EXACT_CHECKS.json
Paper X: Universal Residual Seeds and Conditional Occupied-System Completion
EXACT_CHECKS.json
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6 "scope": "Finite examples and exact symbolic identities. No universal Galois occurrence, automorphic occupancy, or Lean proof checked.",
7 "coefficient_domains": [
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9 "rationals",
10 "symbolic polynomials",
11 "finite fields F3,F5,F25,F9",
12 "Z/(2^n), n <= 4"
13 ],
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778 "status": "PASS",
779 "scope": "exact worked example"
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783 "status": "PASS",
784 "scope": "exact worked example"
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889 "scope": "exact worked example"
890 },
891 {
892 "name": "coprimality_not_necessary",
893 "status": "PASS",
894 "scope": "exact worked example"
895 },
896 {
897 "name": "exact_scalar_criterion_k0_d1",
898 "status": "PASS",
899 "scope": "exact worked example"
900 },
901 {
902 "name": "exact_scalar_criterion_k0_d2",
903 "status": "PASS",
904 "scope": "exact worked example"
905 },
906 {
907 "name": "exact_scalar_criterion_k0_d3",
908 "status": "PASS",
909 "scope": "exact worked example"
910 },
911 {
912 "name": "exact_scalar_criterion_k0_d4",
913 "status": "PASS",
914 "scope": "exact worked example"
915 },
916 {
917 "name": "exact_scalar_criterion_k0_d5",
918 "status": "PASS",
919 "scope": "exact worked example"
920 },
921 {
922 "name": "exact_scalar_criterion_k0_d6",
923 "status": "PASS",
924 "scope": "exact worked example"
925 },
926 {
927 "name": "exact_scalar_criterion_k1_d1",
928 "status": "PASS",
929 "scope": "exact worked example"
930 },
931 {
932 "name": "exact_scalar_criterion_k1_d2",
933 "status": "PASS",
934 "scope": "exact worked example"
935 },
936 {
937 "name": "exact_scalar_criterion_k1_d3",
938 "status": "PASS",
939 "scope": "exact worked example"
940 },
941 {
942 "name": "exact_scalar_criterion_k1_d4",
943 "status": "PASS",
944 "scope": "exact worked example"
945 },
946 {
947 "name": "exact_scalar_criterion_k1_d5",
948 "status": "PASS",
949 "scope": "exact worked example"
950 },
951 {
952 "name": "exact_scalar_criterion_k1_d6",
953 "status": "PASS",
954 "scope": "exact worked example"
955 },
956 {
957 "name": "exact_scalar_criterion_k2_d1",
958 "status": "PASS",
959 "scope": "exact worked example"
960 },
961 {
962 "name": "exact_scalar_criterion_k2_d2",
963 "status": "PASS",
964 "scope": "exact worked example"
965 },
966 {
967 "name": "exact_scalar_criterion_k2_d3",
968 "status": "PASS",
969 "scope": "exact worked example"
970 },
971 {
972 "name": "exact_scalar_criterion_k2_d4",
973 "status": "PASS",
974 "scope": "exact worked example"
975 },
976 {
977 "name": "exact_scalar_criterion_k2_d5",
978 "status": "PASS",
979 "scope": "exact worked example"
980 },
981 {
982 "name": "exact_scalar_criterion_k2_d6",
983 "status": "PASS",
984 "scope": "exact worked example"
985 },
986 {
987 "name": "exact_scalar_criterion_k3_d1",
988 "status": "PASS",
989 "scope": "exact worked example"
990 },
991 {
992 "name": "exact_scalar_criterion_k3_d2",
993 "status": "PASS",
994 "scope": "exact worked example"
995 },
996 {
997 "name": "exact_scalar_criterion_k3_d3",
998 "status": "PASS",
999 "scope": "exact worked example"
1000 },
1001 {
1002 "name": "exact_scalar_criterion_k3_d4",
1003 "status": "PASS",
1004 "scope": "exact worked example"
1005 },
1006 {
1007 "name": "exact_scalar_criterion_k3_d5",
1008 "status": "PASS",
1009 "scope": "exact worked example"
1010 },
1011 {
1012 "name": "exact_scalar_criterion_k3_d6",
1013 "status": "PASS",
1014 "scope": "exact worked example"
1015 },
1016 {
1017 "name": "crt_solution",
1018 "status": "PASS",
1019 "scope": "exact worked example"
1020 },
1021 {
1022 "name": "crt_avoidance",
1023 "status": "PASS",
1024 "scope": "exact worked example"
1025 },
1026 {
1027 "name": "crt_units",
1028 "status": "PASS",
1029 "scope": "exact worked example"
1030 },
1031 {
1032 "name": "lattice_boundary_L1",
1033 "status": "PASS",
1034 "scope": "exact worked example"
1035 },
1036 {
1037 "name": "lattice_boundary_L2",
1038 "status": "PASS",
1039 "scope": "exact worked example"
1040 },
1041 {
1042 "name": "lattice_boundary_L3",
1043 "status": "PASS",
1044 "scope": "exact worked example"
1045 },
1046 {
1047 "name": "lattice_boundary_L4",
1048 "status": "PASS",
1049 "scope": "exact worked example"
1050 },
1051 {
1052 "name": "lattice_boundary_L5",
1053 "status": "PASS",
1054 "scope": "exact worked example"
1055 },
1056 {
1057 "name": "lattice_boundary_L6",
1058 "status": "PASS",
1059 "scope": "exact worked example"
1060 },
1061 {
1062 "name": "lattice_boundary_L7",
1063 "status": "PASS",
1064 "scope": "exact worked example"
1065 },
1066 {
1067 "name": "lattice_boundary_L8",
1068 "status": "PASS",
1069 "scope": "exact worked example"
1070 },
1071 {
1072 "name": "lattice_boundary_L9",
1073 "status": "PASS",
1074 "scope": "exact worked example"
1075 },
1076 {
1077 "name": "lattice_boundary_L10",
1078 "status": "PASS",
1079 "scope": "exact worked example"
1080 },
1081 {
1082 "name": "lattice_boundary_L11",
1083 "status": "PASS",
1084 "scope": "exact worked example"
1085 },
1086 {
1087 "name": "lattice_boundary_L12",
1088 "status": "PASS",
1089 "scope": "exact worked example"
1090 },
1091 {
1092 "name": "lattice_boundary_L13",
1093 "status": "PASS",
1094 "scope": "exact worked example"
1095 },
1096 {
1097 "name": "lattice_boundary_L14",
1098 "status": "PASS",
1099 "scope": "exact worked example"
1100 },
1101 {
1102 "name": "lattice_boundary_L15",
1103 "status": "PASS",
1104 "scope": "exact worked example"
1105 },
1106 {
1107 "name": "lattice_boundary_L16",
1108 "status": "PASS",
1109 "scope": "exact worked example"
1110 },
1111 {
1112 "name": "lattice_boundary_L17",
1113 "status": "PASS",
1114 "scope": "exact worked example"
1115 },
1116 {
1117 "name": "lattice_boundary_L18",
1118 "status": "PASS",
1119 "scope": "exact worked example"
1120 },
1121 {
1122 "name": "lattice_boundary_L19",
1123 "status": "PASS",
1124 "scope": "exact worked example"
1125 },
1126 {
1127 "name": "lattice_boundary_L20",
1128 "status": "PASS",
1129 "scope": "exact worked example"
1130 },
1131 {
1132 "name": "lattice_boundary_L21",
1133 "status": "PASS",
1134 "scope": "exact worked example"
1135 },
1136 {
1137 "name": "lattice_boundary_L22",
1138 "status": "PASS",
1139 "scope": "exact worked example"
1140 },
1141 {
1142 "name": "lattice_boundary_L23",
1143 "status": "PASS",
1144 "scope": "exact worked example"
1145 },
1146 {
1147 "name": "lattice_boundary_L24",
1148 "status": "PASS",
1149 "scope": "exact worked example"
1150 },
1151 {
1152 "name": "lattice_boundary_L25",
1153 "status": "PASS",
1154 "scope": "exact worked example"
1155 },
1156 {
1157 "name": "complete_lattice_tiles_zero",
1158 "status": "PASS",
1159 "scope": "exact worked example"
1160 },
1161 {
1162 "name": "boundary_area_at_12",
1163 "status": "PASS",
1164 "scope": "exact worked example"
1165 },
1166 {
1167 "name": "mellin_envelope_difference",
1168 "status": "PASS",
1169 "scope": "exact worked example"
1170 },
1171 {
1172 "name": "mellin_bound_h-1/4",
1173 "status": "PASS",
1174 "scope": "exact worked example"
1175 },
1176 {
1177 "name": "mellin_bound_h-1/8",
1178 "status": "PASS",
1179 "scope": "exact worked example"
1180 },
1181 {
1182 "name": "mellin_bound_h0",
1183 "status": "PASS",
1184 "scope": "exact worked example"
1185 },
1186 {
1187 "name": "mellin_bound_h1/8",
1188 "status": "PASS",
1189 "scope": "exact worked example"
1190 },
1191 {
1192 "name": "mellin_bound_h1/4",
1193 "status": "PASS",
1194 "scope": "exact worked example"
1195 },
1196 {
1197 "name": "mellin_derivative_at_one",
1198 "status": "PASS",
1199 "scope": "exact worked example"
1200 },
1201 {
1202 "name": "repeated_identity_trace_rows_rank_one",
1203 "status": "PASS",
1204 "scope": "exact worked example"
1205 },
1206 {
1207 "name": "quadratic_factorization_prime_3",
1208 "status": "PASS",
1209 "scope": "exact worked example"
1210 },
1211 {
1212 "name": "quadratic_factorization_prime_5",
1213 "status": "PASS",
1214 "scope": "exact worked example"
1215 },
1216 {
1217 "name": "quadratic_factorization_prime_7",
1218 "status": "PASS",
1219 "scope": "exact worked example"
1220 },
1221 {
1222 "name": "quadratic_factorization_prime_11",
1223 "status": "PASS",
1224 "scope": "exact worked example"
1225 },
1226 {
1227 "name": "quadratic_factorization_prime_13",
1228 "status": "PASS",
1229 "scope": "exact worked example"
1230 },
1231 {
1232 "name": "quadratic_factorization_prime_17",
1233 "status": "PASS",
1234 "scope": "exact worked example"
1235 },
1236 {
1237 "name": "quadratic_factorization_prime_19",
1238 "status": "PASS",
1239 "scope": "exact worked example"
1240 },
1241 {
1242 "name": "quadratic_factorization_prime_23",
1243 "status": "PASS",
1244 "scope": "exact worked example"
1245 },
1246 {
1247 "name": "quadratic_factorization_prime_29",
1248 "status": "PASS",
1249 "scope": "exact worked example"
1250 },
1251 {
1252 "name": "quadratic_factorization_prime_31",
1253 "status": "PASS",
1254 "scope": "exact worked example"
1255 },
1256 {
1257 "name": "quadratic_factorization_prime_37",
1258 "status": "PASS",
1259 "scope": "exact worked example"
1260 },
1261 {
1262 "name": "quadratic_factorization_prime_41",
1263 "status": "PASS",
1264 "scope": "exact worked example"
1265 },
1266 {
1267 "name": "quadratic_factorization_prime_43",
1268 "status": "PASS",
1269 "scope": "exact worked example"
1270 },
1271 {
1272 "name": "quadratic_factorization_prime_47",
1273 "status": "PASS",
1274 "scope": "exact worked example"
1275 },
1276 {
1277 "name": "matrix_root_exists_over_F3",
1278 "status": "PASS",
1279 "scope": "exact worked example"
1280 },
1281 {
1282 "name": "scalar_root_absent_over_F3",
1283 "status": "PASS",
1284 "scope": "exact worked example"
1285 },
1286 {
1287 "name": "extension_roots_over_F9",
1288 "status": "PASS",
1289 "scope": "exact worked example"
1290 },
1291 {
1292 "name": "companion_charpoly",
1293 "status": "PASS",
1294 "scope": "exact worked example"
1295 },
1296 {
1297 "name": "adding_F_to_G_reduces_source_rank",
1298 "status": "PASS",
1299 "scope": "exact worked example"
1300 },
1301 {
1302 "name": "every_smooth_parent_has_nine_children",
1303 "status": "PASS",
1304 "scope": "exact worked example"
1305 },
1306 {
1307 "name": "joint_packet_sum_identity",
1308 "status": "PASS",
1309 "scope": "exact worked example"
1310 },
1311 {
1312 "name": "joint_packet_pairwise_annihilation",
1313 "status": "PASS",
1314 "scope": "exact worked example"
1315 },
1316 {
1317 "name": "norm_basis_change_invariance_all25",
1318 "status": "PASS",
1319 "scope": "exact worked example"
1320 },
1321 {
1322 "name": "boundary_sum_at_12",
1323 "status": "PASS",
1324 "scope": "exact worked example"
1325 },
1326 {
1327 "name": "zero_bulk_at_12",
1328 "status": "PASS",
1329 "scope": "exact worked example"
1330 },
1331 {
1332 "name": "mellin_logarithmic_moment",
1333 "status": "PASS",
1334 "scope": "exact worked example"
1335 },
1336 {
1337 "name": "fourth_power_representation_over_Q",
1338 "status": "PASS",
1339 "scope": "exact worked example"
1340 }
1341 ],
1342 "negative_controls": [
1343 {
1344 "name": "arbitrary_residues_not_a_branch",
1345 "status": "REJECTED",
1346 "expected_reason": "Second residue must reduce to first.",
1347 "actual_exception": "ValueError"
1348 },
1349 {
1350 "name": "growing_counts_do_not_mean_all_nodes_lift",
1351 "status": "REJECTED",
1352 "expected_reason": "The depth-two node 3 has no child.",
1353 "actual_exception": "AssertionError"
1354 },
1355 {
1356 "name": "residual_root_does_not_ensure_deep_root",
1357 "status": "REJECTED",
1358 "expected_reason": "x^2+1 has a root mod 2 but no root mod 4.",
1359 "actual_exception": "AssertionError"
1360 },
1361 {
1362 "name": "degreewise_projectors_need_chain_condition",
1363 "status": "REJECTED",
1364 "expected_reason": "Degreewise idempotence does not imply differential compatibility.",
1365 "actual_exception": "AssertionError"
1366 },
1367 {
1368 "name": "one_seed_cannot_cover_three_sources",
1369 "status": "REJECTED",
1370 "expected_reason": "A seed outside a source component cannot reach it.",
1371 "actual_exception": "AssertionError"
1372 },
1373 {
1374 "name": "trace_solution_not_integral",
1375 "status": "REJECTED",
1376 "expected_reason": "Rational solution is not an integral multiplicity vector.",
1377 "actual_exception": "ValueError"
1378 },
1379 {
1380 "name": "negative_multiplicity",
1381 "status": "REJECTED",
1382 "expected_reason": "Representations do not have negative multiplicities.",
1383 "actual_exception": "ValueError"
1384 },
1385 {
1386 "name": "capacity_failure",
1387 "status": "REJECTED",
1388 "expected_reason": "Target multiplicity exceeds known carrier capacity.",
1389 "actual_exception": "ValueError"
1390 },
1391 {
1392 "name": "equal_precision_trace_recovery",
1393 "status": "REJECTED",
1394 "expected_reason": "Distinct multiplicities modulo 8 can give the same traces modulo 8.",
1395 "actual_exception": "AssertionError"
1396 },
1397 {
1398 "name": "pairwise_occupancy_does_not_imply_joint",
1399 "status": "REJECTED",
1400 "expected_reason": "The selected triple 011 is absent although each pair occurs.",
1401 "actual_exception": "AssertionError"
1402 },
1403 {
1404 "name": "lagrange_formula_without_semisimplicity",
1405 "status": "REJECTED",
1406 "expected_reason": "The sole-eigenvalue Lagrange product is I, not the ordinary eigenspace projector.",
1407 "actual_exception": "AssertionError"
1408 },
1409 {
1410 "name": "absolute_norm_is_residue_function_over_Q",
1411 "status": "REJECTED",
1412 "expected_reason": "Opposite real signs can change absolute-norm residues.",
1413 "actual_exception": "AssertionError"
1414 },
1415 {
1416 "name": "nontrivial_scalar_character_alone_insufficient",
1417 "status": "REJECTED",
1418 "expected_reason": "A nontrivial quadratic character is trivial on every scalar square.",
1419 "actual_exception": "AssertionError"
1420 },
1421 {
1422 "name": "no_scalar_root_does_not_mean_no_representation",
1423 "status": "REJECTED",
1424 "expected_reason": "A 2 by 2 companion matrix realizes the equation over F3.",
1425 "actual_exception": "AssertionError"
1426 }
1427 ],
1428 "limits": [
1429 "Exact finite results do not assert an infinite arithmetic existence theorem.",
1430 "The finite-tail counterexample and Mellin analytic argument have their stated prose proofs, not proofs inferred from sampling.",
1431 "No fresh Lean compilation."
1432 ],
1433 "data": {
1434 "quarter_residues": [
1435 4,
1436 19,
1437 94,
1438 469,
1439 2344,
1440 11719
1441 ],
1442 "weighted_counts": [
1443 1,
1444 2,
1445 8,
1446 32,
1447 256,
1448 2048,
1449 16384
1450 ],
1451 "norm_fiber_counts": [
1452 1,
1453 6,
1454 6,
1455 6,
1456 6
1457 ],
1458 "lattice_side_12_sum": 1,
1459 "source_components": [
1460 [
1461 "A",
1462 "B"
1463 ],
1464 [
1465 "C"
1466 ],
1467 [
1468 "D",
1469 "E"
1470 ],
1471 [
1472 "F"
1473 ],
1474 [
1475 "G"
1476 ]
1477 ],
1478 "minimum_seed_sets": [
1479 [
1480 "A",
1481 "D",
1482 "G"
1483 ],
1484 [
1485 "A",
1486 "E",
1487 "G"
1488 ],
1489 [
1490 "B",
1491 "D",
1492 "G"
1493 ],
1494 [
1495 "B",
1496 "E",
1497 "G"
1498 ]
1499 ]
1500 },
1501 "source_sha256": {
1502 "source/models.py": "47727d61f486819929352395a1bf840dc443e68c075e855517d07e6877705149",
1503 "checks/verify_examples.py": "d2ba2641bd3d130fa8b258d579677563a06063badf4f4315d8d7aa893e3806a5"
1504 }
1505 }
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Back to Paper X: Universal Residual Seeds and Conditional Occupied-System Completion