     "runtime_only": false
35115   },
35116   {
35117     "axioms": [
35118       "propext",
35119       "Classical.choice",
35120       "Quot.sound"
35121     ],
35122     "in_project_namespace": true,
35123     "kind": "theorem",
35124     "module": "KomorebiVerification.SeedRankOperations",
35125     "name": "Komorebi.SeedRankOperations.seedRank_le_of_surjective_semilinear",
35126     "runtime_only": false
35127   },
35128   {
35129     "axioms": [
35130       "propext",
35131       "Classical.choice",
35132       "Quot.sound"
35133     ],
35134     "in_project_namespace": true,
35135     "kind": "theorem",
35136     "module": "PaperICompletion6.ScalarExtension",
35137     "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_natDegree_baseChange",
35138     "runtime_only": false
35139   },
35140   {
35141     "axioms": [
35142       "propext",
35143       "Classical.choice",
35144       "Quot.sound"
35145     ],
35146     "in_project_namespace": true,
35147     "kind": "definition",
35148     "module": "PaperIRelease.TopologyCategories",
35149     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism._sizeOf_1",
35150     "runtime_only": false
35151   },
35152   {
35153     "axioms": [
35154       "propext",
35155       "Classical.choice",
35156       "Quot.sound"
35157     ],
35158     "in_project_namespace": true,
35159     "kind": "theorem",
35160     "module": "PaperIRelease.GraphSourceBoundary",
35161     "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_not_source_boundary",
35162     "runtime_only": false
35163   },
35164   {
35165     "axioms": [],
35166     "in_project_namespace": true,
35167     "kind": "definition",
35168     "module": "KomorebiVerification.SingleOperatorGraph",
35169     "name": "Komorebi.SingleOperatorGraph.OneJordanBlockPerEigenvalue",
35170     "runtime_only": false
35171   },
35172   {
35173     "axioms": [
35174       "propext",
35175       "Classical.choice",
35176       "Quot.sound"
35177     ],
35178     "in_project_namespace": false,
35179     "kind": "theorem",
35180     "module": "PaperIRelease.TopologyDenseCompletion",
35181     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv_apply_coe",
35182     "runtime_only": false
35183   },
35184   {
35185     "axioms": [
35186       "propext",
35187       "Quot.sound"
35188     ],
35189     "in_project_namespace": true,
35190     "kind": "theorem",
35191     "module": "KomorebiVerification.PathGraphKrylov",
35192     "name": "Komorebi.PathGraphKrylov.pathStep.eq_1",
35193     "runtime_only": false
35194   },
35195   {
35196     "axioms": [
35197       "propext",
35198       "Classical.choice",
35199       "Quot.sound"
35200     ],
35201     "in_project_namespace": true,
35202     "kind": "definition",
35203     "module": "KomorebiVerification.PacketNaturalityCompletion",
35204     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockAlgEquiv",
35205     "runtime_only": false
35206   },
35207   {
35208     "axioms": [
35209       "propext",
35210       "Classical.choice",
35211       "Quot.sound"
35212     ],
35213     "in_project_namespace": true,
35214     "kind": "theorem",
35215     "module": "PaperIRelease.PacketAggregation",
35216     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_5",
35217     "runtime_only": false
35218   },
35219   {
35220     "axioms": [
35221       "propext",
35222       "Classical.choice",
35223       "Quot.sound"
35224     ],
35225     "in_project_namespace": true,
35226     "kind": "theorem",
35227     "module": "PaperIRelease.PacketDescent",
35228     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_1",
35229     "runtime_only": false
35230   },
35231   {
35232     "axioms": [
35233       "propext",
35234       "Classical.choice",
35235       "Quot.sound"
35236     ],
35237     "in_project_namespace": false,
35238     "kind": "theorem",
35239     "module": "PaperIRelease.TopologyCountablePackets",
35240     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.sizeOf_spec",
35241     "runtime_only": false
35242   },
35243   {
35244     "axioms": [
35245       "propext",
35246       "Quot.sound"
35247     ],
35248     "in_project_namespace": false,
35249     "kind": "definition",
35250     "module": "PaperIRelease.TopologySemilinearRank",
35251     "name": "PaperIRelease.TopologySemilinearRank.actingOperators",
35252     "runtime_only": false
35253   },
35254   {
35255     "axioms": [],
35256     "in_project_namespace": true,
35257     "kind": "theorem",
35258     "module": "KomorebiVerification.ProjectorCore",
35259     "name": "Komorebi.ClaimKind.definitionClaim.sizeOf_spec",
35260     "runtime_only": false
35261   },
35262   {
35263     "axioms": [
35264       "propext"
35265     ],
35266     "in_project_namespace": true,
35267     "kind": "theorem",
35268     "module": "KomorebiVerification.SingleOperatorGraph",
35269     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_8",
35270     "runtime_only": false
35271   },
35272   {
35273     "axioms": [
35274       "propext",
35275       "Classical.choice",
35276       "Quot.sound"
35277     ],
35278     "in_project_namespace": true,
35279     "kind": "theorem",
35280     "module": "PaperIRelease.PacketTopology",
35281     "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientMapCLM._proof_1",
35282     "runtime_only": false
35283   },
35284   {
35285     "axioms": [
35286       "propext",
35287       "Quot.sound"
35288     ],
35289     "in_project_namespace": true,
35290     "kind": "theorem",
35291     "module": "PaperICompletion8.RegularMultiplicity",
35292     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_2",
35293     "runtime_only": false
35294   },
35295   {
35296     "axioms": [
35297       "propext",
35298       "Classical.choice",
35299       "Quot.sound"
35300     ],
35301     "in_project_namespace": true,
35302     "kind": "theorem",
35303     "module": "KomorebiVerification.SeedRankBasics",
35304     "name": "Komorebi.SeedRankBasics.seedRank_quotient_le",
35305     "runtime_only": false
35306   },
35307   {
35308     "axioms": [
35309       "propext",
35310       "Classical.choice",
35311       "Quot.sound"
35312     ],
35313     "in_project_namespace": true,
35314     "kind": "theorem",
35315     "module": "KomorebiVerification.EllipticAlgorithms",
35316     "name": "Komorebi.EllipticCoordinates.relationPolynomial_eval_y",
35317     "runtime_only": false
35318   },
35319   {
35320     "axioms": [],
35321     "in_project_namespace": true,
35322     "kind": "definition",
35323     "module": "KomorebiVerification.PacketNaturalityCompletion",
35324     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._f",
35325     "runtime_only": false
35326   },
35327   {
35328     "axioms": [
35329       "propext",
35330       "Classical.choice",
35331       "Quot.sound"
35332     ],
35333     "in_project_namespace": true,
35334     "kind": "theorem",
35335     "module": "PaperIRelease.PacketDescent",
35336     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap_surjective",
35337     "runtime_only": false
35338   },
35339   {
35340     "axioms": [
35341       "propext",
35342       "Quot.sound"
35343     ],
35344     "in_project_namespace": true,
35345     "kind": "theorem",
35346     "module": "PaperIRelease.PacketDescent",
35347     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv._proof_1",
35348     "runtime_only": false
35349   },
35350   {
35351     "axioms": [
35352       "propext",
35353       "Classical.choice",
35354       "Quot.sound"
35355     ],
35356     "in_project_namespace": false,
35357     "kind": "definition",
35358     "module": "PaperIRelease.TopologyCountablePackets",
35359     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedSpace",
35360     "runtime_only": false
35361   },
35362   {
35363     "axioms": [
35364       "propext",
35365       "Classical.choice",
35366       "Quot.sound"
35367     ],
35368     "in_project_namespace": true,
35369     "kind": "definition",
35370     "module": "PaperIRelease.AlgebraClassGrouping",
35371     "name": "Komorebi.PaperIRelease.preorderClassesDecidableEq",
35372     "runtime_only": false
35373   },
35374   {
35375     "axioms": [
35376       "propext",
35377       "Classical.choice",
35378       "Quot.sound"
35379     ],
35380     "in_project_namespace": true,
35381     "kind": "definition",
35382     "module": "PaperIRelease.GrammarTyped",
35383     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.toTypedData",
35384     "runtime_only": false
35385   },
35386   {
35387     "axioms": [
35388       "propext",
35389       "Classical.choice",
35390       "Quot.sound"
35391     ],
35392     "in_project_namespace": true,
35393     "kind": "definition",
35394     "module": "KomorebiVerification.SingleOperatorGraph",
35395     "name": "Komorebi.SingleOperatorGraph.complexCycleRoot",
35396     "runtime_only": false
35397   },
35398   {
35399     "axioms": [
35400       "propext",
35401       "Classical.choice",
35402       "Quot.sound"
35403     ],
35404     "in_project_namespace": true,
35405     "kind": "theorem",
35406     "module": "PaperIRelease.CoordinateTransport",
35407     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_12",
35408     "runtime_only": false
35409   },
35410   {
35411     "axioms": [
35412       "propext",
35413       "Classical.choice",
35414       "Quot.sound"
35415     ],
35416     "in_project_namespace": true,
35417     "kind": "theorem",
35418     "module": "PaperIRelease.PacketTopologyGeneral",
35419     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjector_bounded",
35420     "runtime_only": false
35421   },
35422   {
35423     "axioms": [],
35424     "in_project_namespace": true,
35425     "kind": "theorem",
35426     "module": "KomorebiVerification.PathGraphKrylov",
35427     "name": "Komorebi.PathGraphKrylov.endpoint.eq_1",
35428     "runtime_only": false
35429   },
35430   {
35431     "axioms": [],
35432     "in_project_namespace": true,
35433     "kind": "definition",
35434     "module": "KomorebiVerification.SingleOperatorGraph",
35435     "name": "Komorebi.SingleOperatorGraph.AllGeometricMultiplicitiesOne",
35436     "runtime_only": false
35437   },
35438   {
35439     "axioms": [
35440       "propext",
35441       "Quot.sound"
35442     ],
35443     "in_project_namespace": true,
35444     "kind": "definition",
35445     "module": "PaperIRelease.GraphSources",
35446     "name": "Komorebi.PaperIRelease.FiniteDigraph.Sources",
35447     "runtime_only": false
35448   },
35449   {
35450     "axioms": [
35451       "propext",
35452       "Quot.sound"
35453     ],
35454     "in_project_namespace": true,
35455     "kind": "theorem",
35456     "module": "PaperIRelease.GrammarModules",
35457     "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_7",
35458     "runtime_only": false
35459   },
35460   {
35461     "axioms": [
35462       "propext",
35463       "Classical.choice",
35464       "Quot.sound"
35465     ],
35466     "in_project_namespace": true,
35467     "kind": "theorem",
35468     "module": "PaperIRelease.GrammarEquivalence",
35469     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_3",
35470     "runtime_only": false
35471   },
35472   {
35473     "axioms": [
35474       "propext",
35475       "Quot.sound"
35476     ],
35477     "in_project_namespace": true,
35478     "kind": "theorem",
35479     "module": "KomorebiVerification.SeedRankOperations",
35480     "name": "Komorebi.SeedRankOperations.prodFstSemilinear._proof_1",
35481     "runtime_only": false
35482   },
35483   {
35484     "axioms": [],
35485     "in_project_namespace": true,
35486     "kind": "theorem",
35487     "module": "PaperIRelease.CategoryExport",
35488     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.inj",
35489     "runtime_only": false
35490   },
35491   {
35492     "axioms": [
35493       "propext",
35494       "Classical.choice",
35495       "Quot.sound"
35496     ],
35497     "in_project_namespace": false,
35498     "kind": "theorem",
35499     "module": "PaperIRelease.TopologyDenseCompletion",
35500     "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion._proof_2",
35501     "runtime_only": false
35502   },
35503   {
35504     "axioms": [
35505       "propext",
35506       "Classical.choice",
35507       "Quot.sound"
35508     ],
35509     "in_project_namespace": true,
35510     "kind": "theorem",
35511     "module": "KomorebiVerification.ProjectorCore",
35512     "name": "Komorebi.Foundation.LinearProjectorFamily.mk.inj",
35513     "runtime_only": false
35514   },
35515   {
35516     "axioms": [
35517       "propext",
35518       "Classical.choice",
35519       "Quot.sound"
35520     ],
35521     "in_project_namespace": false,
35522     "kind": "theorem",
35523     "module": "PaperIRelease.TopologyCountablePackets",
35524     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_6",
35525     "runtime_only": false
35526   },
35527   {
35528     "axioms": [],
35529     "in_project_namespace": true,
35530     "kind": "definition",
35531     "module": "PaperIRelease.CategoryExport",
35532     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.noConfusion",
35533     "runtime_only": false
35534   },
35535   {
35536     "axioms": [
35537       "propext",
35538       "Quot.sound"
35539     ],
35540     "in_project_namespace": true,
35541     "kind": "theorem",
35542     "module": "PaperICompletion4.ResidueQuotient",
35543     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap._proof_1",
35544     "runtime_only": false
35545   },
35546   {
35547     "axioms": [
35548       "propext",
35549       "Classical.choice",
35550       "Quot.sound"
35551     ],
35552     "in_project_namespace": true,
35553     "kind": "definition",
35554     "module": "PaperICompletion3.OperatorPrimaryAPI",
35555     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.Index",
35556     "runtime_only": false
35557   },
35558   {
35559     "axioms": [
35560       "propext",
35561       "Quot.sound"
35562     ],
35563     "in_project_namespace": true,
35564     "kind": "definition",
35565     "module": "KomorebiVerification.SeedRankBasics",
35566     "name": "Komorebi.SeedRankBasics.Generates",
35567     "runtime_only": false
35568   },
35569   {
35570     "axioms": [
35571       "propext",
35572       "Classical.choice",
35573       "Quot.sound"
35574     ],
35575     "in_project_namespace": false,
35576     "kind": "theorem",
35577     "module": "PaperIRelease.TopologyDenseCompletion",
35578     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._simp_3",
35579     "runtime_only": false
35580   },
35581   {
35582     "axioms": [
35583       "propext",
35584       "Classical.choice",
35585       "Quot.sound"
35586     ],
35587     "in_project_namespace": true,
35588     "kind": "theorem",
35589     "module": "KomorebiVerification.PaperITransport",
35590     "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_3",
35591     "runtime_only": false
35592   },
35593   {
35594     "axioms": [
35595       "propext",
35596       "Classical.choice",
35597       "Quot.sound"
35598     ],
35599     "in_project_namespace": true,
35600     "kind": "definition",
35601     "module": "PaperIRelease.PacketDescent",
35602     "name": "Komorebi.Foundation.LinearProjectorFamily.Preserves",
35603     "runtime_only": false
35604   },
35605   {
35606     "axioms": [
35607       "propext",
35608       "Classical.choice",
35609       "Quot.sound"
35610     ],
35611     "in_project_namespace": true,
35612     "kind": "definition",
35613     "module": "PaperIRelease.CategoryPackets",
35614     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.noConfusionType",
35615     "runtime_only": false
35616   },
35617   {
35618     "axioms": [
35619       "propext",
35620       "Classical.choice",
35621       "Quot.sound"
35622     ],
35623     "in_project_namespace": false,
35624     "kind": "theorem",
35625     "module": "PaperIRelease.TopologyUnconditional",
35626     "name": "PaperIRelease.TopologyUnconditional.summable_finiteSum_bounded",
35627     "runtime_only": false
35628   },
35629   {
35630     "axioms": [
35631       "propext",
35632       "Classical.choice",
35633       "Quot.sound"
35634     ],
35635     "in_project_namespace": false,
35636     "kind": "definition",
35637     "module": "PaperIRelease.TopologyFiniteCompletion",
35638     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily",
35639     "runtime_only": false
35640   },
35641   {
35642     "axioms": [
35643       "propext",
35644       "Classical.choice",
35645       "Quot.sound"
35646     ],
35647     "in_project_namespace": true,
35648     "kind": "definition",
35649     "module": "PaperIRelease.GrammarAlgebra",
35650     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow",
35651     "runtime_only": false
35652   },
35653   {
35654     "axioms": [
35655       "propext",
35656       "Quot.sound"
35657     ],
35658     "in_project_namespace": false,
35659     "kind": "theorem",
35660     "module": "PaperIRelease.GrammarPaths",
35661     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.eq_1",
35662     "runtime_only": false
35663   },
35664   {
35665     "axioms": [
35666       "propext",
35667       "Classical.choice",
35668       "Quot.sound"
35669     ],
35670     "in_project_namespace": true,
35671     "kind": "theorem",
35672     "module": "KomorebiVerification.PacketNaturalityCompletion",
35673     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_mem_ker_arrowB",
35674     "runtime_only": false
35675   },
35676   {
35677     "axioms": [
35678       "propext",
35679       "Classical.choice",
35680       "Quot.sound"
35681     ],
35682     "in_project_namespace": true,
35683     "kind": "theorem",
35684     "module": "KomorebiVerification.SingleOperatorGraph",
35685     "name": "Komorebi.SingleOperatorGraph.graph_seedNumber_eq_max_eigenspace_multiplicity_of_distinct",
35686     "runtime_only": false
35687   },
35688   {
35689     "axioms": [
35690       "propext",
35691       "Classical.choice",
35692       "Quot.sound"
35693     ],
35694     "in_project_namespace": true,
35695     "kind": "theorem",
35696     "module": "PaperICompletion.SpectralCertificates",
35697     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenFibreEquiv._proof_1",
35698     "runtime_only": false
35699   },
35700   {
35701     "axioms": [],
35702     "in_project_namespace": true,
35703     "kind": "definition",
35704     "module": "PaperIRelease.CategoryExport",
35705     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorIdx",
35706     "runtime_only": false
35707   },
35708   {
35709     "axioms": [
35710       "propext",
35711       "Classical.choice",
35712       "Quot.sound"
35713     ],
35714     "in_project_namespace": true,
35715     "kind": "theorem",
35716     "module": "PaperIRelease.PolynomialModule",
35717     "name": "Komorebi.PaperIRelease.PolynomialModule.intrinsic_primary_finite_power_sum",
35718     "runtime_only": false
35719   },
35720   {
35721     "axioms": [
35722       "propext",
35723       "Quot.sound"
35724     ],
35725     "in_project_namespace": true,
35726     "kind": "definition",
35727     "module": "PaperIRelease.GrammarModules",
35728     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom._sizeOf_inst",
35729     "runtime_only": false
35730   },
35731   {
35732     "axioms": [
35733       "propext",
35734       "Classical.choice",
35735       "Quot.sound"
35736     ],
35737     "in_project_namespace": true,
35738     "kind": "theorem",
35739     "module": "PaperIRelease.PacketAggregation",
35740     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_6",
35741     "runtime_only": false
35742   },
35743   {
35744     "axioms": [
35745       "propext",
35746       "Classical.choice",
35747       "Quot.sound"
35748     ],
35749     "in_project_namespace": false,
35750     "kind": "theorem",
35751     "module": "PaperIRelease.TopologyUnconditionalBridge",
35752     "name": "PaperIRelease.TopologyCountablePackets.Projectors.countable_synthesis_norm_le",
35753     "runtime_only": false
35754   },
35755   {
35756     "axioms": [
35757       "propext",
35758       "Classical.choice",
35759       "Quot.sound"
35760     ],
35761     "in_project_namespace": true,
35762     "kind": "theorem",
35763     "module": "PaperICompletion4.ResidueQuotient",
35764     "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap_ker",
35765     "runtime_only": false
35766   },
35767   {
35768     "axioms": [],
35769     "in_project_namespace": true,
35770     "kind": "definition",
35771     "module": "KomorebiVerification.ProjectorCore",
35772     "name": "Komorebi.FormalizationStatus.noConfusionType",
35773     "runtime_only": false
35774   },
35775   {
35776     "axioms": [
35777       "propext",
35778       "Classical.choice",
35779       "Quot.sound"
35780     ],
35781     "in_project_namespace": true,
35782     "kind": "theorem",
35783     "module": "PaperICompletion5.GeometricSeedFormula",
35784     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedFinrank_eq_geometricSeedMaximum",
35785     "runtime_only": false
35786   },
35787   {
35788     "axioms": [
35789       "propext",
35790       "Classical.choice",
35791       "Quot.sound"
35792     ],
35793     "in_project_namespace": true,
35794     "kind": "theorem",
35795     "module": "PaperICompletion5.CyclicGeometricCriterion",
35796     "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff",
35797     "runtime_only": false
35798   },
35799   {
35800     "axioms": [
35801       "propext",
35802       "Classical.choice",
35803       "Quot.sound"
35804     ],
35805     "in_project_namespace": true,
35806     "kind": "theorem",
35807     "module": "KomorebiVerification.PaperIBlockCompletion",
35808     "name": "Komorebi.Algebra.matrixSupported_one_iff_reflexive",
35809     "runtime_only": false
35810   },
35811   {
35812     "axioms": [
35813       "propext",
35814       "Classical.choice",
35815       "Quot.sound"
35816     ],
35817     "in_project_namespace": true,
35818     "kind": "definition",
35819     "module": "PaperIRelease.PacketBoundaryTests",
35820     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily",
35821     "runtime_only": false
35822   },
35823   {
35824     "axioms": [
35825       "propext",
35826       "Classical.choice",
35827       "Quot.sound"
35828     ],
35829     "in_project_namespace": false,
35830     "kind": "constructor",
35831     "module": "PaperIRelease.TopologyCountablePackets",
35832     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk",
35833     "runtime_only": false
35834   },
35835   {
35836     "axioms": [
35837       "propext",
35838       "Classical.choice",
35839       "Quot.sound"
35840     ],
35841     "in_project_namespace": true,
35842     "kind": "theorem",
35843     "module": "PaperICompletion8.ProductPresentation",
35844     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_7",
35845     "runtime_only": false
35846   },
35847   {
35848     "axioms": [
35849       "propext",
35850       "Quot.sound"
35851     ],
35852     "in_project_namespace": true,
35853     "kind": "theorem",
35854     "module": "PaperICompletion6.OneInvariantFactor",
35855     "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_6",
35856     "runtime_only": false
35857   },
35858   {
35859     "axioms": [
35860       "propext",
35861       "Classical.choice",
35862       "Quot.sound"
35863     ],
35864     "in_project_namespace": true,
35865     "kind": "definition",
35866     "module": "KomorebiVerification.TopologicalCompletion",
35867     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.transferBlock",
35868     "runtime_only": false
35869   },
35870   {
35871     "axioms": [
35872       "propext",
35873       "Classical.choice",
35874       "Quot.sound"
35875     ],
35876     "in_project_namespace": true,
35877     "kind": "theorem",
35878     "module": "KomorebiVerification.EllipticAlgorithms",
35879     "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_5",
35880     "runtime_only": false
35881   },
35882   {
35883     "axioms": [
35884       "propext",
35885       "Classical.choice",
35886       "Quot.sound"
35887     ],
35888     "in_project_namespace": true,
35889     "kind": "theorem",
35890     "module": "KomorebiVerification.EllipticAlgorithms",
35891     "name": "Komorebi.EllipticCoordinates.product_normal_form",
35892     "runtime_only": false
35893   },
35894   {
35895     "axioms": [],
35896     "in_project_namespace": true,
35897     "kind": "definition",
35898     "module": "PaperIRelease.GraphSources",
35899     "name": "Komorebi.PaperIRelease.FiniteDigraph.reachPreorder",
35900     "runtime_only": false
35901   },
35902   {
35903     "axioms": [
35904       "propext",
35905       "Classical.choice",
35906       "Quot.sound"
35907     ],
35908     "in_project_namespace": true,
35909     "kind": "theorem",
35910     "module": "PaperIRelease.AlgebraPreorder",
35911     "name": "Komorebi.PaperIRelease.no_strictPath_after_maximal._proof_1_1",
35912     "runtime_only": false
35913   },
35914   {
35915     "axioms": [
35916       "propext"
35917     ],
35918     "in_project_namespace": true,
35919     "kind": "theorem",
35920     "module": "KomorebiVerification.SingleOperatorGraph",
35921     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_2",
35922     "runtime_only": false
35923   },
35924   {
35925     "axioms": [
35926       "propext",
35927       "Classical.choice",
35928       "Quot.sound"
35929     ],
35930     "in_project_namespace": true,
35931     "kind": "recursor",
35932     "module": "PaperIRelease.GrammarTyped",
35933     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.rec",
35934     "runtime_only": false
35935   },
35936   {
35937     "axioms": [
35938       "propext",
35939       "Classical.choice",
35940       "Quot.sound"
35941     ],
35942     "in_project_namespace": true,
35943     "kind": "theorem",
35944     "module": "PaperIRelease.TopologyCategories",
35945     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.topologicalAdd",
35946     "runtime_only": false
35947   },
35948   {
35949     "axioms": [
35950       "propext",
35951       "Classical.choice",
35952       "Quot.sound"
35953     ],
35954     "in_project_namespace": false,
35955     "kind": "theorem",
35956     "module": "PaperIRelease.TopologyFiniteCompletion",
35957     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_3",
35958     "runtime_only": false
35959   },
35960   {
35961     "axioms": [
35962       "propext",
35963       "Quot.sound"
35964     ],
35965     "in_project_namespace": true,
35966     "kind": "definition",
35967     "module": "KomorebiVerification.PacketNaturalityCompletion",
35968     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2081",
35969     "runtime_only": false
35970   },
35971   {
35972     "axioms": [
35973       "propext",
35974       "Classical.choice",
35975       "Quot.sound"
35976     ],
35977     "in_project_namespace": true,
35978     "kind": "definition",
35979     "module": "PaperIRelease.TopologyCategories",
35980     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk._flat_ctor",
35981     "runtime_only": false
35982   },
35983   {
35984     "axioms": [
35985       "propext",
35986       "Quot.sound"
35987     ],
35988     "in_project_namespace": true,
35989     "kind": "theorem",
35990     "module": "PaperIRelease.GrammarAlgebra",
35991     "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrowWord.eq_1",
35992     "runtime_only": false
35993   },
35994   {
35995     "axioms": [
35996       "propext"
35997     ],
35998     "in_project_namespace": true,
35999     "kind": "theorem",
36000     "module": "PaperIRelease.CategoryExport",
36001     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.injEq",
36002     "runtime_only": false
36003   },
36004   {
36005     "axioms": [
36006       "propext",
36007       "Classical.choice",
36008       "Quot.sound"
36009     ],
36010     "in_project_namespace": true,
36011     "kind": "definition",
36012     "module": "PaperIRelease.GeneralConditionedCoordinates",
36013     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear",
36014     "runtime_only": false
36015   },
36016   {
36017     "axioms": [
36018       "propext",
36019       "Classical.choice",
36020       "Quot.sound"
36021     ],
36022     "in_project_namespace": true,
36023     "kind": "theorem",
36024     "module": "PaperIRelease.CategoryPackets",
36025     "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector.eq_1",
36026     "runtime_only": false
36027   },
36028   {
36029     "axioms": [],
36030     "in_project_namespace": true,
36031     "kind": "theorem",
36032     "module": "PaperICompletion8.RegularMultiplicity",
36033     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_5",
36034     "runtime_only": false
36035   },
36036   {
36037     "axioms": [
36038       "propext",
36039       "Quot.sound"
36040     ],
36041     "in_project_namespace": true,
36042     "kind": "theorem",
36043     "module": "KomorebiVerification.SeedRankOperations",
36044     "name": "Komorebi.SeedRankOperations.tensorActionsCommute",
36045     "runtime_only": false
36046   },
36047   {
36048     "axioms": [
36049       "propext",
36050       "Classical.choice",
36051       "Quot.sound"
36052     ],
36053     "in_project_namespace": true,
36054     "kind": "theorem",
36055     "module": "KomorebiVerification.ProjectorCore",
36056     "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize.eq_1",
36057     "runtime_only": false
36058   },
36059   {
36060     "axioms": [
36061       "propext"
36062     ],
36063     "in_project_namespace": true,
36064     "kind": "theorem",
36065     "module": "KomorebiVerification.PacketNaturalityCompletion",
36066     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable._simp_1_3",
36067     "runtime_only": false
36068   },
36069   {
36070     "axioms": [
36071       "propext",
36072       "Classical.choice",
36073       "Quot.sound"
36074     ],
36075     "in_project_namespace": true,
36076     "kind": "theorem",
36077     "module": "PaperIRelease.GrammarEquivalence",
36078     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_1",
36079     "runtime_only": false
36080   },
36081   {
36082     "axioms": [
36083       "propext",
36084       "Classical.choice",
36085       "Quot.sound"
36086     ],
36087     "in_project_namespace": true,
36088     "kind": "theorem",
36089     "module": "PaperICompletion3.OperatorPrimaryAPI",
36090     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.operator_seedFinrank_eq_primaryGeneratorCount",
36091     "runtime_only": false
36092   },
36093   {
36094     "axioms": [
36095       "propext",
36096       "Classical.choice",
36097       "Quot.sound"
36098     ],
36099     "in_project_namespace": true,
36100     "kind": "theorem",
36101     "module": "PaperIRelease.AlgebraClassGrouping",
36102     "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq._simp_1_2",
36103     "runtime_only": false
36104   },
36105   {
36106     "axioms": [
36107       "propext",
36108       "Classical.choice",
36109       "Quot.sound"
36110     ],
36111     "in_project_namespace": true,
36112     "kind": "theorem",
36113     "module": "PaperIRelease.PacketBoundaryTests",
36114     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_3",
36115     "runtime_only": false
36116   },
36117   {
36118     "axioms": [
36119       "propext",
36120       "Classical.choice",
36121       "Quot.sound"
36122     ],
36123     "in_project_namespace": true,
36124     "kind": "theorem",
36125     "module": "PaperICompletion4.OperatorIntrinsicFormula",
36126     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_6",
36127     "runtime_only": false
36128   },
36129   {
36130     "axioms": [],
36131     "in_project_namespace": true,
36132     "kind": "definition",
36133     "module": "PaperIRelease.CategoryExport",
36134     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn",
36135     "runtime_only": false
36136   },
36137   {
36138     "axioms": [],
36139     "in_project_namespace": true,
36140     "kind": "definition",
36141     "module": "PaperIRelease.GrammarPaths",
36142     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.elim",
36143     "runtime_only": false
36144   },
36145   {
36146     "axioms": [
36147       "propext",
36148       "Classical.choice",
36149       "Quot.sound"
36150     ],
36151     "in_project_namespace": true,
36152     "kind": "theorem",
36153     "module": "PaperICompletion3.PrimarySeedFormula",
36154     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primePowerProduct_seedNumber_isLeast",
36155     "runtime_only": false
36156   },
36157   {
36158     "axioms": [
36159       "propext",
36160       "Classical.choice",
36161       "Quot.sound"
36162     ],
36163     "in_project_namespace": true,
36164     "kind": "definition",
36165     "module": "KomorebiVerification.PacketNaturalityCompletion",
36166     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.ctorIdx",
36167     "runtime_only": false
36168   },
36169   {
36170     "axioms": [
36171       "propext",
36172       "Classical.choice",
36173       "Quot.sound"
36174     ],
36175     "in_project_namespace": true,
36176     "kind": "definition",
36177     "module": "KomorebiVerification.TopologicalCompletion",
36178     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis",
36179     "runtime_only": false
36180   },
36181   {
36182     "axioms": [
36183       "propext",
36184       "Classical.choice",
36185       "Quot.sound"
36186     ],
36187     "in_project_namespace": true,
36188     "kind": "theorem",
36189     "module": "KomorebiVerification.TopologicalCompletion",
36190     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta_dense_span",
36191     "runtime_only": false
36192   },
36193   {
36194     "axioms": [
36195       "propext",
36196       "Classical.choice",
36197       "Quot.sound"
36198     ],
36199     "in_project_namespace": true,
36200     "kind": "theorem",
36201     "module": "PaperIRelease.AlgebraClassGrouping",
36202     "name": "Komorebi.PaperIRelease.grouped_operatorSupported_iff",
36203     "runtime_only": false
36204   },
36205   {
36206     "axioms": [
36207       "propext"
36208     ],
36209     "in_project_namespace": true,
36210     "kind": "theorem",
36211     "module": "PaperIRelease.CategoryExport",
36212     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.injEq",
36213     "runtime_only": false
36214   },
36215   {
36216     "axioms": [
36217       "propext",
36218       "Classical.choice",
36219       "Quot.sound"
36220     ],
36221     "in_project_namespace": true,
36222     "kind": "theorem",
36223     "module": "PaperICompletion3.PrimarySeedFormula",
36224     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap.eq_1",
36225     "runtime_only": false
36226   },
36227   {
36228     "axioms": [],
36229     "in_project_namespace": true,
36230     "kind": "inductive",
36231     "module": "KomorebiVerification.ProjectorCore",
36232     "name": "Komorebi.ClaimKind",
36233     "runtime_only": false
36234   },
36235   {
36236     "axioms": [],
36237     "in_project_namespace": true,
36238     "kind": "definition",
36239     "module": "KomorebiVerification.ProjectorCore",
36240     "name": "Komorebi.Seed.OperatorExpr.brecOn",
36241     "runtime_only": false
36242   },
36243   {
36244     "axioms": [
36245       "propext",
36246       "Classical.choice",
36247       "Quot.sound"
36248     ],
36249     "in_project_namespace": false,
36250     "kind": "definition",
36251     "module": "PaperIRelease.TopologyCountablePackets",
36252     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedAddCommGroup",
36253     "runtime_only": false
36254   },
36255   {
36256     "axioms": [
36257       "propext",
36258       "Quot.sound"
36259     ],
36260     "in_project_namespace": true,
36261     "kind": "definition",
36262     "module": "PaperIRelease.GrammarModules",
36263     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.action",
36264     "runtime_only": false
36265   },
36266   {
36267     "axioms": [],
36268     "in_project_namespace": true,
36269     "kind": "theorem",
36270     "module": "PaperIRelease.GrammarPaths",
36271     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.sizeOf_spec",
36272     "runtime_only": false
36273   },
36274   {
36275     "axioms": [
36276       "propext",
36277       "Classical.choice",
36278       "Quot.sound"
36279     ],
36280     "in_project_namespace": false,
36281     "kind": "theorem",
36282     "module": "PaperIRelease.TopologySemilinearRank",
36283     "name": "PaperIRelease.TopologySemilinearRank.rank_eq_of_continuous_semilinear_equiv",
36284     "runtime_only": false
36285   },
36286   {
36287     "axioms": [
36288       "propext",
36289       "Classical.choice",
36290       "Quot.sound"
36291     ],
36292     "in_project_namespace": false,
36293     "kind": "definition",
36294     "module": "PaperIRelease.TopologyUnconditional",
36295     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_12",
36296     "runtime_only": false
36297   },
36298   {
36299     "axioms": [
36300       "propext",
36301       "Classical.choice",
36302       "Quot.sound"
36303     ],
36304     "in_project_namespace": true,
36305     "kind": "theorem",
36306     "module": "KomorebiVerification.PaperIBlockCompletion",
36307     "name": "Komorebi.Foundation.transferBlock_reconstruction_linearMap",
36308     "runtime_only": false
36309   },
36310   {
36311     "axioms": [
36312       "propext",
36313       "Classical.choice",
36314       "Quot.sound"
36315     ],
36316     "in_project_namespace": false,
36317     "kind": "theorem",
36318     "module": "PaperIRelease.TopologyCountablePackets",
36319     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_10",
36320     "runtime_only": false
36321   },
36322   {
36323     "axioms": [
36324       "propext",
36325       "Classical.choice",
36326       "Quot.sound"
36327     ],
36328     "in_project_namespace": true,
36329     "kind": "theorem",
36330     "module": "KomorebiVerification.PacketNaturalityCompletion",
36331     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_3",
36332     "runtime_only": false
36333   },
36334   {
36335     "axioms": [
36336       "propext",
36337       "Quot.sound"
36338     ],
36339     "in_project_namespace": true,
36340     "kind": "definition",
36341     "module": "PaperIRelease.GrammarModules",
36342     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.space",
36343     "runtime_only": false
36344   },
36345   {
36346     "axioms": [
36347       "propext",
36348       "Classical.choice",
36349       "Quot.sound"
36350     ],
36351     "in_project_namespace": true,
36352     "kind": "theorem",
36353     "module": "PaperIRelease.TopologyCategories",
36354     "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_2",
36355     "runtime_only": false
36356   },
36357   {
36358     "axioms": [
36359       "propext",
36360       "Quot.sound"
36361     ],
36362     "in_project_namespace": true,
36363     "kind": "theorem",
36364     "module": "PaperICompletion4.GroupedPrimary",
36365     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_8",
36366     "runtime_only": false
36367   },
36368   {
36369     "axioms": [
36370       "propext"
36371     ],
36372     "in_project_namespace": true,
36373     "kind": "theorem",
36374     "module": "KomorebiVerification.SingleOperatorGraph",
36375     "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun._simp_1_2",
36376     "runtime_only": false
36377   },
36378   {
36379     "axioms": [
36380       "propext",
36381       "Quot.sound"
36382     ],
36383     "in_project_namespace": false,
36384     "kind": "definition",
36385     "module": "PaperIRelease.TopologySemilinearRank",
36386     "name": "PaperIRelease.TopologySemilinearRank.actingOperator",
36387     "runtime_only": false
36388   },
36389   {
36390     "axioms": [
36391       "propext",
36392       "Classical.choice",
36393       "Quot.sound"
36394     ],
36395     "in_project_namespace": true,
36396     "kind": "theorem",
36397     "module": "PaperICompletion5.GeometricSeedFormula",
36398     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum._simp_1_2",
36399     "runtime_only": false
36400   },
36401   {
36402     "axioms": [
36403       "propext",
36404       "Classical.choice",
36405       "Quot.sound"
36406     ],
36407     "in_project_namespace": true,
36408     "kind": "definition",
36409     "module": "PaperIRelease.GrammarEquivalence",
36410     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedModuleEquivalence",
36411     "runtime_only": false
36412   },
36413   {
36414     "axioms": [
36415       "propext",
36416       "Classical.choice",
36417       "Quot.sound"
36418     ],
36419     "in_project_namespace": true,
36420     "kind": "theorem",
36421     "module": "KomorebiVerification.EllipticAlgorithms",
36422     "name": "Komorebi.EllipticCoordinates.Mx_eq_multiplication",
36423     "runtime_only": false
36424   },
36425   {
36426     "axioms": [
36427       "propext",
36428       "Classical.choice",
36429       "Quot.sound"
36430     ],
36431     "in_project_namespace": true,
36432     "kind": "definition",
36433     "module": "KomorebiVerification.TopologicalCompletion",
36434     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.noConfusionType",
36435     "runtime_only": false
36436   },
36437   {
36438     "axioms": [
36439       "propext",
36440       "Classical.choice",
36441       "Quot.sound"
36442     ],
36443     "in_project_namespace": true,
36444     "kind": "constructor",
36445     "module": "KomorebiVerification.TopologicalCompletion",
36446     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk",
36447     "runtime_only": false
36448   },
36449   {
36450     "axioms": [
36451       "propext"
36452     ],
36453     "in_project_namespace": true,
36454     "kind": "theorem",
36455     "module": "PaperICompletion4.IntrinsicPrimary",
36456     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_1",
36457     "runtime_only": false
36458   },
36459   {
36460     "axioms": [
36461       "propext",
36462       "Classical.choice",
36463       "Quot.sound"
36464     ],
36465     "in_project_namespace": false,
36466     "kind": "definition",
36467     "module": "PaperIRelease.TopologyUnconditionalBridge",
36468     "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets",
36469     "runtime_only": false
36470   },
36471   {
36472     "axioms": [
36473       "propext",
36474       "Classical.choice",
36475       "Quot.sound"
36476     ],
36477     "in_project_namespace": true,
36478     "kind": "definition",
36479     "module": "PaperIRelease.GeneralNormedPackets",
36480     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.ctorIdx",
36481     "runtime_only": false
36482   },
36483   {
36484     "axioms": [],
36485     "in_project_namespace": true,
36486     "kind": "theorem",
36487     "module": "KomorebiVerification.ProjectorCore",
36488     "name": "Komorebi.ClaimRecord.mk.inj",
36489     "runtime_only": false
36490   },
36491   {
36492     "axioms": [
36493       "propext",
36494       "Classical.choice",
36495       "Quot.sound"
36496     ],
36497     "in_project_namespace": true,
36498     "kind": "theorem",
36499     "module": "PaperIRelease.CategoryPackets",
36500     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.operator_natural",
36501     "runtime_only": false
36502   },
36503   {
36504     "axioms": [
36505       "propext",
36506       "Classical.choice",
36507       "Quot.sound"
36508     ],
36509     "in_project_namespace": true,
36510     "kind": "theorem",
36511     "module": "KomorebiVerification.PacketNaturalityCompletion",
36512     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks.eq_1",
36513     "runtime_only": false
36514   },
36515   {
36516     "axioms": [
36517       "propext"
36518     ],
36519     "in_project_namespace": true,
36520     "kind": "definition",
36521     "module": "PaperICompletion4.IntrinsicPrimary",
36522     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule",
36523     "runtime_only": false
36524   },
36525   {
36526     "axioms": [
36527       "propext",
36528       "Classical.choice",
36529       "Quot.sound"
36530     ],
36531     "in_project_namespace": true,
36532     "kind": "definition",
36533     "module": "PaperIRelease.TopologyCategories",
36534     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.casesOn",
36535     "runtime_only": false
36536   },
36537   {
36538     "axioms": [
36539       "propext",
36540       "Classical.choice",
36541       "Quot.sound"
36542     ],
36543     "in_project_namespace": true,
36544     "kind": "theorem",
36545     "module": "PaperICompletion5.LinearPrimaryEigenspace",
36546     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_2",
36547     "runtime_only": false
36548   },
36549   {
36550     "axioms": [
36551       "propext",
36552       "Classical.choice",
36553       "Quot.sound"
36554     ],
36555     "in_project_namespace": false,
36556     "kind": "theorem",
36557     "module": "PaperIRelease.TopologyFiniteCompletion",
36558     "name": "PaperIRelease.TopologyFiniteCompletion.extension_unique",
36559     "runtime_only": false
36560   },
36561   {
36562     "axioms": [
36563       "propext",
36564       "Classical.choice",
36565       "Quot.sound"
36566     ],
36567     "in_project_namespace": true,
36568     "kind": "theorem",
36569     "module": "PaperIRelease.TopologyCategories",
36570     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.injEq",
36571     "runtime_only": false
36572   },
36573   {
36574     "axioms": [
36575       "propext",
36576       "Quot.sound"
36577     ],
36578     "in_project_namespace": false,
36579     "kind": "theorem",
36580     "module": "PaperIRelease.GrammarPaths",
36581     "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1._arg_pusher",
36582     "runtime_only": false
36583   },
36584   {
36585     "axioms": [
36586       "propext",
36587       "Quot.sound"
36588     ],
36589     "in_project_namespace": true,
36590     "kind": "theorem",
36591     "module": "KomorebiVerification.PacketNaturalityCompletion",
36592     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_3",
36593     "runtime_only": false
36594   },
36595   {
36596     "axioms": [
36597       "propext",
36598       "Classical.choice",
36599       "Quot.sound"
36600     ],
36601     "in_project_namespace": true,
36602     "kind": "theorem",
36603     "module": "PaperICompletion7.Nakayama",
36604     "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_surjective",
36605     "runtime_only": false
36606   },
36607   {
36608     "axioms": [],
36609     "in_project_namespace": true,
36610     "kind": "theorem",
36611     "module": "KomorebiVerification.ProjectorCore",
36612     "name": "Komorebi.Packet.coordinateProj.eq_1",
36613     "runtime_only": false
36614   },
36615   {
36616     "axioms": [],
36617     "in_project_namespace": true,
36618     "kind": "definition",
36619     "module": "KomorebiVerification.ProjectorCore",
36620     "name": "Komorebi.ClaimKind.recOn",
36621     "runtime_only": false
36622   },
36623   {
36624     "axioms": [
36625       "propext",
36626       "Classical.choice",
36627       "Quot.sound"
36628     ],
36629     "in_project_namespace": true,
36630     "kind": "theorem",
36631     "module": "KomorebiVerification.SeedRankBasics",
36632     "name": "Komorebi.SeedRankBasics.range_multiSeedMap",
36633     "runtime_only": false
36634   },
36635   {
36636     "axioms": [
36637       "propext",
36638       "Quot.sound"
36639     ],
36640     "in_project_namespace": true,
36641     "kind": "theorem",
36642     "module": "PaperICompletion5.LinearPrimaryEigenspace",
36643     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_7",
36644     "runtime_only": false
36645   },
36646   {
36647     "axioms": [
36648       "propext",
36649       "Classical.choice",
36650       "Quot.sound"
36651     ],
36652     "in_project_namespace": false,
36653     "kind": "definition",
36654     "module": "PaperIRelease.TopologyUnconditional",
36655     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space",
36656     "runtime_only": false
36657   },
36658   {
36659     "axioms": [],
36660     "in_project_namespace": true,
36661     "kind": "constructor",
36662     "module": "KomorebiVerification.ProjectorCore",
36663     "name": "Komorebi.FormalizationStatus.contextOnly",
36664     "runtime_only": false
36665   },
36666   {
36667     "axioms": [
36668       "propext",
36669       "Classical.choice",
36670       "Quot.sound"
36671     ],
36672     "in_project_namespace": false,
36673     "kind": "theorem",
36674     "module": "PaperIRelease.TopologyCountablePackets",
36675     "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis_synthesis",
36676     "runtime_only": false
36677   },
36678   {
36679     "axioms": [
36680       "propext",
36681       "Classical.choice",
36682       "Quot.sound"
36683     ],
36684     "in_project_namespace": true,
36685     "kind": "theorem",
36686     "module": "PaperICompletion4.IntrinsicPrimary",
36687     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_2",
36688     "runtime_only": false
36689   },
36690   {
36691     "axioms": [
36692       "propext",
36693       "Quot.sound"
36694     ],
36695     "in_project_namespace": true,
36696     "kind": "definition",
36697     "module": "PaperIRelease.GrammarAlgebra",
36698     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.equations",
36699     "runtime_only": false
36700   },
36701   {
36702     "axioms": [
36703       "propext",
36704       "Classical.choice",
36705       "Quot.sound"
36706     ],
36707     "in_project_namespace": true,
36708     "kind": "inductive",
36709     "module": "PaperIRelease.GrammarTyped",
36710     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization",
36711     "runtime_only": false
36712   },
36713   {
36714     "axioms": [],
36715     "in_project_namespace": true,
36716     "kind": "definition",
36717     "module": "KomorebiVerification.ProjectorCore",
36718     "name": "Komorebi.FormalizationStatus._sizeOf_1",
36719     "runtime_only": false
36720   },
36721   {
36722     "axioms": [
36723       "propext",
36724       "Classical.choice",
36725       "Quot.sound"
36726     ],
36727     "in_project_namespace": true,
36728     "kind": "definition",
36729     "module": "KomorebiVerification.ProjectorCore",
36730     "name": "Komorebi.Foundation.LinearProjectorFamily.noConfusion",
36731     "runtime_only": false
36732   },
36733   {
36734     "axioms": [
36735       "propext",
36736       "Classical.choice",
36737       "Quot.sound"
36738     ],
36739     "in_project_namespace": true,
36740     "kind": "theorem",
36741     "module": "PaperIRelease.GrammarEquivalence",
36742     "name": "Komorebi.PaperIRelease.GrammarAlgebra.liftActionHom._proof_1",
36743     "runtime_only": false
36744   },
36745   {
36746     "axioms": [
36747       "propext",
36748       "Quot.sound"
36749     ],
36750     "in_project_namespace": true,
36751     "kind": "definition",
36752     "module": "KomorebiVerification.PacketNaturalityCompletion",
36753     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.missingSeed",
36754     "runtime_only": false
36755   },
36756   {
36757     "axioms": [],
36758     "in_project_namespace": true,
36759     "kind": "theorem",
36760     "module": "KomorebiVerification.PathGraphKrylov",
36761     "name": "Komorebi.PathGraphKrylov.rightTerm.eq_1",
36762     "runtime_only": false
36763   },
36764   {
36765     "axioms": [],
36766     "in_project_namespace": true,
36767     "kind": "definition",
36768     "module": "KomorebiVerification.ProjectorCore",
36769     "name": "Komorebi.ClaimKind.definitionClaim.elim",
36770     "runtime_only": false
36771   },
36772   {
36773     "axioms": [
36774       "propext",
36775       "Classical.choice",
36776       "Quot.sound"
36777     ],
36778     "in_project_namespace": true,
36779     "kind": "theorem",
36780     "module": "PaperICompletion4.OperatorIntrinsicFormula",
36781     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_fiber._simp_1_2",
36782     "runtime_only": false
36783   },
36784   {
36785     "axioms": [
36786       "propext",
36787       "Quot.sound"
36788     ],
36789     "in_project_namespace": true,
36790     "kind": "definition",
36791     "module": "PaperIRelease.GrammarModules",
36792     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.recOn",
36793     "runtime_only": false
36794   },
36795   {
36796     "axioms": [
36797       "propext",
36798       "Classical.choice",
36799       "Quot.sound"
36800     ],
36801     "in_project_namespace": true,
36802     "kind": "theorem",
36803     "module": "KomorebiVerification.EllipticAlgorithms",
36804     "name": "Komorebi.EllipticCoordinates.quotient_root_sq",
36805     "runtime_only": false
36806   },
36807   {
36808     "axioms": [
36809       "propext",
36810       "Classical.choice",
36811       "Quot.sound"
36812     ],
36813     "in_project_namespace": true,
36814     "kind": "theorem",
36815     "module": "PaperICompletion8.DivisionRows",
36816     "name": "Komorebi.PaperICompletion8.DivisionRows.exists_leftGenerators_of_le",
36817     "runtime_only": false
36818   },
36819   {
36820     "axioms": [
36821       "propext",
36822       "Quot.sound"
36823     ],
36824     "in_project_namespace": true,
36825     "kind": "definition",
36826     "module": "PaperIRelease.GrammarModules",
36827     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.casesOn",
36828     "runtime_only": false
36829   },
36830   {
36831     "axioms": [
36832       "propext",
36833       "Classical.choice",
36834       "Quot.sound"
36835     ],
36836     "in_project_namespace": false,
36837     "kind": "definition",
36838     "module": "PaperIRelease.TopologySeedRank",
36839     "name": "PaperIRelease.TopologyTransport.topologicalSeedRank",
36840     "runtime_only": false
36841   },
36842   {
36843     "axioms": [
36844       "propext",
36845       "Classical.choice",
36846       "Quot.sound"
36847     ],
36848     "in_project_namespace": true,
36849     "kind": "definition",
36850     "module": "PaperIRelease.CategoryPackets",
36851     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.noConfusion",
36852     "runtime_only": false
36853   },
36854   {
36855     "axioms": [
36856       "propext",
36857       "Classical.choice",
36858       "Quot.sound"
36859     ],
36860     "in_project_namespace": true,
36861     "kind": "theorem",
36862     "module": "PaperICompletion3.PrimarySeedFormula",
36863     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coprime_primePower_ideals",
36864     "runtime_only": false
36865   },
36866   {
36867     "axioms": [],
36868     "in_project_namespace": true,
36869     "kind": "definition",
36870     "module": "PaperIRelease.AlgebraClassGrouping",
36871     "name": "Komorebi.PaperIRelease.packetClass",
36872     "runtime_only": false
36873   },
36874   {
36875     "axioms": [
36876       "propext",
36877       "Classical.choice",
36878       "Quot.sound"
36879     ],
36880     "in_project_namespace": true,
36881     "kind": "theorem",
36882     "module": "PaperICompletion.SpectralCertificates",
36883     "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList_multiplicity_eq_finrank",
36884     "runtime_only": false
36885   },
36886   {
36887     "axioms": [
36888       "propext",
36889       "Classical.choice",
36890       "Quot.sound"
36891     ],
36892     "in_project_namespace": true,
36893     "kind": "theorem",
36894     "module": "PaperIRelease.GrammarAlgebra",
36895     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_arrow",
36896     "runtime_only": false
36897   },
36898   {
36899     "axioms": [
36900       "propext",
36901       "Quot.sound"
36902     ],
36903     "in_project_namespace": true,
36904     "kind": "theorem",
36905     "module": "PaperIRelease.GraphPropagation",
36906     "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_3",
36907     "runtime_only": false
36908   },
36909   {
36910     "axioms": [
36911       "propext",
36912       "Classical.choice",
36913       "Quot.sound"
36914     ],
36915     "in_project_namespace": true,
36916     "kind": "theorem",
36917     "module": "PaperIRelease.AlgebraQuotient",
36918     "name": "Komorebi.PaperIRelease.diagonalClassHom_surjective",
36919     "runtime_only": false
36920   },
36921   {
36922     "axioms": [],
36923     "in_project_namespace": true,
36924     "kind": "constructor",
36925     "module": "KomorebiVerification.ProjectorCore",
36926     "name": "Komorebi.Seed.OperatorExpr.atom",
36927     "runtime_only": false
36928   },
36929   {
36930     "axioms": [
36931       "propext",
36932       "Classical.choice",
36933       "Quot.sound"
36934     ],
36935     "in_project_namespace": true,
36936     "kind": "theorem",
36937     "module": "PaperICompletion4.OperatorIntrinsicFormula",
36938     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_4",
36939     "runtime_only": false
36940   },
36941   {
36942     "axioms": [
36943       "propext",
36944       "Classical.choice",
36945       "Quot.sound"
36946     ],
36947     "in_project_namespace": true,
36948     "kind": "theorem",
36949     "module": "PaperIRelease.PacketCorners",
36950     "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_3",
36951     "runtime_only": false
36952   },
36953   {
36954     "axioms": [
36955       "propext",
36956       "Classical.choice",
36957       "Quot.sound"
36958     ],
36959     "in_project_namespace": true,
36960     "kind": "definition",
36961     "module": "PaperIRelease.TopologyCategories",
36962     "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.noConfusion",
36963     "runtime_only": false
36964   },
36965   {
36966     "axioms": [
36967       "propext",
36968       "Classical.choice",
36969       "Quot.sound"
36970     ],
36971     "in_project_namespace": false,
36972     "kind": "theorem",
36973     "module": "PaperIRelease.TopologySemilinearRank",
36974     "name": "PaperIRelease.TopologySemilinearRank.generates_image",
36975     "runtime_only": false
36976   },
36977   {
36978     "axioms": [],
36979     "in_project_namespace": true,
36980     "kind": "theorem",
36981     "module": "KomorebiVerification.ProjectorCore",
36982     "name": "Komorebi.Seed.OperatorRelation.satisfied_refl",
36983     "runtime_only": false
36984   },
36985   {
36986     "axioms": [
36987       "propext",
36988       "Classical.choice",
36989       "Quot.sound"
36990     ],
36991     "in_project_namespace": true,
36992     "kind": "theorem",
36993     "module": "PaperICompletion8.ProductPresentation",
36994     "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_1",
36995     "runtime_only": false
36996   },
36997   {
36998     "axioms": [
36999       "propext",
37000       "Classical.choice",
37001       "Quot.sound"
37002     ],
37003     "in_project_namespace": true,
37004     "kind": "theorem",
37005     "module": "PaperIRelease.AlgebraPreorder",
37006     "name": "Komorebi.PaperIRelease.strict_word_zero",
37007     "runtime_only": false
37008   },
37009   {
37010     "axioms": [
37011       "propext",
37012       "Classical.choice",
37013       "Quot.sound"
37014     ],
37015     "in_project_namespace": true,
37016     "kind": "theorem",
37017     "module": "KomorebiVerification.TopologicalCompletion",
37018     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv_apply",
37019     "runtime_only": false
37020   },
37021   {
37022     "axioms": [
37023       "propext"
37024     ],
37025     "in_project_namespace": true,
37026     "kind": "definition",
37027     "module": "PaperIRelease.CategoryExport",
37028     "name": "Komorebi.PaperIRelease.CategoryExport.evaluate",
37029     "runtime_only": false
37030   },
37031   {
37032     "axioms": [
37033       "propext",
37034       "Classical.choice",
37035       "Quot.sound"
37036     ],
37037     "in_project_namespace": true,
37038     "kind": "theorem",
37039     "module": "PaperIRelease.GrammarAlgebra",
37040     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex.eq_1",
37041     "runtime_only": false
37042   },
37043   {
37044     "axioms": [
37045       "propext",
37046       "Classical.choice",
37047       "Quot.sound"
37048     ],
37049     "in_project_namespace": false,
37050     "kind": "theorem",
37051     "module": "PaperIRelease.TopologyCountablePackets",
37052     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_3",
37053     "runtime_only": false
37054   },
37055   {
37056     "axioms": [
37057       "propext",
37058       "Quot.sound"
37059     ],
37060     "in_project_namespace": true,
37061     "kind": "theorem",
37062     "module": "PaperIRelease.GraphSourceCount",
37063     "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_3",
37064     "runtime_only": false
37065   },
37066   {
37067     "axioms": [
37068       "propext",
37069       "Classical.choice",
37070       "Quot.sound"
37071     ],
37072     "in_project_namespace": true,
37073     "kind": "theorem",
37074     "module": "KomorebiVerification.PacketNaturalityCompletion",
37075     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA_eU\u2082",
37076     "runtime_only": false
37077   },
37078   {
37079     "axioms": [
37080       "propext",
37081       "Classical.choice",
37082       "Quot.sound"
37083     ],
37084     "in_project_namespace": true,
37085     "kind": "theorem",
37086     "module": "PaperIRelease.PacketCorners",
37087     "name": "Komorebi.PaperIRelease.cornerCompression._proof_6",
37088     "runtime_only": false
37089   },
37090   {
37091     "axioms": [
37092       "propext",
37093       "Classical.choice",
37094       "Quot.sound"
37095     ],
37096     "in_project_namespace": true,
37097     "kind": "theorem",
37098     "module": "PaperIRelease.PacketDescent",
37099     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_range",
37100     "runtime_only": false
37101   },
37102   {
37103     "axioms": [
37104       "propext",
37105       "Classical.choice",
37106       "Quot.sound"
37107     ],
37108     "in_project_namespace": true,
37109     "kind": "theorem",
37110     "module": "PaperIRelease.PacketDescent",
37111     "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_proj_mkQ",
37112     "runtime_only": false
37113   },
37114   {
37115     "axioms": [
37116       "propext",
37117       "Quot.sound"
37118     ],
37119     "in_project_namespace": true,
37120     "kind": "definition",
37121     "module": "PaperIRelease.GrammarModules",
37122     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.noConfusion",
37123     "runtime_only": false
37124   },
37125   {
37126     "axioms": [
37127       "propext",
37128       "Classical.choice",
37129       "Quot.sound"
37130     ],
37131     "in_project_namespace": true,
37132     "kind": "theorem",
37133     "module": "KomorebiVerification.EllipticAlgorithms",
37134     "name": "Komorebi.FiniteAlgorithms.graphSpectrum.eq_1",
37135     "runtime_only": false
37136   },
37137   {
37138     "axioms": [
37139       "propext",
37140       "Classical.choice",
37141       "Quot.sound"
37142     ],
37143     "in_project_namespace": true,
37144     "kind": "definition",
37145     "module": "PaperIRelease.AlgebraPreorder",
37146     "name": "Komorebi.PaperIRelease.preorderSupportAlgebra",
37147     "runtime_only": false
37148   },
37149   {
37150     "axioms": [
37151       "propext",
37152       "Quot.sound"
37153     ],
37154     "in_project_namespace": true,
37155     "kind": "theorem",
37156     "module": "PaperIRelease.PacketLocalRank",
37157     "name": "Komorebi.PaperIRelease.localPacketFamily._proof_1",
37158     "runtime_only": false
37159   },
37160   {
37161     "axioms": [
37162       "propext",
37163       "Classical.choice",
37164       "Quot.sound"
37165     ],
37166     "in_project_namespace": true,
37167     "kind": "theorem",
37168     "module": "PaperICompletion6.ScalarExtension",
37169     "name": "Komorebi.PaperICompletion6.ScalarExtension.hasCyclicVector_iff_extended_spectral_multiplicities_one",
37170     "runtime_only": false
37171   },
37172   {
37173     "axioms": [
37174       "propext",
37175       "Classical.choice",
37176       "Quot.sound"
37177     ],
37178     "in_project_namespace": true,
37179     "kind": "theorem",
37180     "module": "PaperIRelease.AlgebraQuotient",
37181     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_7",
37182     "runtime_only": false
37183   },
37184   {
37185     "axioms": [
37186       "propext",
37187       "Quot.sound"
37188     ],
37189     "in_project_namespace": true,
37190     "kind": "theorem",
37191     "module": "PaperIRelease.GrammarAlgebra",
37192     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_1",
37193     "runtime_only": false
37194   },
37195   {
37196     "axioms": [
37197       "propext",
37198       "Classical.choice",
37199       "Quot.sound"
37200     ],
37201     "in_project_namespace": false,
37202     "kind": "definition",
37203     "module": "PaperIRelease.TopologyCountablePackets",
37204     "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_8",
37205     "runtime_only": false
37206   },
37207   {
37208     "axioms": [
37209       "propext",
37210       "Classical.choice",
37211       "Quot.sound"
37212     ],
37213     "in_project_namespace": true,
37214     "kind": "definition",
37215     "module": "PaperIRelease.GrammarEquivalence",
37216     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.noConfusion",
37217     "runtime_only": false
37218   },
37219   {
37220     "axioms": [
37221       "propext",
37222       "Classical.choice",
37223       "Quot.sound"
37224     ],
37225     "in_project_namespace": true,
37226     "kind": "inductive",
37227     "module": "KomorebiVerification.ProjectorCore",
37228     "name": "Komorebi.Foundation.LinearProjectorFamily",
37229     "runtime_only": false
37230   },
37231   {
37232     "axioms": [
37233       "propext",
37234       "Classical.choice",
37235       "Quot.sound"
37236     ],
37237     "in_project_namespace": true,
37238     "kind": "theorem",
37239     "module": "PaperIRelease.PacketBoundaryTests",
37240     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.all_preserve_bot",
37241     "runtime_only": false
37242   },
37243   {
37244     "axioms": [
37245       "propext",
37246       "Classical.choice",
37247       "Quot.sound"
37248     ],
37249     "in_project_namespace": true,
37250     "kind": "theorem",
37251     "module": "PaperIRelease.PacketDescent",
37252     "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_1",
37253     "runtime_only": false
37254   },
37255   {
37256     "axioms": [
37257       "propext"
37258     ],
37259     "in_project_namespace": true,
37260     "kind": "theorem",
37261     "module": "KomorebiVerification.SingleOperatorGraph",
37262     "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_4",
37263     "runtime_only": false
37264   },
37265   {
37266     "axioms": [
37267       "propext",
37268       "Classical.choice",
37269       "Quot.sound"
37270     ],
37271     "in_project_namespace": true,
37272     "kind": "theorem",
37273     "module": "KomorebiVerification.EllipticAlgorithms",
37274     "name": "Komorebi.EllipticCoordinates.P1_P0_orthogonal",
37275     "runtime_only": false
37276   },
37277   {
37278     "axioms": [
37279       "propext",
37280       "Classical.choice",
37281       "Quot.sound"
37282     ],
37283     "in_project_namespace": true,
37284     "kind": "theorem",
37285     "module": "PaperIRelease.GrammarIdeal",
37286     "name": "Komorebi.PaperIRelease.GrammarAlgebra.presentedToIdeal_quotient",
37287     "runtime_only": false
37288   },
37289   {
37290     "axioms": [
37291       "propext",
37292       "Classical.choice",
37293       "Quot.sound"
37294     ],
37295     "in_project_namespace": false,
37296     "kind": "theorem",
37297     "module": "PaperIRelease.TopologyDenseCompletion",
37298     "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_1",
37299     "runtime_only": false
37300   },
37301   {
37302     "axioms": [
37303       "propext",
37304       "Classical.choice",
37305       "Quot.sound"
37306     ],
37307     "in_project_namespace": false,
37308     "kind": "theorem",
37309     "module": "PaperIRelease.TopologyCountablePackets",
37310     "name": "PaperIRelease.TopologyCountablePackets.Projectors.signed_sum_le",
37311     "runtime_only": false
37312   },
37313   {
37314     "axioms": [
37315       "propext",
37316       "Classical.choice",
37317       "Quot.sound"
37318     ],
37319     "in_project_namespace": true,
37320     "kind": "theorem",
37321     "module": "PaperIRelease.PolynomialMonic",
37322     "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec._proof_1",
37323     "runtime_only": false
37324   },
37325   {
37326     "axioms": [
37327       "propext",
37328       "Quot.sound"
37329     ],
37330     "in_project_namespace": true,
37331     "kind": "definition",
37332     "module": "KomorebiVerification.PacketNaturalityCompletion",
37333     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet",
37334     "runtime_only": false
37335   },
37336   {
37337     "axioms": [
37338       "propext",
37339       "Classical.choice",
37340       "Quot.sound"
37341     ],
37342     "in_project_namespace": true,
37343     "kind": "theorem",
37344     "module": "PaperIRelease.PacketTopologyGeneral",
37345     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_3",
37346     "runtime_only": false
37347   },
37348   {
37349     "axioms": [
37350       "propext",
37351       "Classical.choice",
37352       "Quot.sound"
37353     ],
37354     "in_project_namespace": true,
37355     "kind": "recursor",
37356     "module": "PaperIRelease.GrammarAlgebra",
37357     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.rec",
37358     "runtime_only": false
37359   },
37360   {
37361     "axioms": [
37362       "propext",
37363       "Quot.sound"
37364     ],
37365     "in_project_namespace": true,
37366     "kind": "definition",
37367     "module": "KomorebiVerification.PathGraphKrylov",
37368     "name": "Komorebi.PathGraphKrylov.krylov._unsafe_rec",
37369     "runtime_only": true
37370   },
37371   {
37372     "axioms": [
37373       "propext",
37374       "Quot.sound"
37375     ],
37376     "in_project_namespace": true,
37377     "kind": "theorem",
37378     "module": "KomorebiVerification.ProjectorCore",
37379     "name": "Komorebi.Packet.fibreProj_idempotent",
37380     "runtime_only": false
37381   },
37382   {
37383     "axioms": [
37384       "propext",
37385       "Classical.choice",
37386       "Quot.sound"
37387     ],
37388     "in_project_namespace": false,
37389     "kind": "theorem",
37390     "module": "PaperIRelease.TopologyUnconditional",
37391     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_22",
37392     "runtime_only": false
37393   },
37394   {
37395     "axioms": [
37396       "propext",
37397       "Classical.choice",
37398       "Quot.sound"
37399     ],
37400     "in_project_namespace": true,
37401     "kind": "theorem",
37402     "module": "PaperIRelease.AlgebraClassGrouping",
37403     "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_4",
37404     "runtime_only": false
37405   },
37406   {
37407     "axioms": [
37408       "propext",
37409       "Classical.choice",
37410       "Quot.sound"
37411     ],
37412     "in_project_namespace": true,
37413     "kind": "theorem",
37414     "module": "KomorebiVerification.PacketNaturalityCompletion",
37415     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA.eq_1",
37416     "runtime_only": false
37417   },
37418   {
37419     "axioms": [],
37420     "in_project_namespace": false,
37421     "kind": "definition",
37422     "module": "PaperIRelease.CategoryExport",
37423     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.splitter",
37424     "runtime_only": false
37425   },
37426   {
37427     "axioms": [],
37428     "in_project_namespace": true,
37429     "kind": "definition",
37430     "module": "KomorebiVerification.ProjectorCore",
37431     "name": "Komorebi.FiniteDifference.iteratedDiff._unsafe_rec",
37432     "runtime_only": true
37433   },
37434   {
37435     "axioms": [],
37436     "in_project_namespace": true,
37437     "kind": "definition",
37438     "module": "KomorebiVerification.ProjectorCore",
37439     "name": "Komorebi.FormalizationStatus.externalInput.elim",
37440     "runtime_only": false
37441   },
37442   {
37443     "axioms": [
37444       "propext",
37445       "Classical.choice",
37446       "Quot.sound"
37447     ],
37448     "in_project_namespace": true,
37449     "kind": "theorem",
37450     "module": "KomorebiVerification.PacketNaturalityCompletion",
37451     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA.eq_1",
37452     "runtime_only": false
37453   },
37454   {
37455     "axioms": [
37456       "propext",
37457       "Classical.choice",
37458       "Quot.sound"
37459     ],
37460     "in_project_namespace": true,
37461     "kind": "definition",
37462     "module": "PaperIRelease.PacketTopologyGeneral",
37463     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM",
37464     "runtime_only": false
37465   },
37466   {
37467     "axioms": [
37468       "propext",
37469       "Classical.choice",
37470       "Quot.sound"
37471     ],
37472     "in_project_namespace": true,
37473     "kind": "theorem",
37474     "module": "PaperICompletion.SpectralCertificates",
37475     "name": "Komorebi.PaperICompletion.SpectralCertificates.hermitian_matrix_seedNumber_isLeast",
37476     "runtime_only": false
37477   },
37478   {
37479     "axioms": [
37480       "propext",
37481       "Classical.choice",
37482       "Quot.sound"
37483     ],
37484     "in_project_namespace": true,
37485     "kind": "theorem",
37486     "module": "PaperIRelease.AlgebraClassGrouping",
37487     "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_4",
37488     "runtime_only": false
37489   },
37490   {
37491     "axioms": [
37492       "propext",
37493       "Classical.choice",
37494       "Quot.sound"
37495     ],
37496     "in_project_namespace": true,
37497     "kind": "theorem",
37498     "module": "PaperICompletion8.SemisimpleFormula",
37499     "name": "Komorebi.PaperICompletion8.SemisimpleFormula.split_radicalTop_seedRank",
37500     "runtime_only": false
37501   },
37502   {
37503     "axioms": [
37504       "propext",
37505       "Classical.choice",
37506       "Quot.sound"
37507     ],
37508     "in_project_namespace": true,
37509     "kind": "definition",
37510     "module": "PaperICompletion.SpectralCertificates",
37511     "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenFibreEquiv",
37512     "runtime_only": false
37513   },
37514   {
37515     "axioms": [],
37516     "in_project_namespace": true,
37517     "kind": "definition",
37518     "module": "KomorebiVerification.ProjectorCore",
37519     "name": "Komorebi.instReprFormalizationStatus.repr",
37520     "runtime_only": false
37521   },
37522   {
37523     "axioms": [
37524       "propext",
37525       "Quot.sound"
37526     ],
37527     "in_project_namespace": true,
37528     "kind": "theorem",
37529     "module": "PaperIRelease.GrammarAlgebra",
37530     "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.sizeOf_spec",
37531     "runtime_only": false
37532   },
37533   {
37534     "axioms": [
37535       "propext",
37536       "Quot.sound"
37537     ],
37538     "in_project_namespace": true,
37539     "kind": "theorem",
37540     "module": "KomorebiVerification.SeedRankOperations",
37541     "name": "Komorebi.SeedRankOperations.prodSndSemilinear._proof_1",
37542     "runtime_only": false
37543   },
37544   {
37545     "axioms": [
37546       "propext",
37547       "Classical.choice",
37548       "Quot.sound"
37549     ],
37550     "in_project_namespace": true,
37551     "kind": "theorem",
37552     "module": "KomorebiVerification.SingleOperatorGraph",
37553     "name": "Komorebi.SingleOperatorGraph.basis_generates_under_operator",
37554     "runtime_only": false
37555   },
37556   {
37557     "axioms": [],
37558     "in_project_namespace": true,
37559     "kind": "definition",
37560     "module": "KomorebiVerification.ProjectorCore",
37561     "name": "Komorebi.ClaimKind.noConfusion",
37562     "runtime_only": false
37563   },
37564   {
37565     "axioms": [
37566       "propext",
37567       "Classical.choice",
37568       "Quot.sound"
37569     ],
37570     "in_project_namespace": true,
37571     "kind": "theorem",
37572     "module": "PaperIRelease.BoundedStar",
37573     "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_2",
37574     "runtime_only": false
37575   },
37576   {
37577     "axioms": [
37578       "propext",
37579       "Classical.choice",
37580       "Quot.sound"
37581     ],
37582     "in_project_namespace": true,
37583     "kind": "theorem",
37584     "module": "PaperICompletion7.ModuleTop",
37585     "name": "Komorebi.PaperICompletion7.ModuleTop.generates_iff_radicalTop",
37586     "runtime_only": false
37587   },
37588   {
37589     "axioms": [
37590       "propext",
37591       "Quot.sound"
37592     ],
37593     "in_project_namespace": true,
37594     "kind": "theorem",
37595     "module": "KomorebiVerification.SeedRankOperations",
37596     "name": "Komorebi.SeedRankOperations.tensorRightTowerInstalled",
37597     "runtime_only": false
37598   },
37599   {
37600     "axioms": [
37601       "propext",
37602       "Classical.choice",
37603       "Quot.sound"
37604     ],
37605     "in_project_namespace": true,
37606     "kind": "definition",
37607     "module": "PaperICompletion4.OperatorIntrinsicFormula",
37608     "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv",
37609     "runtime_only": false
37610   },
37611   {
37612     "axioms": [
37613       "propext",
37614       "Classical.choice",
37615       "Quot.sound"
37616     ],
37617     "in_project_namespace": false,
37618     "kind": "theorem",
37619     "module": "PaperIRelease.AlgebraPreorder",
37620     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_height",
37621     "runtime_only": false
37622   },
37623   {
37624     "axioms": [
37625       "propext",
37626       "Classical.choice",
37627       "Quot.sound"
37628     ],
37629     "in_project_namespace": true,
37630     "kind": "theorem",
37631     "module": "PaperICompletion.SpectralCertificates",
37632     "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList.congr_simp",
37633     "runtime_only": false
37634   },
37635   {
37636     "axioms": [
37637       "propext",
37638       "Quot.sound"
37639     ],
37640     "in_project_namespace": true,
37641     "kind": "theorem",
37642     "module": "KomorebiVerification.SeedRankBasics",
37643     "name": "Komorebi.SeedRankBasics.cyclic_iff_top_isPrincipal",
37644     "runtime_only": false
37645   },
37646   {
37647     "axioms": [
37648       "propext",
37649       "Classical.choice",
37650       "Quot.sound"
37651     ],
37652     "in_project_namespace": true,
37653     "kind": "theorem",
37654     "module": "PaperIRelease.CoordinateTransport",
37655     "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_5",
37656     "runtime_only": false
37657   },
37658   {
37659     "axioms": [
37660       "propext",
37661       "Classical.choice",
37662       "Quot.sound"
37663     ],
37664     "in_project_namespace": true,
37665     "kind": "definition",
37666     "module": "KomorebiVerification.EllipticAlgorithms",
37667     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates",
37668     "runtime_only": false
37669   },
37670   {
37671     "axioms": [
37672       "propext",
37673       "Classical.choice",
37674       "Quot.sound"
37675     ],
37676     "in_project_namespace": true,
37677     "kind": "definition",
37678     "module": "PaperIRelease.TopologyCategories",
37679     "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory",
37680     "runtime_only": false
37681   },
37682   {
37683     "axioms": [
37684       "propext",
37685       "Classical.choice",
37686       "Quot.sound"
37687     ],
37688     "in_project_namespace": true,
37689     "kind": "theorem",
37690     "module": "PaperIRelease.GrammarEquivalence",
37691     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_3",
37692     "runtime_only": false
37693   },
37694   {
37695     "axioms": [
37696       "propext",
37697       "Classical.choice",
37698       "Quot.sound"
37699     ],
37700     "in_project_namespace": true,
37701     "kind": "theorem",
37702     "module": "PaperIRelease.PacketExactSequence",
37703     "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient._proof_1",
37704     "runtime_only": false
37705   },
37706   {
37707     "axioms": [
37708       "propext",
37709       "Classical.choice",
37710       "Quot.sound"
37711     ],
37712     "in_project_namespace": true,
37713     "kind": "theorem",
37714     "module": "PaperIRelease.PacketAggregation",
37715     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_5",
37716     "runtime_only": false
37717   },
37718   {
37719     "axioms": [
37720       "propext",
37721       "Classical.choice",
37722       "Quot.sound"
37723     ],
37724     "in_project_namespace": true,
37725     "kind": "theorem",
37726     "module": "PaperICompletion.ConditionedCoordinates",
37727     "name": "Komorebi.PaperICompletion.ConditionedCoordinates.norm_le_conditionNumber_mul_coordinateOperator",
37728     "runtime_only": false
37729   },
37730   {
37731     "axioms": [],
37732     "in_project_namespace": true,
37733     "kind": "definition",
37734     "module": "KomorebiVerification.ProjectorCore",
37735     "name": "Komorebi.Seed.OperatorRelation.recOn",
37736     "runtime_only": false
37737   },
37738   {
37739     "axioms": [
37740       "propext",
37741       "Classical.choice",
37742       "Quot.sound"
37743     ],
37744     "in_project_namespace": true,
37745     "kind": "theorem",
37746     "module": "PaperIRelease.PacketTopologyGeneral",
37747     "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM._proof_2",
37748     "runtime_only": false
37749   },
37750   {
37751     "axioms": [
37752       "propext",
37753       "Classical.choice",
37754       "Quot.sound"
37755     ],
37756     "in_project_namespace": true,
37757     "kind": "theorem",
37758     "module": "KomorebiVerification.SemisimpleCompletion",
37759     "name": "Komorebi.SemisimpleCompletion.exists_splitProduct_generators_iff_maxCeilDiv_le",
37760     "runtime_only": false
37761   },
37762   {
37763     "axioms": [
37764       "propext",
37765       "Classical.choice",
37766       "Quot.sound"
37767     ],
37768     "in_project_namespace": true,
37769     "kind": "theorem",
37770     "module": "PaperIRelease.GrammarEquivalence",
37771     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_6",
37772     "runtime_only": false
37773   },
37774   {
37775     "axioms": [
37776       "propext",
37777       "Classical.choice",
37778       "Quot.sound"
37779     ],
37780     "in_project_namespace": true,
37781     "kind": "theorem",
37782     "module": "KomorebiVerification.PacketNaturalityCompletion",
37783     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR.eq_1",
37784     "runtime_only": false
37785   },
37786   {
37787     "axioms": [],
37788     "in_project_namespace": true,
37789     "kind": "recursor",
37790     "module": "PaperIRelease.CategoryExport",
37791     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.rec",
37792     "runtime_only": false
37793   },
37794   {
37795     "axioms": [
37796       "propext",
37797       "Classical.choice",
37798       "Quot.sound"
37799     ],
37800     "in_project_namespace": true,
37801     "kind": "theorem",
37802     "module": "PaperIRelease.GrammarEquivalence",
37803     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_10",
37804     "runtime_only": false
37805   },
37806   {
37807     "axioms": [
37808       "propext",
37809       "Classical.choice",
37810       "Quot.sound"
37811     ],
37812     "in_project_namespace": true,
37813     "kind": "definition",
37814     "module": "PaperIRelease.CategoryPackets",
37815     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk._flat_ctor",
37816     "runtime_only": false
37817   },
37818   {
37819     "axioms": [],
37820     "in_project_namespace": true,
37821     "kind": "theorem",
37822     "module": "KomorebiVerification.KernelAudit",
37823     "name": "Komorebi.Verification.fineAddress.eq_1",
37824     "runtime_only": false
37825   },
37826   {
37827     "axioms": [
37828       "propext",
37829       "Quot.sound"
37830     ],
37831     "in_project_namespace": true,
37832     "kind": "definition",
37833     "module": "PaperIRelease.ScalarExtension",
37834     "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease_1",
37835     "runtime_only": false
37836   },
37837   {
37838     "axioms": [],
37839     "in_project_namespace": true,
37840     "kind": "definition",
37841     "module": "KomorebiVerification.ProjectorCore",
37842     "name": "Komorebi.instBEqClaimKind.beq",
37843     "runtime_only": false
37844   },
37845   {
37846     "axioms": [
37847       "propext",
37848       "Classical.choice",
37849       "Quot.sound"
37850     ],
37851     "in_project_namespace": true,
37852     "kind": "definition",
37853     "module": "PaperIRelease.CategoryBoundaries",
37854     "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets",
37855     "runtime_only": false
37856   },
37857   {
37858     "axioms": [
37859       "propext",
37860       "Classical.choice",
37861       "Quot.sound"
37862     ],
37863     "in_project_namespace": false,
37864     "kind": "theorem",
37865     "module": "PaperIRelease.TopologyUnconditional",
37866     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_2",
37867     "runtime_only": false
37868   },
37869   {
37870     "axioms": [
37871       "propext",
37872       "Classical.choice",
37873       "Quot.sound"
37874     ],
37875     "in_project_namespace": true,
37876     "kind": "theorem",
37877     "module": "PaperICompletion3.OperatorPrimaryAPI",
37878     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.sizeOf_spec",
37879     "runtime_only": false
37880   },
37881   {
37882     "axioms": [
37883       "propext",
37884       "Classical.choice",
37885       "Quot.sound"
37886     ],
37887     "in_project_namespace": false,
37888     "kind": "theorem",
37889     "module": "PaperIRelease.TopologyFiniteCompletion",
37890     "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_5",
37891     "runtime_only": false
37892   },
37893   {
37894     "axioms": [
37895       "propext",
37896       "Classical.choice",
37897       "Quot.sound"
37898     ],
37899     "in_project_namespace": true,
37900     "kind": "theorem",
37901     "module": "PaperIRelease.GrammarAlgebra",
37902     "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_4",
37903     "runtime_only": false
37904   },
37905   {
37906     "axioms": [
37907       "propext",
37908       "Classical.choice",
37909       "Quot.sound"
37910     ],
37911     "in_project_namespace": true,
37912     "kind": "definition",
37913     "module": "PaperIRelease.GrammarPaths",
37914     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedPathRelationModuleEquivalence",
37915     "runtime_only": false
37916   },
37917   {
37918     "axioms": [
37919       "propext",
37920       "Classical.choice",
37921       "Quot.sound"
37922     ],
37923     "in_project_namespace": true,
37924     "kind": "theorem",
37925     "module": "PaperIRelease.CategoryPackets",
37926     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.sizeOf_spec",
37927     "runtime_only": false
37928   },
37929   {
37930     "axioms": [
37931       "propext",
37932       "Classical.choice",
37933       "Quot.sound"
37934     ],
37935     "in_project_namespace": false,
37936     "kind": "theorem",
37937     "module": "PaperIRelease.TopologyCountablePackets",
37938     "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.inj",
37939     "runtime_only": false
37940   },
37941   {
37942     "axioms": [
37943       "propext",
37944       "Classical.choice",
37945       "Quot.sound"
37946     ],
37947     "in_project_namespace": true,
37948     "kind": "theorem",
37949     "module": "PaperIRelease.BoundedStar",
37950     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_1",
37951     "runtime_only": false
37952   },
37953   {
37954     "axioms": [
37955       "propext",
37956       "Classical.choice",
37957       "Quot.sound"
37958     ],
37959     "in_project_namespace": true,
37960     "kind": "theorem",
37961     "module": "PaperIRelease.TensorPackets",
37962     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_6",
37963     "runtime_only": false
37964   },
37965   {
37966     "axioms": [
37967       "propext",
37968       "Classical.choice",
37969       "Quot.sound"
37970     ],
37971     "in_project_namespace": true,
37972     "kind": "definition",
37973     "module": "PaperIRelease.CategoryPackets",
37974     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.index",
37975     "runtime_only": false
37976   },
37977   {
37978     "axioms": [
37979       "propext",
37980       "Quot.sound"
37981     ],
37982     "in_project_namespace": true,
37983     "kind": "theorem",
37984     "module": "PaperICompletion5.LinearPrimaryEigenspace",
37985     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_2",
37986     "runtime_only": false
37987   },
37988   {
37989     "axioms": [
37990       "propext",
37991       "Classical.choice",
37992       "Quot.sound"
37993     ],
37994     "in_project_namespace": true,
37995     "kind": "theorem",
37996     "module": "KomorebiVerification.TopologicalCompletion",
37997     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.map_operatorHull_le",
37998     "runtime_only": false
37999   },
38000   {
38001     "axioms": [
38002       "propext",
38003       "Classical.choice",
38004       "Quot.sound"
38005     ],
38006     "in_project_namespace": true,
38007     "kind": "theorem",
38008     "module": "PaperIRelease.CategoryPackets",
38009     "name": "Komorebi.PaperIRelease.CategoryPackets.hull_eq_span",
38010     "runtime_only": false
38011   },
38012   {
38013     "axioms": [
38014       "propext",
38015       "Classical.choice",
38016       "Quot.sound"
38017     ],
38018     "in_project_namespace": true,
38019     "kind": "theorem",
38020     "module": "PaperICompletion8.RegularMultiplicity",
38021     "name": "Komorebi.PaperICompletion8.RegularMultiplicity.naturalCopies_seedRank",
38022     "runtime_only": false
38023   },
38024   {
38025     "axioms": [
38026       "propext",
38027       "Classical.choice",
38028       "Quot.sound"
38029     ],
38030     "in_project_namespace": true,
38031     "kind": "theorem",
38032     "module": "PaperIRelease.GeneralNormedPackets",
38033     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.inj",
38034     "runtime_only": false
38035   },
38036   {
38037     "axioms": [],
38038     "in_project_namespace": true,
38039     "kind": "definition",
38040     "module": "KomorebiVerification.ProjectorCore",
38041     "name": "Komorebi.instReprFormalizationStatus.repr.match_1",
38042     "runtime_only": false
38043   },
38044   {
38045     "axioms": [
38046       "propext",
38047       "Classical.choice",
38048       "Quot.sound"
38049     ],
38050     "in_project_namespace": true,
38051     "kind": "theorem",
38052     "module": "PaperICompletion6.ScalarExtension",
38053     "name": "Komorebi.PaperICompletion6.ScalarExtension.linearIndependent_baseChange",
38054     "runtime_only": false
38055   },
38056   {
38057     "axioms": [
38058       "propext",
38059       "Classical.choice",
38060       "Quot.sound"
38061     ],
38062     "in_project_namespace": true,
38063     "kind": "definition",
38064     "module": "PaperIRelease.AlgebraSupport",
38065     "name": "Komorebi.PaperIRelease.OperatorSupported",
38066     "runtime_only": false
38067   },
38068   {
38069     "axioms": [],
38070     "in_project_namespace": true,
38071     "kind": "constructor",
38072     "module": "KomorebiVerification.ProjectorCore",
38073     "name": "Komorebi.ClaimKind.definitionClaim",
38074     "runtime_only": false
38075   },
38076   {
38077     "axioms": [],
38078     "in_project_namespace": true,
38079     "kind": "constructor",
38080     "module": "KomorebiVerification.ProjectorCore",
38081     "name": "Komorebi.FormalizationStatus.blockedByLibrary",
38082     "runtime_only": false
38083   },
38084   {
38085     "axioms": [
38086       "propext",
38087       "Classical.choice",
38088       "Quot.sound"
38089     ],
38090     "in_project_namespace": true,
38091     "kind": "theorem",
38092     "module": "KomorebiVerification.TopologicalCompletion",
38093     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense.congr_simp",
38094     "runtime_only": false
38095   },
38096   {
38097     "axioms": [
38098       "propext",
38099       "Classical.choice",
38100       "Quot.sound"
38101     ],
38102     "in_project_namespace": true,
38103     "kind": "theorem",
38104     "module": "KomorebiVerification.TopologicalCompletion",
38105     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv._proof_1",
38106     "runtime_only": false
38107   },
38108   {
38109     "axioms": [
38110       "propext",
38111       "Classical.choice",
38112       "Quot.sound"
38113     ],
38114     "in_project_namespace": true,
38115     "kind": "definition",
38116     "module": "PaperIRelease.GeneralNormedPackets",
38117     "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.casesOn",
38118     "runtime_only": false
38119   },
38120   {
38121     "axioms": [
38122       "propext"
38123     ],
38124     "in_project_namespace": true,
38125     "kind": "theorem",
38126     "module": "KomorebiVerification.SingleOperatorGraph",
38127     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_5",
38128     "runtime_only": false
38129   },
38130   {
38131     "axioms": [
38132       "propext",
38133       "Classical.choice",
38134       "Quot.sound"
38135     ],
38136     "in_project_namespace": true,
38137     "kind": "theorem",
38138     "module": "KomorebiVerification.SeedRankBasics",
38139     "name": "Komorebi.SeedRankBasics.seedRank_linearEquiv",
38140     "runtime_only": false
38141   },
38142   {
38143     "axioms": [
38144       "propext",
38145       "Classical.choice",
38146       "Quot.sound"
38147     ],
38148     "in_project_namespace": true,
38149     "kind": "definition",
38150     "module": "PaperICompletion5.GeometricSeedFormula",
38151     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues",
38152     "runtime_only": false
38153   },
38154   {
38155     "axioms": [
38156       "propext",
38157       "Classical.choice",
38158       "Quot.sound"
38159     ],
38160     "in_project_namespace": true,
38161     "kind": "theorem",
38162     "module": "PaperICompletion3.OperatorPrimaryAPI",
38163     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryPresentation_nonempty",
38164     "runtime_only": false
38165   },
38166   {
38167     "axioms": [
38168       "propext",
38169       "Classical.choice",
38170       "Quot.sound"
38171     ],
38172     "in_project_namespace": false,
38173     "kind": "theorem",
38174     "module": "PaperIRelease.TopologyTransport",
38175     "name": "PaperIRelease.TopologyTransport.dense_operatorHull_image",
38176     "runtime_only": false
38177   },
38178   {
38179     "axioms": [
38180       "propext",
38181       "Classical.choice",
38182       "Quot.sound"
38183     ],
38184     "in_project_namespace": false,
38185     "kind": "theorem",
38186     "module": "PaperIRelease.TopologyUnconditional",
38187     "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceCompleteSpace",
38188     "runtime_only": false
38189   },
38190   {
38191     "axioms": [
38192       "propext",
38193       "Classical.choice",
38194       "Quot.sound"
38195     ],
38196     "in_project_namespace": true,
38197     "kind": "theorem",
38198     "module": "PaperICompletion5.LinearPrimaryEigenspace",
38199     "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.finrank_cokernel_eq_finrank_kernel",
38200     "runtime_only": false
38201   },
38202   {
38203     "axioms": [
38204       "propext",
38205       "Classical.choice",
38206       "Quot.sound"
38207     ],
38208     "in_project_namespace": true,
38209     "kind": "theorem",
38210     "module": "PaperIRelease.PacketDescent",
38211     "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_7",
38212     "runtime_only": false
38213   },
38214   {
38215     "axioms": [
38216       "propext",
38217       "Classical.choice",
38218       "Quot.sound"
38219     ],
38220     "in_project_namespace": true,
38221     "kind": "theorem",
38222     "module": "PaperICompletion.SpectralCertificates",
38223     "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedRank_eq_max_eigenspace_finrank",
38224     "runtime_only": false
38225   },
38226   {
38227     "axioms": [
38228       "propext",
38229       "Classical.choice",
38230       "Quot.sound"
38231     ],
38232     "in_project_namespace": true,
38233     "kind": "definition",
38234     "module": "KomorebiVerification.TopologicalCompletion",
38235     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power",
38236     "runtime_only": false
38237   },
38238   {
38239     "axioms": [
38240       "propext",
38241       "Classical.choice",
38242       "Quot.sound"
38243     ],
38244     "in_project_namespace": false,
38245     "kind": "theorem",
38246     "module": "PaperIRelease.TopologyDenseCompletion",
38247     "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_3",
38248     "runtime_only": false
38249   },
38250   {
38251     "axioms": [
38252       "propext",
38253       "Classical.choice",
38254       "Quot.sound"
38255     ],
38256     "in_project_namespace": true,
38257     "kind": "theorem",
38258     "module": "KomorebiVerification.EllipticAlgorithms",
38259     "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_le_orbitHull",
38260     "runtime_only": false
38261   },
38262   {
38263     "axioms": [
38264       "propext",
38265       "Classical.choice",
38266       "Quot.sound"
38267     ],
38268     "in_project_namespace": true,
38269     "kind": "theorem",
38270     "module": "PaperIRelease.PacketDescent",
38271     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_5",
38272     "runtime_only": false
38273   },
38274   {
38275     "axioms": [
38276       "propext",
38277       "Classical.choice",
38278       "Quot.sound"
38279     ],
38280     "in_project_namespace": true,
38281     "kind": "definition",
38282     "module": "PaperIRelease.CategoryPackets",
38283     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.carrier",
38284     "runtime_only": false
38285   },
38286   {
38287     "axioms": [
38288       "propext",
38289       "Classical.choice",
38290       "Quot.sound"
38291     ],
38292     "in_project_namespace": true,
38293     "kind": "theorem",
38294     "module": "PaperICompletion.SpectralCertificates",
38295     "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis.eq_1",
38296     "runtime_only": false
38297   },
38298   {
38299     "axioms": [
38300       "propext",
38301       "Quot.sound"
38302     ],
38303     "in_project_namespace": true,
38304     "kind": "theorem",
38305     "module": "KomorebiVerification.EllipticAlgorithms",
38306     "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_1",
38307     "runtime_only": false
38308   },
38309   {
38310     "axioms": [
38311       "propext",
38312       "Classical.choice",
38313       "Quot.sound"
38314     ],
38315     "in_project_namespace": true,
38316     "kind": "definition",
38317     "module": "PaperIRelease.TopologyCategories",
38318     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.seeds",
38319     "runtime_only": false
38320   },
38321   {
38322     "axioms": [
38323       "propext",
38324       "Quot.sound"
38325     ],
38326     "in_project_namespace": true,
38327     "kind": "theorem",
38328     "module": "PaperIRelease.AlgebraPreorder",
38329     "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_1",
38330     "runtime_only": false
38331   },
38332   {
38333     "axioms": [
38334       "propext",
38335       "Classical.choice",
38336       "Quot.sound"
38337     ],
38338     "in_project_namespace": true,
38339     "kind": "definition",
38340     "module": "KomorebiVerification.PacketNaturalityCompletion",
38341     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraTransferEdge",
38342     "runtime_only": false
38343   },
38344   {
38345     "axioms": [],
38346     "in_project_namespace": true,
38347     "kind": "definition",
38348     "module": "PaperIRelease.GraphSources",
38349     "name": "Komorebi.PaperIRelease.FiniteDigraph.Reach",
38350     "runtime_only": false
38351   },
38352   {
38353     "axioms": [
38354       "propext",
38355       "Classical.choice",
38356       "Quot.sound"
38357     ],
38358     "in_project_namespace": true,
38359     "kind": "theorem",
38360     "module": "KomorebiVerification.ProjectorCore",
38361     "name": "Komorebi.Foundation.transferBlock_reconstruction",
38362     "runtime_only": false
38363   },
38364   {
38365     "axioms": [
38366       "propext",
38367       "Classical.choice",
38368       "Quot.sound"
38369     ],
38370     "in_project_namespace": true,
38371     "kind": "theorem",
38372     "module": "PaperIRelease.CategoryPackets",
38373     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp._proof_2",
38374     "runtime_only": false
38375   },
38376   {
38377     "axioms": [
38378       "propext",
38379       "Classical.choice",
38380       "Quot.sound"
38381     ],
38382     "in_project_namespace": true,
38383     "kind": "theorem",
38384     "module": "PaperIRelease.PacketExactSequence",
38385     "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_4",
38386     "runtime_only": false
38387   },
38388   {
38389     "axioms": [
38390       "propext",
38391       "Classical.choice",
38392       "Quot.sound"
38393     ],
38394     "in_project_namespace": true,
38395     "kind": "theorem",
38396     "module": "PaperIRelease.PacketTopology",
38397     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM_norm_le_one",
38398     "runtime_only": false
38399   },
38400   {
38401     "axioms": [
38402       "propext",
38403       "Classical.choice",
38404       "Quot.sound"
38405     ],
38406     "in_project_namespace": true,
38407     "kind": "definition",
38408     "module": "PaperIRelease.AlgebraPreorder",
38409     "name": "Komorebi.PaperIRelease.maximalStrictSteps",
38410     "runtime_only": false
38411   },
38412   {
38413     "axioms": [
38414       "propext",
38415       "Classical.choice",
38416       "Quot.sound"
38417     ],
38418     "in_project_namespace": true,
38419     "kind": "theorem",
38420     "module": "PaperIRelease.AlgebraDiagonal",
38421     "name": "Komorebi.PaperIRelease.commutes_iff_offdiagonal_zero",
38422     "runtime_only": false
38423   },
38424   {
38425     "axioms": [
38426       "propext",
38427       "Classical.choice",
38428       "Quot.sound"
38429     ],
38430     "in_project_namespace": true,
38431     "kind": "theorem",
38432     "module": "KomorebiVerification.ExactCoordinates",
38433     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis._proof_2",
38434     "runtime_only": false
38435   },
38436   {
38437     "axioms": [
38438       "propext",
38439       "Classical.choice",
38440       "Quot.sound"
38441     ],
38442     "in_project_namespace": true,
38443     "kind": "theorem",
38444     "module": "PaperIRelease.GrammarEquivalence",
38445     "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_4",
38446     "runtime_only": false
38447   },
38448   {
38449     "axioms": [
38450       "propext",
38451       "Classical.choice",
38452       "Quot.sound"
38453     ],
38454     "in_project_namespace": true,
38455     "kind": "theorem",
38456     "module": "PaperIRelease.PolynomialMonic",
38457     "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec_surjective",
38458     "runtime_only": false
38459   },
38460   {
38461     "axioms": [
38462       "propext",
38463       "Classical.choice",
38464       "Quot.sound"
38465     ],
38466     "in_project_namespace": true,
38467     "kind": "theorem",
38468     "module": "KomorebiVerification.SeedRankOperations",
38469     "name": "Komorebi.SeedRankOperations.seedRank_imageAlgebra_eq",
38470     "runtime_only": false
38471   },
38472   {
38473     "axioms": [
38474       "propext",
38475       "Classical.choice",
38476       "Quot.sound"
38477     ],
38478     "in_project_namespace": true,
38479     "kind": "definition",
38480     "module": "PaperICompletion3.OperatorPrimaryAPI",
38481     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.noConfusionType",
38482     "runtime_only": false
38483   },
38484   {
38485     "axioms": [
38486       "propext",
38487       "Quot.sound"
38488     ],
38489     "in_project_namespace": true,
38490     "kind": "theorem",
38491     "module": "PaperIRelease.GrammarModules",
38492     "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_5",
38493     "runtime_only": false
38494   },
38495   {
38496     "axioms": [
38497       "propext",
38498       "Classical.choice",
38499       "Quot.sound"
38500     ],
38501     "in_project_namespace": true,
38502     "kind": "theorem",
38503     "module": "PaperICompletion3.PrimarySeedFormula",
38504     "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_positive_primaryProduct_equiv",
38505     "runtime_only": false
38506   },
38507   {
38508     "axioms": [],
38509     "in_project_namespace": true,
38510     "kind": "theorem",
38511     "module": "KomorebiVerification.ProjectorCore",
38512     "name": "Komorebi.FormalizationStatus.blockedByLibrary.sizeOf_spec",
38513     "runtime_only": false
38514   },
38515   {
38516     "axioms": [
38517       "propext",
38518       "Quot.sound"
38519     ],
38520     "in_project_namespace": true,
38521     "kind": "theorem",
38522     "module": "KomorebiVerification.ProjectorCore",
38523     "name": "Komorebi.Seed.hull_univ",
38524     "runtime_only": false
38525   },
38526   {
38527     "axioms": [
38528       "propext",
38529       "Classical.choice",
38530       "Quot.sound"
38531     ],
38532     "in_project_namespace": true,
38533     "kind": "theorem",
38534     "module": "PaperIRelease.PacketAggregation",
38535     "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._simp_2",
38536     "runtime_only": false
38537   },
38538   {
38539     "axioms": [
38540       "propext",
38541       "Classical.choice",
38542       "Quot.sound"
38543     ],
38544     "in_project_namespace": true,
38545     "kind": "theorem",
38546     "module": "PaperICompletion5.GeometricSeedFormula",
38547     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum_eq_spectralSeedMaximum",
38548     "runtime_only": false
38549   },
38550   {
38551     "axioms": [
38552       "propext",
38553       "Classical.choice",
38554       "Quot.sound"
38555     ],
38556     "in_project_namespace": true,
38557     "kind": "theorem",
38558     "module": "KomorebiVerification.EllipticAlgorithms",
38559     "name": "Komorebi.EllipticCoordinates.Mx_apply",
38560     "runtime_only": false
38561   },
38562   {
38563     "axioms": [
38564       "propext",
38565       "Classical.choice",
38566       "Quot.sound"
38567     ],
38568     "in_project_namespace": true,
38569     "kind": "definition",
38570     "module": "PaperIRelease.PacketUniversal",
38571     "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut",
38572     "runtime_only": false
38573   },
38574   {
38575     "axioms": [
38576       "propext"
38577     ],
38578     "in_project_namespace": true,
38579     "kind": "theorem",
38580     "module": "KomorebiVerification.SingleOperatorGraph",
38581     "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_7",
38582     "runtime_only": false
38583   },
38584   {
38585     "axioms": [
38586       "propext",
38587       "Classical.choice",
38588       "Quot.sound"
38589     ],
38590     "in_project_namespace": true,
38591     "kind": "definition",
38592     "module": "PaperICompletion8.DivisionProduct",
38593     "name": "Komorebi.PaperICompletion8.DivisionProduct.blockModuleAction",
38594     "runtime_only": false
38595   },
38596   {
38597     "axioms": [
38598       "propext",
38599       "Classical.choice",
38600       "Quot.sound"
38601     ],
38602     "in_project_namespace": true,
38603     "kind": "theorem",
38604     "module": "PaperIRelease.AlgebraTransfer",
38605     "name": "Komorebi.PaperIRelease.packetPure_mem_range",
38606     "runtime_only": false
38607   },
38608   {
38609     "axioms": [
38610       "propext",
38611       "Classical.choice",
38612       "Quot.sound"
38613     ],
38614     "in_project_namespace": true,
38615     "kind": "theorem",
38616     "module": "KomorebiVerification.TopologicalCompletion",
38617     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_5",
38618     "runtime_only": false
38619   },
38620   {
38621     "axioms": [
38622       "propext",
38623       "Classical.choice",
38624       "Quot.sound"
38625     ],
38626     "in_project_namespace": true,
38627     "kind": "theorem",
38628     "module": "KomorebiVerification.PathGraphKrylov",
38629     "name": "Komorebi.PathGraphKrylov.walkMatrix_isUpperTriangular",
38630     "runtime_only": false
38631   },
38632   {
38633     "axioms": [
38634       "propext",
38635       "Classical.choice",
38636       "Quot.sound"
38637     ],
38638     "in_project_namespace": true,
38639     "kind": "theorem",
38640     "module": "PaperIRelease.GrammarAlgebra",
38641     "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow_corner",
38642     "runtime_only": false
38643   },
38644   {
38645     "axioms": [
38646       "propext",
38647       "Classical.choice",
38648       "Quot.sound"
38649     ],
38650     "in_project_namespace": true,
38651     "kind": "theorem",
38652     "module": "PaperIRelease.CategoryBoundaries",
38653     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.congr_simp",
38654     "runtime_only": false
38655   },
38656   {
38657     "axioms": [
38658       "propext",
38659       "Classical.choice",
38660       "Quot.sound"
38661     ],
38662     "in_project_namespace": true,
38663     "kind": "theorem",
38664     "module": "PaperIRelease.GrammarTyped",
38665     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.declared",
38666     "runtime_only": false
38667   },
38668   {
38669     "axioms": [
38670       "propext",
38671       "Classical.choice",
38672       "Quot.sound"
38673     ],
38674     "in_project_namespace": false,
38675     "kind": "theorem",
38676     "module": "ReleaseBoundary",
38677     "name": "PaperIBlock08Tests.dualLinearEquiv._proof_1",
38678     "runtime_only": false
38679   },
38680   {
38681     "axioms": [
38682       "propext",
38683       "Classical.choice",
38684       "Quot.sound"
38685     ],
38686     "in_project_namespace": true,
38687     "kind": "theorem",
38688     "module": "PaperICompletion5.GeometricSeedFormula",
38689     "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.primaryValues_eq_geometricValues",
38690     "runtime_only": false
38691   },
38692   {
38693     "axioms": [
38694       "propext",
38695       "Classical.choice",
38696       "Quot.sound"
38697     ],
38698     "in_project_namespace": true,
38699     "kind": "theorem",
38700     "module": "PaperIRelease.AlgebraClassGrouping",
38701     "name": "Komorebi.PaperIRelease.classSupport_iff",
38702     "runtime_only": false
38703   },
38704   {
38705     "axioms": [],
38706     "in_project_namespace": true,
38707     "kind": "definition",
38708     "module": "KomorebiVerification.ProjectorCore",
38709     "name": "Komorebi.ClaimRecord.casesOn",
38710     "runtime_only": false
38711   },
38712   {
38713     "axioms": [
38714       "propext"
38715     ],
38716     "in_project_namespace": true,
38717     "kind": "theorem",
38718     "module": "KomorebiVerification.ProjectorCore",
38719     "name": "Komorebi.FiniteDifference.forwardDiff_add",
38720     "runtime_only": false
38721   },
38722   {
38723     "axioms": [
38724       "propext",
38725       "Classical.choice",
38726       "Quot.sound"
38727     ],
38728     "in_project_namespace": true,
38729     "kind": "theorem",
38730     "module": "PaperICompletion3.OperatorPrimaryAPI",
38731     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.positive",
38732     "runtime_only": false
38733   },
38734   {
38735     "axioms": [
38736       "propext",
38737       "Classical.choice",
38738       "Quot.sound"
38739     ],
38740     "in_project_namespace": false,
38741     "kind": "theorem",
38742     "module": "ReleaseBoundary",
38743     "name": "PaperIBlock08Tests.dualLinearEquiv._proof_3",
38744     "runtime_only": false
38745   },
38746   {
38747     "axioms": [
38748       "propext",
38749       "Classical.choice",
38750       "Quot.sound"
38751     ],
38752     "in_project_namespace": false,
38753     "kind": "definition",
38754     "module": "ReleaseBoundary",
38755     "name": "PaperIBlock08Tests.qi",
38756     "runtime_only": false
38757   },
38758   {
38759     "axioms": [
38760       "propext",
38761       "Classical.choice",
38762       "Quot.sound"
38763     ],
38764     "in_project_namespace": true,
38765     "kind": "theorem",
38766     "module": "PaperIRelease.AlgebraQuotient",
38767     "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_12",
38768     "runtime_only": false
38769   },
38770   {
38771     "axioms": [],
38772     "in_project_namespace": true,
38773     "kind": "definition",
38774     "module": "KomorebiVerification.ProjectorCore",
38775     "name": "Komorebi.FormalizationStatus.blockedByLibrary.elim",
38776     "runtime_only": false
38777   },
38778   {
38779     "axioms": [
38780       "propext",
38781       "Classical.choice",
38782       "Quot.sound"
38783     ],
38784     "in_project_namespace": true,
38785     "kind": "theorem",
38786     "module": "PaperIRelease.GeneralConditionedCoordinates",
38787     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear._proof_1",
38788     "runtime_only": false
38789   },
38790   {
38791     "axioms": [
38792       "propext",
38793       "Classical.choice",
38794       "Quot.sound"
38795     ],
38796     "in_project_namespace": true,
38797     "kind": "theorem",
38798     "module": "PaperIRelease.GraphSourceCount",
38799     "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_source_count",
38800     "runtime_only": false
38801   },
38802   {
38803     "axioms": [],
38804     "in_project_namespace": true,
38805     "kind": "constructor",
38806     "module": "PaperIRelease.CategoryExport",
38807     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity",
38808     "runtime_only": false
38809   },
38810   {
38811     "axioms": [
38812       "propext",
38813       "Classical.choice",
38814       "Quot.sound"
38815     ],
38816     "in_project_namespace": true,
38817     "kind": "theorem",
38818     "module": "PaperIRelease.GrammarAlgebra",
38819     "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_orthogonal",
38820     "runtime_only": false
38821   },
38822   {
38823     "axioms": [
38824       "propext",
38825       "Classical.choice",
38826       "Quot.sound"
38827     ],
38828     "in_project_namespace": true,
38829     "kind": "definition",
38830     "module": "PaperIRelease.GraphSources",
38831     "name": "Komorebi.PaperIRelease.FiniteDigraph.sccDecidableEq",
38832     "runtime_only": false
38833   },
38834   {
38835     "axioms": [
38836       "propext",
38837       "Quot.sound"
38838     ],
38839     "in_project_namespace": true,
38840     "kind": "theorem",
38841     "module": "KomorebiVerification.FibreRefinement",
38842     "name": "Komorebi.Packet.fibreLinearProj.congr_simp",
38843     "runtime_only": false
38844   },
38845   {
38846     "axioms": [
38847       "propext",
38848       "Classical.choice",
38849       "Quot.sound"
38850     ],
38851     "in_project_namespace": true,
38852     "kind": "theorem",
38853     "module": "PaperICompletion.CyclicClassification",
38854     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_7",
38855     "runtime_only": false
38856   },
38857   {
38858     "axioms": [
38859       "propext",
38860       "Quot.sound"
38861     ],
38862     "in_project_namespace": true,
38863     "kind": "theorem",
38864     "module": "PaperICompletion4.IntrinsicPrimary",
38865     "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal._proof_2",
38866     "runtime_only": false
38867   },
38868   {
38869     "axioms": [
38870       "propext",
38871       "Classical.choice",
38872       "Quot.sound"
38873     ],
38874     "in_project_namespace": true,
38875     "kind": "theorem",
38876     "module": "KomorebiVerification.PacketNaturalityCompletion",
38877     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_2",
38878     "runtime_only": false
38879   },
38880   {
38881     "axioms": [],
38882     "in_project_namespace": false,
38883     "kind": "theorem",
38884     "module": "KomorebiVerification.PacketNaturalityCompletion",
38885     "name": "_private.KomorebiVerification.PacketNaturalityCompletion.0.Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1.eq_1",
38886     "runtime_only": false
38887   },
38888   {
38889     "axioms": [
38890       "propext",
38891       "Classical.choice",
38892       "Quot.sound"
38893     ],
38894     "in_project_namespace": true,
38895     "kind": "theorem",
38896     "module": "KomorebiVerification.TopologicalCompletion",
38897     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis._proof_1",
38898     "runtime_only": false
38899   },
38900   {
38901     "axioms": [
38902       "propext",
38903       "Classical.choice",
38904       "Quot.sound"
38905     ],
38906     "in_project_namespace": true,
38907     "kind": "theorem",
38908     "module": "KomorebiVerification.EllipticAlgorithms",
38909     "name": "Komorebi.EllipticCoordinates.P1_My",
38910     "runtime_only": false
38911   },
38912   {
38913     "axioms": [
38914       "propext",
38915       "Classical.choice",
38916       "Quot.sound"
38917     ],
38918     "in_project_namespace": true,
38919     "kind": "definition",
38920     "module": "PaperIRelease.PacketDescent",
38921     "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap",
38922     "runtime_only": false
38923   },
38924   {
38925     "axioms": [
38926       "propext",
38927       "Classical.choice",
38928       "Quot.sound"
38929     ],
38930     "in_project_namespace": false,
38931     "kind": "theorem",
38932     "module": "ReleaseBoundary",
38933     "name": "PaperIBlock08Tests.reversed_quaternion_coefficient_fails",
38934     "runtime_only": false
38935   },
38936   {
38937     "axioms": [],
38938     "in_project_namespace": true,
38939     "kind": "theorem",
38940     "module": "PaperIRelease.GrammarPaths",
38941     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn.eq",
38942     "runtime_only": false
38943   },
38944   {
38945     "axioms": [
38946       "propext",
38947       "Classical.choice",
38948       "Quot.sound"
38949     ],
38950     "in_project_namespace": true,
38951     "kind": "definition",
38952     "module": "PaperIRelease.GrammarAlgebra",
38953     "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.casesOn",
38954     "runtime_only": false
38955   },
38956   {
38957     "axioms": [
38958       "propext",
38959       "Quot.sound"
38960     ],
38961     "in_project_namespace": true,
38962     "kind": "inductive",
38963     "module": "PaperIRelease.GrammarTyped",
38964     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData",
38965     "runtime_only": false
38966   },
38967   {
38968     "axioms": [
38969       "propext",
38970       "Quot.sound"
38971     ],
38972     "in_project_namespace": true,
38973     "kind": "theorem",
38974     "module": "KomorebiVerification.PacketNaturalityCompletion",
38975     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._proof_1",
38976     "runtime_only": false
38977   },
38978   {
38979     "axioms": [
38980       "propext",
38981       "Quot.sound"
38982     ],
38983     "in_project_namespace": true,
38984     "kind": "theorem",
38985     "module": "KomorebiVerification.PacketNaturalityCompletion",
38986     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_1",
38987     "runtime_only": false
38988   },
38989   {
38990     "axioms": [
38991       "propext",
38992       "Classical.choice",
38993       "Quot.sound"
38994     ],
38995     "in_project_namespace": true,
38996     "kind": "theorem",
38997     "module": "PaperIRelease.TopologyCategories",
38998     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ext_iff",
38999     "runtime_only": false
39000   },
39001   {
39002     "axioms": [
39003       "propext",
39004       "Classical.choice",
39005       "Quot.sound"
39006     ],
39007     "in_project_namespace": true,
39008     "kind": "theorem",
39009     "module": "KomorebiVerification.PacketNaturalityCompletion",
39010     "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.operator_natural",
39011     "runtime_only": false
39012   },
39013   {
39014     "axioms": [
39015       "propext",
39016       "Classical.choice",
39017       "Quot.sound"
39018     ],
39019     "in_project_namespace": true,
39020     "kind": "theorem",
39021     "module": "KomorebiVerification.TopologicalCompletion",
39022     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula",
39023     "runtime_only": false
39024   },
39025   {
39026     "axioms": [
39027       "propext",
39028       "Classical.choice",
39029       "Quot.sound"
39030     ],
39031     "in_project_namespace": true,
39032     "kind": "theorem",
39033     "module": "PaperIRelease.BoundedStar",
39034     "name": "Komorebi.PaperIRelease.BoundedSupport.proj_other",
39035     "runtime_only": false
39036   },
39037   {
39038     "axioms": [
39039       "propext",
39040       "Classical.choice",
39041       "Quot.sound"
39042     ],
39043     "in_project_namespace": true,
39044     "kind": "theorem",
39045     "module": "KomorebiVerification.PacketNaturalityCompletion",
39046     "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.congr_simp",
39047     "runtime_only": false
39048   },
39049   {
39050     "axioms": [
39051       "propext",
39052       "Classical.choice",
39053       "Quot.sound"
39054     ],
39055     "in_project_namespace": true,
39056     "kind": "definition",
39057     "module": "PaperIRelease.TopologyCategories",
39058     "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.noConfusion",
39059     "runtime_only": false
39060   },
39061   {
39062     "axioms": [
39063       "propext",
39064       "Quot.sound"
39065     ],
39066     "in_project_namespace": true,
39067     "kind": "constructor",
39068     "module": "PaperIRelease.GrammarModules",
39069     "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk",
39070     "runtime_only": false
39071   },
39072   {
39073     "axioms": [
39074       "propext",
39075       "Quot.sound"
39076     ],
39077     "in_project_namespace": true,
39078     "kind": "theorem",
39079     "module": "PaperICompletion4.GroupedPrimary",
39080     "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_6",
39081     "runtime_only": false
39082   },
39083   {
39084     "axioms": [
39085       "propext",
39086       "Classical.choice",
39087       "Quot.sound"
39088     ],
39089     "in_project_namespace": true,
39090     "kind": "theorem",
39091     "module": "KomorebiVerification.PacketNaturalityCompletion",
39092     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection.eq_1",
39093     "runtime_only": false
39094   },
39095   {
39096     "axioms": [],
39097     "in_project_namespace": true,
39098     "kind": "definition",
39099     "module": "PaperIRelease.GrammarPaths",
39100     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.noConfusion",
39101     "runtime_only": false
39102   },
39103   {
39104     "axioms": [
39105       "propext",
39106       "Classical.choice",
39107       "Quot.sound"
39108     ],
39109     "in_project_namespace": true,
39110     "kind": "theorem",
39111     "module": "KomorebiVerification.EllipticAlgorithms",
39112     "name": "Komorebi.EllipticCoordinates.My._proof_2",
39113     "runtime_only": false
39114   },
39115   {
39116     "axioms": [
39117       "propext",
39118       "Classical.choice",
39119       "Quot.sound"
39120     ],
39121     "in_project_namespace": true,
39122     "kind": "theorem",
39123     "module": "PaperIRelease.TensorPackets",
39124     "name": "Komorebi.PaperIRelease.tensorPackets.eq_1",
39125     "runtime_only": false
39126   },
39127   {
39128     "axioms": [
39129       "propext",
39130       "Classical.choice",
39131       "Quot.sound"
39132     ],
39133     "in_project_namespace": true,
39134     "kind": "theorem",
39135     "module": "PaperIRelease.BoundedStar",
39136     "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_8",
39137     "runtime_only": false
39138   },
39139   {
39140     "axioms": [],
39141     "in_project_namespace": true,
39142     "kind": "theorem",
39143     "module": "PaperIRelease.GraphSources",
39144     "name": "Komorebi.PaperIRelease.FiniteDigraph.reachPreorder._proof_1",
39145     "runtime_only": false
39146   },
39147   {
39148     "axioms": [
39149       "propext",
39150       "Classical.choice",
39151       "Quot.sound"
39152     ],
39153     "in_project_namespace": true,
39154     "kind": "theorem",
39155     "module": "PaperIRelease.GrammarEquivalence",
39156     "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_6",
39157     "runtime_only": false
39158   },
39159   {
39160     "axioms": [
39161       "propext",
39162       "Classical.choice",
39163       "Quot.sound"
39164     ],
39165     "in_project_namespace": true,
39166     "kind": "theorem",
39167     "module": "PaperIRelease.CategoryPackets",
39168     "name": "Komorebi.PaperIRelease.CategoryPackets.imageHull_eq_top",
39169     "runtime_only": false
39170   },
39171   {
39172     "axioms": [
39173       "propext",
39174       "Classical.choice",
39175       "Quot.sound"
39176     ],
39177     "in_project_namespace": true,
39178     "kind": "theorem",
39179     "module": "PaperICompletion.CyclicClassification",
39180     "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_3",
39181     "runtime_only": false
39182   },
39183   {
39184     "axioms": [
39185       "propext",
39186       "Quot.sound"
39187     ],
39188     "in_project_namespace": true,
39189     "kind": "theorem",
39190     "module": "PaperIRelease.GrammarModules",
39191     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ext",
39192     "runtime_only": false
39193   },
39194   {
39195     "axioms": [
39196       "propext",
39197       "Classical.choice",
39198       "Quot.sound"
39199     ],
39200     "in_project_namespace": true,
39201     "kind": "definition",
39202     "module": "KomorebiVerification.SingleOperatorGraph",
39203     "name": "Komorebi.SingleOperatorGraph.orbitFamily",
39204     "runtime_only": false
39205   },
39206   {
39207     "axioms": [
39208       "propext",
39209       "Quot.sound"
39210     ],
39211     "in_project_namespace": true,
39212     "kind": "definition",
39213     "module": "PaperIRelease.GraphSources",
39214     "name": "Komorebi.PaperIRelease.FiniteDigraph.sccPartialOrder",
39215     "runtime_only": false
39216   },
39217   {
39218     "axioms": [],
39219     "in_project_namespace": true,
39220     "kind": "definition",
39221     "module": "KomorebiVerification.PacketNaturalityCompletion",
39222     "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._sunfold",
39223     "runtime_only": false
39224   },
39225   {
39226     "axioms": [
39227       "propext",
39228       "Classical.choice",
39229       "Quot.sound"
39230     ],
39231     "in_project_namespace": true,
39232     "kind": "theorem",
39233     "module": "KomorebiVerification.TopologicalCompletion",
39234     "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_2",
39235     "runtime_only": false
39236   },
39237   {
39238     "axioms": [
39239       "propext",
39240       "Classical.choice",
39241       "Quot.sound"
39242     ],
39243     "in_project_namespace": true,
39244     "kind": "definition",
39245     "module": "PaperIRelease.CategoryPackets",
39246     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.algebraMap",
39247     "runtime_only": false
39248   },
39249   {
39250     "axioms": [
39251       "propext",
39252       "Quot.sound"
39253     ],
39254     "in_project_namespace": true,
39255     "kind": "theorem",
39256     "module": "PaperICompletion4.GroupedPrimary",
39257     "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv._proof_1",
39258     "runtime_only": false
39259   },
39260   {
39261     "axioms": [
39262       "propext"
39263     ],
39264     "in_project_namespace": true,
39265     "kind": "theorem",
39266     "module": "KomorebiVerification.ProjectorCore",
39267     "name": "Komorebi.Seed.OperatorExpr.atom.injEq",
39268     "runtime_only": false
39269   },
39270   {
39271     "axioms": [],
39272     "in_project_namespace": true,
39273     "kind": "definition",
39274     "module": "PaperIRelease.GrammarPaths",
39275     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.noConfusionType",
39276     "runtime_only": false
39277   },
39278   {
39279     "axioms": [
39280       "propext",
39281       "Classical.choice",
39282       "Quot.sound"
39283     ],
39284     "in_project_namespace": true,
39285     "kind": "theorem",
39286     "module": "PaperIRelease.GraphSourceCount",
39287     "name": "Komorebi.PaperIRelease.one_le_source_localPureSeedRank",
39288     "runtime_only": false
39289   },
39290   {
39291     "axioms": [
39292       "propext",
39293       "Classical.choice",
39294       "Quot.sound"
39295     ],
39296     "in_project_namespace": true,
39297     "kind": "constructor",
39298     "module": "PaperIRelease.CategoryPackets",
39299     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk",
39300     "runtime_only": false
39301   },
39302   {
39303     "axioms": [
39304       "propext",
39305       "Quot.sound"
39306     ],
39307     "in_project_namespace": false,
39308     "kind": "theorem",
39309     "module": "KomorebiVerification.SeedRankOperations",
39310     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRight_smul_tmul",
39311     "runtime_only": false
39312   },
39313   {
39314     "axioms": [],
39315     "in_project_namespace": true,
39316     "kind": "definition",
39317     "module": "PaperIRelease.GraphSources",
39318     "name": "Komorebi.PaperIRelease.FiniteDigraph.component",
39319     "runtime_only": false
39320   },
39321   {
39322     "axioms": [
39323       "propext",
39324       "Quot.sound"
39325     ],
39326     "in_project_namespace": true,
39327     "kind": "theorem",
39328     "module": "PaperIRelease.GrammarModules",
39329     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ext_iff",
39330     "runtime_only": false
39331   },
39332   {
39333     "axioms": [
39334       "propext",
39335       "Quot.sound"
39336     ],
39337     "in_project_namespace": true,
39338     "kind": "theorem",
39339     "module": "KomorebiVerification.SeedRankOperations",
39340     "name": "Komorebi.SeedRankOperations.productModule._proof_2",
39341     "runtime_only": false
39342   },
39343   {
39344     "axioms": [
39345       "propext",
39346       "Classical.choice",
39347       "Quot.sound"
39348     ],
39349     "in_project_namespace": true,
39350     "kind": "theorem",
39351     "module": "PaperIRelease.PacketPureRank",
39352     "name": "Komorebi.PaperIRelease.seedRank_le_packetPureSeedRank",
39353     "runtime_only": false
39354   },
39355   {
39356     "axioms": [
39357       "propext",
39358       "Classical.choice",
39359       "Quot.sound"
39360     ],
39361     "in_project_namespace": false,
39362     "kind": "theorem",
39363     "module": "ReleaseBoundary",
39364     "name": "PaperIBlock08Tests.quaternion_three_copies_rank_two",
39365     "runtime_only": false
39366   },
39367   {
39368     "axioms": [
39369       "propext",
39370       "Classical.choice",
39371       "Quot.sound"
39372     ],
39373     "in_project_namespace": true,
39374     "kind": "definition",
39375     "module": "PaperICompletion3.OperatorPrimaryAPI",
39376     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.chosenPrimaryPresentation",
39377     "runtime_only": false
39378   },
39379   {
39380     "axioms": [
39381       "propext"
39382     ],
39383     "in_project_namespace": true,
39384     "kind": "definition",
39385     "module": "PaperIRelease.CategoryExport",
39386     "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported",
39387     "runtime_only": false
39388   },
39389   {
39390     "axioms": [
39391       "propext",
39392       "Classical.choice",
39393       "Quot.sound"
39394     ],
39395     "in_project_namespace": true,
39396     "kind": "theorem",
39397     "module": "PaperIRelease.CategoryPackets",
39398     "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.injEq",
39399     "runtime_only": false
39400   },
39401   {
39402     "axioms": [
39403       "propext",
39404       "Classical.choice",
39405       "Quot.sound"
39406     ],
39407     "in_project_namespace": true,
39408     "kind": "theorem",
39409     "module": "PaperIRelease.GrammarEquivalence",
39410     "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_essSurj",
39411     "runtime_only": false
39412   },
39413   {
39414     "axioms": [
39415       "propext",
39416       "Classical.choice",
39417       "Quot.sound"
39418     ],
39419     "in_project_namespace": false,
39420     "kind": "theorem",
39421     "module": "PaperIRelease.AlgebraPreorder",
39422     "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono",
39423     "runtime_only": false
39424   },
39425   {
39426     "axioms": [
39427       "propext",
39428       "Classical.choice",
39429       "Quot.sound"
39430     ],
39431     "in_project_namespace": true,
39432     "kind": "definition",
39433     "module": "PaperIRelease.CategoryPackets",
39434     "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk._flat_ctor",
39435     "runtime_only": false
39436   },
39437   {
39438     "axioms": [
39439       "propext",
39440       "Classical.choice",
39441       "Quot.sound"
39442     ],
39443     "in_project_namespace": true,
39444     "kind": "theorem",
39445     "module": "PaperICompletion8.DivisionBlock",
39446     "name": "Komorebi.PaperICompletion8.DivisionBlock.block_smul_eq_mul",
39447     "runtime_only": false
39448   },
39449   {
39450     "axioms": [
39451       "propext",
39452       "Classical.choice",
39453       "Quot.sound"
39454     ],
39455     "in_project_namespace": true,
39456     "kind": "theorem",
39457     "module": "PaperIRelease.PacketBoundaryTests",
39458     "name": "Komorebi.PaperIRelease.PacketBoundaryTests.coordinate_swap_cannot_descend",
39459     "runtime_only": false
39460   },
39461   {
39462     "axioms": [
39463       "propext",
39464       "Quot.sound"
39465     ],
39466     "in_project_namespace": true,
39467     "kind": "definition",
39468     "module": "KomorebiVerification.ResidueProjectors",
39469     "name": "Komorebi.Residue.residueProj",
39470     "runtime_only": false
39471   },
39472   {
39473     "axioms": [
39474       "propext",
39475       "Classical.choice",
39476       "Quot.sound"
39477     ],
39478     "in_project_namespace": true,
39479     "kind": "theorem",
39480     "module": "PaperICompletion3.OperatorPrimaryAPI",
39481     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedNumber_isLeast",
39482     "runtime_only": false
39483   },
39484   {
39485     "axioms": [
39486       "propext",
39487       "Classical.choice",
39488       "Quot.sound"
39489     ],
39490     "in_project_namespace": true,
39491     "kind": "theorem",
39492     "module": "KomorebiVerification.EllipticAlgorithms",
39493     "name": "Komorebi.EllipticCoordinates.P1._proof_2",
39494     "runtime_only": false
39495   },
39496   {
39497     "axioms": [],
39498     "in_project_namespace": false,
39499     "kind": "theorem",
39500     "module": "PaperIRelease.CategoryExport",
39501     "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_5",
39502     "runtime_only": false
39503   },
39504   {
39505     "axioms": [
39506       "propext",
39507       "Classical.choice",
39508       "Quot.sound"
39509     ],
39510     "in_project_namespace": true,
39511     "kind": "theorem",
39512     "module": "KomorebiVerification.ExactCoordinates",
39513     "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis_rangeSynthesis",
39514     "runtime_only": false
39515   },
39516   {
39517     "axioms": [
39518       "propext",
39519       "Classical.choice",
39520       "Quot.sound"
39521     ],
39522     "in_project_namespace": true,
39523     "kind": "theorem",
39524     "module": "PaperIRelease.CoordinateTransport",
39525     "name": "Komorebi.PaperIRelease.CoordinateTransport.packet_rank_invariant",
39526     "runtime_only": false
39527   },
39528   {
39529     "axioms": [
39530       "propext",
39531       "Classical.choice",
39532       "Quot.sound"
39533     ],
39534     "in_project_namespace": false,
39535     "kind": "theorem",
39536     "module": "KomorebiVerification.SeedRankOperations",
39537     "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.seedRank_prod_le_right_of_le",
39538     "runtime_only": false
39539   },
39540   {
39541     "axioms": [
39542       "propext",
39543       "Classical.choice",
39544       "Quot.sound"
39545     ],
39546     "in_project_namespace": true,
39547     "kind": "theorem",
39548     "module": "KomorebiVerification.PacketNaturalityCompletion",
39549     "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.range_arrowA_third_zero",
39550     "runtime_only": false
39551   },
39552   {
39553     "axioms": [
39554       "propext",
39555       "Quot.sound"
39556     ],
39557     "in_project_namespace": true,
39558     "kind": "definition",
39559     "module": "PaperIRelease.GrammarModules",
39560     "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk._flat_ctor",
39561     "runtime_only": false
39562   },
39563   {
39564     "axioms": [
39565       "propext",
39566       "Classical.choice",
39567       "Quot.sound"
39568     ],
39569     "in_project_namespace": true,
39570     "kind": "theorem",
39571     "module": "PaperICompletion7.Nakayama",
39572     "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_ideal_smul",
39573     "runtime_only": false
39574   },
39575   {
39576     "axioms": [
39577       "propext",
39578       "Classical.choice",
39579       "Quot.sound"
39580     ],
39581     "in_project_namespace": true,
39582     "kind": "theorem",
39583     "module": "KomorebiVerification.SingleOperatorGraph",
39584     "name": "Komorebi.SingleOperatorGraph.cycleFourierRow._proof_2",
39585     "runtime_only": false
39586   },
39587   {
39588     "axioms": [],
39589     "in_project_namespace": true,
39590     "kind": "definition",
39591     "module": "PaperIRelease.CategoryExport",
39592     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.below",
39593     "runtime_only": false
39594   },
39595   {
39596     "axioms": [
39597       "propext",
39598       "Classical.choice",
39599       "Quot.sound"
39600     ],
39601     "in_project_namespace": true,
39602     "kind": "definition",
39603     "module": "PaperIRelease.GeneralConditionedCoordinates",
39604     "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditionNumber",
39605     "runtime_only": false
39606   },
39607   {
39608     "axioms": [
39609       "propext",
39610       "Classical.choice",
39611       "Quot.sound"
39612     ],
39613     "in_project_namespace": true,
39614     "kind": "definition",
39615     "module": "PaperICompletion3.OperatorPrimaryAPI",
39616     "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label",
39617     "runtime_only": false
39618   },
39619   {
39620     "axioms": [
39621       "propext",
39622       "Quot.sound"
39623     ],
39624     "in_project_namespace": true,
39625     "kind": "theorem",
39626     "module": "PaperIRelease.AlgebraClassGrouping",
39627     "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_2",
39628     "runtime_only": false
39629   },
39630   {
39631     "axioms": [
39632       "propext",
39633       "Classical.choice",
39634       "Quot.sound"
39635     ],
39636     "in_project_namespace": true,
39637     "kind": "theorem",
39638     "module": "KomorebiVerification.PacketNaturalityCompletion",
39639     "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks_restrictBlocks",
39640     "runtime_only": false
39641   },
39642   {
39643     "axioms": [
39644       "propext",
39645       "Classical.choice",
39646       "Quot.sound"
39647     ],
39648     "in_project_namespace": true,
39649     "kind": "definition",
39650     "module": "PaperIRelease.AlgebraClassGrouping",
39651     "name": "Komorebi.PaperIRelease.preorderClassRangeEquiv",
39652     "runtime_only": false
39653   },
39654   {
39655     "axioms": [
39656       "propext",
39657       "Quot.sound"
39658     ],
39659     "in_project_namespace": true,
39660     "kind": "theorem",
39661     "module": "KomorebiVerification.FibreRefinement",
39662     "name": "Komorebi.Packet.fibreLinearProj._proof_1",
39663     "runtime_only": false
39664   },
39665   {
39666     "axioms": [],
39667     "in_project_namespace": true,
39668     "kind": "definition",
39669     "module": "PaperIRelease.CategoryExport",
39670     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.elim",
39671     "runtime_only": false
39672   },
39673   {
39674     "axioms": [
39675       "propext",
39676       "Classical.choice",
39677       "Quot.sound"
39678     ],
39679     "in_project_namespace": true,
39680     "kind": "theorem",
39681     "module": "PaperIRelease.GraphSourceProjection",
39682     "name": "Komorebi.PaperIRelease.componentProjection_other_packet",
39683     "runtime_only": false
39684   },
39685   {
39686     "axioms": [
39687       "propext",
39688       "Quot.sound"
39689     ],
39690     "in_project_namespace": true,
39691     "kind": "theorem",
39692     "module": "KomorebiVerification.SeedRankOperations",
39693     "name": "Komorebi.SeedRankOperations.productModule._proof_3",
39694     "runtime_only": false
39695   },
39696   {
39697     "axioms": [
39698       "propext",
39699       "Quot.sound"
39700     ],
39701     "in_project_namespace": true,
39702     "kind": "theorem",
39703     "module": "PaperIRelease.ScalarExtension",
39704     "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightTower",
39705     "runtime_only": false
39706   },
39707   {
39708     "axioms": [
39709       "propext",
39710       "Classical.choice",
39711       "Quot.sound"
39712     ],
39713     "in_project_namespace": true,
39714     "kind": "theorem",
39715     "module": "PaperIRelease.GrammarTyped",
39716     "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator.eq_1",
39717     "runtime_only": false
39718   },
39719   {
39720     "axioms": [
39721       "propext",
39722       "Classical.choice",
39723       "Quot.sound"
39724     ],
39725     "in_project_namespace": true,
39726     "kind": "theorem",
39727     "module": "PaperIRelease.AlgebraTransfer",
39728     "name": "Komorebi.PaperIRelease.packetPure_zero",
39729     "runtime_only": false
39730   },
39731   {
39732     "axioms": [],
39733     "in_project_namespace": true,
39734     "kind": "constructor",
39735     "module": "KomorebiVerification.ProjectorCore",
39736     "name": "Komorebi.ClaimKind.algorithmClaim",
39737     "runtime_only": false
39738   },
39739   {
39740     "axioms": [
39741       "propext",
39742       "Classical.choice",
39743       "Quot.sound"
39744     ],
39745     "in_project_namespace": true,
39746     "kind": "theorem",
39747     "module": "PaperICompletion8.SemisimpleExistence",
39748     "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_artinian_radicalTop_seed_formula",
39749     "runtime_only": false
39750   },
39751   {
39752     "axioms": [],
39753     "in_project_namespace": true,
39754     "kind": "definition",
39755     "module": "PaperIRelease.CategoryExport",
39756     "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.elim",
39757     "runtime_only": false
39758   },
39759   {
39760     "axioms": [
39761       "propext",
39762       "Quot.sound"
39763     ],
39764     "in_project_namespace": true,
39765     "kind": "theorem",
39766     "module": "PaperIRelease.TensorPackets",
39767     "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_1",
39768     "runtime_only": false
39769   }
39770 ]