{"schema":1,"source_inputs":{"monographs/large-signal-model/Visual_Companion/atlas.tex":"774a2149554f1778b9eeb49530ebacbc5febaaa9d20702c8de863006f568314a","monographs/large-signal-model/Visual_Companion/build/Realization_Calculus_Large_Signal_Model_Theoretical_Atlas.pdf":"ac716187177adb4afdfec9d23889c90787cae29b9db90550d10348fb321cabfe","monographs/large-signal-model/Visual_Companion/PROOF_MAP.json":"df68ebfb5a6e2a4093e22d02725b08d49671a7092ba8299eff1e3833d851737c","monographs/large-signal-model/Visual_Companion/FIGURES.json":"c6650c9df234d52a7a4d65e62df43fa475761d49ab32f7297545374b029b91d6","monographs/large-signal-model/Visual_Companion/figures/exact_example.json":"e19a04469a8d7d1e3263b2553815ca424ce131206e1a4b01472afae0d406ef5d","monographs/large-signal-model/Visual_Companion/generate_figures.py":"a881bb7763522167374683fe45965fff75cc6d9ccee49398c35bd78f7b2d440f"},"source_revision":"2a809785bea01d2eeee161d339dba69a1ef13f1e","index":"read/monographs-large-signal-model/atlas/index.html","original_plates":17,"orientation_pages":1,"html_pages":[{"number":0,"url":"read/monographs-large-signal-model/atlas/orientation.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":54,"end_line":70,"math_expressions":5,"math_sequence_sha256":"b835f4f1fd7888efb6c191079d718af905ca8c240cd1710d22cc2b68a21da438","nodes":[{"id":"L54","line":54,"kind":"text"},{"id":"L55","line":55,"kind":"figure"},{"id":"L56","line":56,"kind":"tabular"},{"id":"L65","line":65,"kind":"text"},{"id":"L69","line":69,"kind":"readerroadmap"}]},{"number":1,"url":"read/monographs-large-signal-model/atlas/v01.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":71,"end_line":85,"math_expressions":12,"math_sequence_sha256":"1d9d0e953429aa85a370706bc7064d02b860add3594f84d84fd9b975efc689aa","nodes":[{"id":"L72","line":72,"kind":"text"},{"id":"L76","line":76,"kind":"figure"},{"id":"L77","line":77,"kind":"text"},{"id":"L82","line":82,"kind":"readerroadmap"},{"id":"L83","line":83,"kind":"readerroadmap"},{"id":"L84","line":84,"kind":"readerroadmap"}]},{"number":2,"url":"read/monographs-large-signal-model/atlas/v02.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":86,"end_line":105,"math_expressions":9,"math_sequence_sha256":"a33719dfeeed3fd56ca1dc7cb792b074f5e5d59a660c7964431282869a0b1291","nodes":[{"id":"L87","line":87,"kind":"text"},{"id":"L88","line":88,"kind":"figure"},{"id":"L89","line":89,"kind":"text"},{"id":"L97","line":97,"kind":"readerroadmap"},{"id":"L98","line":98,"kind":"text"},{"id":"L103","line":103,"kind":"readerroadmap"},{"id":"L104","line":104,"kind":"readerroadmap"}]},{"number":3,"url":"read/monographs-large-signal-model/atlas/v03.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":106,"end_line":122,"math_expressions":10,"math_sequence_sha256":"7af95e7a3a88ac7c6606d6d27ff2b5c68601192b25ec09048bfbfa659a899f2a","nodes":[{"id":"L107","line":107,"kind":"text"},{"id":"L112","line":112,"kind":"figure"},{"id":"L113","line":113,"kind":"text"},{"id":"L119","line":119,"kind":"readerroadmap"},{"id":"L120","line":120,"kind":"readerroadmap"},{"id":"L121","line":121,"kind":"readerroadmap"}]},{"number":4,"url":"read/monographs-large-signal-model/atlas/v04.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":123,"end_line":140,"math_expressions":14,"math_sequence_sha256":"fd78ce2b8531515b6c12f22bd297fd0e347f997aa59cabc31781ac9cd7a76123","nodes":[{"id":"L124","line":124,"kind":"text"},{"id":"L128","line":128,"kind":"figure"},{"id":"L129","line":129,"kind":"text"},{"id":"L137","line":137,"kind":"readerroadmap"},{"id":"L138","line":138,"kind":"readerroadmap"},{"id":"L139","line":139,"kind":"readerroadmap"}]},{"number":5,"url":"read/monographs-large-signal-model/atlas/v05.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":141,"end_line":157,"math_expressions":5,"math_sequence_sha256":"a733afe4081ece1e8d729951e3299fa8d7aa0543613d22f5a9f2d036314a3c1b","nodes":[{"id":"L142","line":142,"kind":"text"},{"id":"L147","line":147,"kind":"figure"},{"id":"L148","line":148,"kind":"text"},{"id":"L154","line":154,"kind":"readerroadmap"},{"id":"L155","line":155,"kind":"readerroadmap"},{"id":"L156","line":156,"kind":"readerroadmap"}]},{"number":6,"url":"read/monographs-large-signal-model/atlas/v06.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":158,"end_line":179,"math_expressions":14,"math_sequence_sha256":"afe3c98611f3673139cedef43242f8878e1df23164d3b7a026f3260fc709bc82","nodes":[{"id":"L159","line":159,"kind":"text"},{"id":"L163","line":163,"kind":"figure"},{"id":"L164","line":164,"kind":"text"},{"id":"L176","line":176,"kind":"readerroadmap"},{"id":"L177","line":177,"kind":"readerroadmap"},{"id":"L178","line":178,"kind":"readerroadmap"}]},{"number":7,"url":"read/monographs-large-signal-model/atlas/v07.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":180,"end_line":200,"math_expressions":17,"math_sequence_sha256":"23552950c1e0971abb87730e235e136046bed5cdefd5a3a7f279c3888b89221c","nodes":[{"id":"L181","line":181,"kind":"text"},{"id":"L185","line":185,"kind":"figure"},{"id":"L186","line":186,"kind":"text"},{"id":"L198","line":198,"kind":"readerroadmap"},{"id":"L199","line":199,"kind":"readerroadmap"}]},{"number":8,"url":"read/monographs-large-signal-model/atlas/v08.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":201,"end_line":220,"math_expressions":10,"math_sequence_sha256":"1dd5547cbd1c343b65c908e83052181e302fe84670268d6f5b57d495ae73ec8e","nodes":[{"id":"L202","line":202,"kind":"text"},{"id":"L211","line":211,"kind":"figure"},{"id":"L212","line":212,"kind":"text"},{"id":"L217","line":217,"kind":"readerroadmap"},{"id":"L218","line":218,"kind":"readerroadmap"},{"id":"L219","line":219,"kind":"readerroadmap"}]},{"number":9,"url":"read/monographs-large-signal-model/atlas/v09.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":221,"end_line":237,"math_expressions":8,"math_sequence_sha256":"d20c777ac4e0ee507063075080b3fe522e8005dab8ef7862067db14bd47361ae","nodes":[{"id":"L222","line":222,"kind":"text"},{"id":"L228","line":228,"kind":"figure"},{"id":"L229","line":229,"kind":"text"},{"id":"L234","line":234,"kind":"readerroadmap"},{"id":"L235","line":235,"kind":"readerroadmap"},{"id":"L236","line":236,"kind":"readerroadmap"}]},{"number":10,"url":"read/monographs-large-signal-model/atlas/v10.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":238,"end_line":259,"math_expressions":8,"math_sequence_sha256":"33e652f63de846a2926431e6d5b89886b5612c1dfb2e3da3352587e2fc59c1e9","nodes":[{"id":"L239","line":239,"kind":"text"},{"id":"L253","line":253,"kind":"readerroadmap"},{"id":"L255","line":255,"kind":"text"},{"id":"L257","line":257,"kind":"readerroadmap"},{"id":"L258","line":258,"kind":"readerroadmap"}]},{"number":11,"url":"read/monographs-large-signal-model/atlas/v11.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":260,"end_line":276,"math_expressions":12,"math_sequence_sha256":"ecaa38f51436a8f54561f9cc3c8d3bf178c9f9c6cee59d1c79858006c752985d","nodes":[{"id":"L261","line":261,"kind":"text"},{"id":"L265","line":265,"kind":"figure"},{"id":"L266","line":266,"kind":"text"},{"id":"L273","line":273,"kind":"readerroadmap"},{"id":"L274","line":274,"kind":"readerroadmap"},{"id":"L275","line":275,"kind":"readerroadmap"}]},{"number":12,"url":"read/monographs-large-signal-model/atlas/v12.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":277,"end_line":294,"math_expressions":9,"math_sequence_sha256":"532441f104d1bd835ba440b32689b4a69a2731efb2c393c3593adf18e20d8c6d","nodes":[{"id":"L278","line":278,"kind":"text"},{"id":"L283","line":283,"kind":"figure"},{"id":"L284","line":284,"kind":"text"},{"id":"L291","line":291,"kind":"readerroadmap"},{"id":"L292","line":292,"kind":"readerroadmap"},{"id":"L293","line":293,"kind":"readerroadmap"}]},{"number":13,"url":"read/monographs-large-signal-model/atlas/v13.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":295,"end_line":310,"math_expressions":15,"math_sequence_sha256":"2fd77a40b0449862de80a0885945aca72d76068bb4d77fba445619081ebbba48","nodes":[{"id":"L296","line":296,"kind":"text"},{"id":"L301","line":301,"kind":"figure"},{"id":"L302","line":302,"kind":"text"},{"id":"L307","line":307,"kind":"readerroadmap"},{"id":"L308","line":308,"kind":"readerroadmap"},{"id":"L309","line":309,"kind":"readerroadmap"}]},{"number":14,"url":"read/monographs-large-signal-model/atlas/v14.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":311,"end_line":326,"math_expressions":14,"math_sequence_sha256":"f88b5215035e93446973e2d7c6508302ad7355919147e2edc872f554774ff99a","nodes":[{"id":"L312","line":312,"kind":"text"},{"id":"L317","line":317,"kind":"figure"},{"id":"L318","line":318,"kind":"text"},{"id":"L323","line":323,"kind":"readerroadmap"},{"id":"L324","line":324,"kind":"readerroadmap"},{"id":"L325","line":325,"kind":"readerroadmap"}]},{"number":15,"url":"read/monographs-large-signal-model/atlas/v15.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":327,"end_line":342,"math_expressions":15,"math_sequence_sha256":"1aaf5d9fd6e3e868ba63f35f67d50c8796948b4d8d9a662a9ff1f51a17a8f15c","nodes":[{"id":"L328","line":328,"kind":"text"},{"id":"L333","line":333,"kind":"figure"},{"id":"L334","line":334,"kind":"text"},{"id":"L339","line":339,"kind":"readerroadmap"},{"id":"L340","line":340,"kind":"readerroadmap"},{"id":"L341","line":341,"kind":"readerroadmap"}]},{"number":16,"url":"read/monographs-large-signal-model/atlas/v16.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":343,"end_line":355,"math_expressions":10,"math_sequence_sha256":"48a9f1f310fd5b32e5a2cc0e5d9009ba51657de8c2460280557e8a1550639048","nodes":[{"id":"L344","line":344,"kind":"text"},{"id":"L345","line":345,"kind":"figure"},{"id":"L346","line":346,"kind":"text"},{"id":"L352","line":352,"kind":"readerroadmap"},{"id":"L353","line":353,"kind":"readerroadmap"},{"id":"L354","line":354,"kind":"readerroadmap"}]},{"number":17,"url":"read/monographs-large-signal-model/atlas/v17.html","source":"monographs/large-signal-model/Visual_Companion/atlas.tex","start_line":356,"end_line":377,"math_expressions":7,"math_sequence_sha256":"b9258c16b56303da7a81993c65460824e19846554439b123684956ff952f5119","nodes":[{"id":"L357","line":357,"kind":"text"},{"id":"L360","line":360,"kind":"tabular"},{"id":"L373","line":373,"kind":"text"}]}],"figures":[{"source":"monographs/large-signal-model/Visual_Companion/figures/00_architecture.pdf","source_sha256":"a33b89b1ba298694db9bf36992c6013e0199706a991329c779fbf618e90cc9a2","image":"assets/atlas/monographs-large-signal-model/00_architecture.png","image_sha256":"083df591e0e2434f7aa74d149eb9eefb4f9b8a8c69596b73a7c062bad50d98f7","interpretation":"Typed map diagram; exact contract definitions","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/01_consistency.pdf","source_sha256":"ca959bacc2a5fb085ad048692aef7944e8658e47f3b92d1a8c2255ea0b802b64","image":"assets/atlas/monographs-large-signal-model/01_consistency.png","image_sha256":"0cc78027e0bdb59701379f652049a1c3f7567e9e135e5958bd5354b1fd9fd463","interpretation":"Geometric redundant-linear-archive example","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/02_transport.pdf","source_sha256":"26d9b8eb39119ff226b69a89e41a9805c2ca2ced5a10a7261edd541795b2d5b3","image":"assets/atlas/monographs-large-signal-model/02_transport.png","image_sha256":"38f5d803a4fd88fe5bc41d32d577af86b7da25a56b968d3950fbb893589fa7da","interpretation":"Exact commuting square","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/03_fibers.pdf","source_sha256":"724e6a5d9bf5524d64bc6b057e1a6f06d44326447e5237e2e1ba1315f5f9a087","image":"assets/atlas/monographs-large-signal-model/03_fibers.png","image_sha256":"6236c521c1bb59b1b6dfb14ca7da701a7b8395247217c904631ae91c6fb18923","interpretation":"Exact rational closure counterexample","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/04_refinement.pdf","source_sha256":"7aec3e6cc56e5c28fbd945382ec53f39af8d54e0816b8b137d5f30abc9c50f41","image":"assets/atlas/monographs-large-signal-model/04_refinement.png","image_sha256":"cda0a786a83a734efaac26b2ca28205cb6b71b2873e64a08faf3e5d3222fb99b","interpretation":"Exact row-space completion example","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/05_packets.pdf","source_sha256":"dbf2283e95c1515b4ed7fec29d4ec83b575d39f59214afdfcdaa55c1b80ff6f7","image":"assets/atlas/monographs-large-signal-model/05_packets.png","image_sha256":"1303c5126613a79b28536cfefe2cbdc3f3759bb5c5978f5b9f3660f3edaab1a6","interpretation":"Exact transfer entries and analytical polynomial terms","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/06_return_path.pdf","source_sha256":"89c4c037dda68a2ad4b2921cd67f3962a71a9e709438e4e4eb631b2c59e02935","image":"assets/atlas/monographs-large-signal-model/06_return_path.png","image_sha256":"85681ab5bd00f5754fd4557cc8f10dd7c57eb95fb022476a23103172e54b6acd","interpretation":"Exact compositional obstruction diagram","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/07_memory.pdf","source_sha256":"8106dd9ddb46d6bed804c1a0c82aa88774a03d53aaa422e0f129c3a214e69634","image":"assets/atlas/monographs-large-signal-model/07_memory.png","image_sha256":"6e89c23dbbe1ceca7fbd83fb23b8b78e20591ab3808209a809f89ece361c1a6b","interpretation":"Exact rational trajectory rendered numerically; analytical kernel coefficients","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/08_defect.pdf","source_sha256":"c54a65535ecf3baa7b68c819e0a60a049cfb4bed4ba40326fa147e14676ed83f","image":"assets/atlas/monographs-large-signal-model/08_defect.png","image_sha256":"29f5bb625a9821396f60d21654025087ec777e3bff235b13ee2c8d7cde2b1d4e","interpretation":"Analytical upper bounds with declared constants, not observed errors","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/09_identification.pdf","source_sha256":"2b04e63b633ae42951ff6a926049e4e9821ccf54a976758569af6cc8fe42438d","image":"assets/atlas/monographs-large-signal-model/09_identification.png","image_sha256":"adf66415ae32e297715416736c5c0e4c1491f1b1434b2d24efd84e3d074ec35c","interpretation":"Exact rational paired history states","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/10_domain.pdf","source_sha256":"4cfed24a03398a3fa130a86c0d05391392b3e2797b403ad57f1edba9490e704d","image":"assets/atlas/monographs-large-signal-model/10_domain.png","image_sha256":"8753d70df25838bb6c9f4c9ecfdaab1405798475355cd03c7ca8d736d0232dd2","interpretation":"Exact instrument semantics diagram","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/11_psd.pdf","source_sha256":"8e97e9bae8226ac6c6be63d9595c06d1d99bdf126a151fed965e02e3d3e0c856","image":"assets/atlas/monographs-large-signal-model/11_psd.png","image_sha256":"c7fb0c2be0366b88a781da16ceb86eebfd1072a590d380be7edda7fbfac06faa","interpretation":"Finite orbit illustration and exact cone/matrix equivalence","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/12_covariance.pdf","source_sha256":"af4b820eb6f5d1abde56412b7fb77e4250a01887e9b12275cf3da47aa2a3b45a","image":"assets/atlas/monographs-large-signal-model/12_covariance.png","image_sha256":"3b371f5b2edbce2423e74da36b8c5be8f6e5c63a23b1440343d1dc4a9478c635","interpretation":"Analytical quadratic and exact covariance identity","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/13_moments.pdf","source_sha256":"dedc1f3ee760c107288bd9be7c8a80a726d131ed39bc084965d75fa20123e255","image":"assets/atlas/monographs-large-signal-model/13_moments.png","image_sha256":"fab236e520d0ad83ae699279fbd4270b3be3e72f5add7e36e360acf7a1736712","interpretation":"Exact normalized moment domain and genuine 3D homogeneous boundary wireframe","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/14_uncertainty.pdf","source_sha256":"93ad7f982236e892b50cd6cb806ea955e9cfcdb3722b040ed0d36b9e2704ef7c","image":"assets/atlas/monographs-large-signal-model/14_uncertainty.png","image_sha256":"ea60d129ec6641d959db7450fda475bd6c06d58d6b80cab7d77f9f903ea458bd","interpretation":"Schematic parameter-set inclusion, not estimated coverage","scale":2},{"source":"monographs/large-signal-model/Visual_Companion/figures/15_horizons.pdf","source_sha256":"3e102e770304c9c4efbfb72ba9a2a102f20b26ecf7a4830c84ed435013b4e81f","image":"assets/atlas/monographs-large-signal-model/15_horizons.png","image_sha256":"8254711bd54634748d481935da3789c1e9b663b501f50e353b4feb1eac13fc6a","interpretation":"Analytical upper bounds with declared constants, not empirical errors","scale":2}],"proof_routes":{"1":[{"number":1,"title":"Exact realization and consistency","statement":"read/monographs-large-signal-model/2-exact-realization-and-atlas-consistency.html#L34","proof":"read/monographs-large-signal-model/2-exact-realization-and-atlas-consistency.html#L43","scope":"read/monographs-large-signal-model/formal-scope.html#p1","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Normed.lean","url":"read/monographs-large-signal-model/normed-949a928d4b38.html","label":"KomorebiLSM/Normed.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Realization.lean","url":"read/monographs-large-signal-model/realization-631171dbbcd3.html","label":"KomorebiLSM/Realization.lean"}]}],"2":[{"number":2,"title":"Coherent transport and operator realization","statement":"read/monographs-large-signal-model/3-coordinate-transport-and-one-underlying-operator.html#L73","proof":"read/monographs-large-signal-model/3-coordinate-transport-and-one-underlying-operator.html#L82","scope":"read/monographs-large-signal-model/formal-scope.html#p2","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Realization.lean","url":"read/monographs-large-signal-model/realization-631171dbbcd3.html","label":"KomorebiLSM/Realization.lean"}]}],"3":[{"number":6,"title":"Exact quotient criterion","statement":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L193","proof":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L202","scope":"read/monographs-large-signal-model/formal-scope.html#p6","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictiveClosure.lean","url":"read/monographs-large-signal-model/predictiveclosure-041f5539ebda.html","label":"KomorebiLSM/PredictiveClosure.lean"}]},{"number":7,"title":"Closure defect and compositional defect","statement":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L216","proof":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L231","scope":"read/monographs-large-signal-model/formal-scope.html#p7","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/LinearClosure.lean","url":"read/monographs-large-signal-model/linearclosure-57adb17a2e78.html","label":"KomorebiLSM/LinearClosure.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Normed.lean","url":"read/monographs-large-signal-model/normed-949a928d4b38.html","label":"KomorebiLSM/Normed.lean"}]}],"4":[{"number":8,"title":"Minimal linear predictive completion","statement":"read/monographs-large-signal-model/6-constructing-the-smallest-closed-linear-refinement.html#L248","proof":"read/monographs-large-signal-model/6-constructing-the-smallest-closed-linear-refinement.html#L256","scope":"read/monographs-large-signal-model/formal-scope.html#p8","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/InvariantCompletion.lean","url":"read/monographs-large-signal-model/invariantcompletion-9a310c24b987.html","label":"KomorebiLSM/InvariantCompletion.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictiveCompletion.lean","url":"read/monographs-large-signal-model/predictivecompletion-01b8c7ecdb90.html","label":"KomorebiLSM/PredictiveCompletion.lean"}]},{"number":14,"title":"Exact causal delay closure","statement":"read/monographs-large-signal-model/15-from-hidden-state-to-an-accessible-predictive-state.html#L580","proof":"read/monographs-large-signal-model/15-from-hidden-state-to-an-accessible-predictive-state.html#L588","scope":"read/monographs-large-signal-model/formal-scope.html#p14","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/DelayClosure.lean","url":"read/monographs-large-signal-model/delayclosure-1be44d841783.html","label":"KomorebiLSM/DelayClosure.lean"}]}],"5":[{"number":3,"title":"Complete refinement preserves reconstruction","statement":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L115","proof":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L123","scope":"read/monographs-large-signal-model/formal-scope.html#p3","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PacketTree.lean","url":"read/monographs-large-signal-model/packettree-c3df089b3b86.html","label":"KomorebiLSM/PacketTree.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/TreeEnergy.lean","url":"read/monographs-large-signal-model/treeenergy-cbebfeb8882b.html","label":"KomorebiLSM/TreeEnergy.lean"}]},{"number":4,"title":"Transfer reconstruction and refinement","statement":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L139","proof":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L157","scope":"read/monographs-large-signal-model/formal-scope.html#p4","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Transfer.lean","url":"read/monographs-large-signal-model/transfer-fedf1a2908c2.html","label":"KomorebiLSM/Transfer.lean"}]},{"number":5,"title":"Polynomial packet interactions","statement":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L165","proof":"read/monographs-large-signal-model/4-packets-refinement-and-transfer-blocks.html#L179","scope":"read/monographs-large-signal-model/formal-scope.html#p5","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Polynomial.lean","url":"read/monographs-large-signal-model/polynomial-9b8fec078276.html","label":"KomorebiLSM/Polynomial.lean"}]},{"number":20,"title":"Packet-interaction truncation bound","statement":"read/monographs-large-signal-model/21-nonlinear-packet-truncation-with-an-explicit-remainder.html#L904","proof":"read/monographs-large-signal-model/21-nonlinear-packet-truncation-with-an-explicit-remainder.html#L922","scope":"read/monographs-large-signal-model/formal-scope.html#p20","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PacketApproximation.lean","url":"read/monographs-large-signal-model/packetapproximation-9b501523309e.html","label":"KomorebiLSM/PacketApproximation.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ReconciliationHilbert.lean","url":"read/monographs-large-signal-model/reconciliationhilbert-8cfe55974667.html","label":"KomorebiLSM/ReconciliationHilbert.lean"}]}],"6":[{"number":7,"title":"Closure defect and compositional defect","statement":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L216","proof":"read/monographs-large-signal-model/5-predictive-closure-is-the-central-contract.html#L231","scope":"read/monographs-large-signal-model/formal-scope.html#p7","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/LinearClosure.lean","url":"read/monographs-large-signal-model/linearclosure-57adb17a2e78.html","label":"KomorebiLSM/LinearClosure.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Normed.lean","url":"read/monographs-large-signal-model/normed-949a928d4b38.html","label":"KomorebiLSM/Normed.lean"}]}],"7":[{"number":10,"title":"Exact projected memory and a conditional tail bound","statement":"read/monographs-large-signal-model/8-memory-is-an-exact-alternative-to-adding-state.html#L332","proof":"read/monographs-large-signal-model/8-memory-is-an-exact-alternative-to-adding-state.html#L349","scope":"read/monographs-large-signal-model/formal-scope.html#p10","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Memory.lean","url":"read/monographs-large-signal-model/memory-ea99617aa47f.html","label":"KomorebiLSM/Memory.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MemoryBounds.lean","url":"read/monographs-large-signal-model/memorybounds-73b6d9f6b59a.html","label":"KomorebiLSM/MemoryBounds.lean"}]},{"number":19,"title":"Uniform prediction bound for a stable finite-memory truncation","statement":"read/monographs-large-signal-model/20-truncating-memory-without-losing-the-prediction-bound.html#L832","proof":"read/monographs-large-signal-model/20-truncating-memory-without-losing-the-prediction-bound.html#L861","scope":"read/monographs-large-signal-model/formal-scope.html#p19","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MemoryApproximation.lean","url":"read/monographs-large-signal-model/memoryapproximation-b12be24138bc.html","label":"KomorebiLSM/MemoryApproximation.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MemoryStability.lean","url":"read/monographs-large-signal-model/memorystability-bf26344a8554.html","label":"KomorebiLSM/MemoryStability.lean"}]}],"8":[{"number":18,"title":"Compositional defect propagation","statement":"read/monographs-large-signal-model/19-a-single-propagation-law-for-typed-defects.html#L746","proof":"read/monographs-large-signal-model/19-a-single-propagation-law-for-typed-defects.html#L768","scope":"read/monographs-large-signal-model/formal-scope.html#p18","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/DefectPropagation.lean","url":"read/monographs-large-signal-model/defectpropagation-f059169968a1.html","label":"KomorebiLSM/DefectPropagation.lean"}]}],"9":[{"number":14,"title":"Exact causal delay closure","statement":"read/monographs-large-signal-model/15-from-hidden-state-to-an-accessible-predictive-state.html#L580","proof":"read/monographs-large-signal-model/15-from-hidden-state-to-an-accessible-predictive-state.html#L588","scope":"read/monographs-large-signal-model/formal-scope.html#p14","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/DelayClosure.lean","url":"read/monographs-large-signal-model/delayclosure-1be44d841783.html","label":"KomorebiLSM/DelayClosure.lean"}]},{"number":15,"title":"Data-span identification and its boundary","statement":"read/monographs-large-signal-model/16-what-finite-data-identify.html#L602","proof":"read/monographs-large-signal-model/16-what-finite-data-identify.html#L616","scope":"read/monographs-large-signal-model/formal-scope.html#p15","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/DataSpan.lean","url":"read/monographs-large-signal-model/dataspan-e03806ff6027.html","label":"KomorebiLSM/DataSpan.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/Pseudoinverse.lean","url":"read/monographs-large-signal-model/pseudoinverse-e823265c0ac3.html","label":"KomorebiLSM/Pseudoinverse.lean"}]},{"number":16,"title":"Fixed-space identification bound","statement":"read/monographs-large-signal-model/16-what-finite-data-identify.html#L638","proof":"read/monographs-large-signal-model/16-what-finite-data-identify.html#L656","scope":"read/monographs-large-signal-model/formal-scope.html#p16","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/IdentificationBound.lean","url":"read/monographs-large-signal-model/identificationbound-c3862aa9ec38.html","label":"KomorebiLSM/IdentificationBound.lean"}]},{"number":17,"title":"Finite-prefix indistinguishability","statement":"read/monographs-large-signal-model/17-why-finite-agreement-is-not-unrestricted-discovery.html#L666","proof":"read/monographs-large-signal-model/17-why-finite-agreement-is-not-unrestricted-discovery.html#L668","scope":"read/monographs-large-signal-model/formal-scope.html#p17","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/FinitePrefix.lean","url":"read/monographs-large-signal-model/finiteprefix-5a2574801de3.html","label":"KomorebiLSM/FinitePrefix.lean"}]}],"10":[{"number":27,"title":"Minimal finite behavior realization","statement":"read/monographs-large-signal-model/28-the-state-is-a-function-of-possible-future-experiments.html#L1217","proof":"read/monographs-large-signal-model/28-the-state-is-a-function-of-possible-future-experiments.html#L1226","scope":"read/monographs-large-signal-model/formal-scope.html#p27","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BehaviorMinimality.lean","url":"read/monographs-large-signal-model/behaviorminimality-ebb598ee29a0.html","label":"KomorebiLSM/BehaviorMinimality.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BehaviorProbability.lean","url":"read/monographs-large-signal-model/behaviorprobability-3e83d8699960.html","label":"KomorebiLSM/BehaviorProbability.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BehaviorSpace.lean","url":"read/monographs-large-signal-model/behaviorspace-1024fdbe0023.html","label":"KomorebiLSM/BehaviorSpace.lean"}]},{"number":28,"title":"Observable table reconstruction","statement":"read/monographs-large-signal-model/29-recovering-the-operators-from-an-observable-probability-table.html#L1256","proof":"read/monographs-large-signal-model/29-recovering-the-operators-from-an-observable-probability-table.html#L1270","scope":"read/monographs-large-signal-model/formal-scope.html#p28","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableCore.lean","url":"read/monographs-large-signal-model/observablecore-19fabc681e31.html","label":"KomorebiLSM/ObservableCore.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableRealization.lean","url":"read/monographs-large-signal-model/observablerealization-5fe979516ac1.html","label":"KomorebiLSM/ObservableRealization.lean"}]}],"11":[{"number":29,"title":"Canonical probability cone","statement":"read/monographs-large-signal-model/30-probability-validity-is-not-a-rank-condition.html#L1288","proof":"read/monographs-large-signal-model/30-probability-validity-is-not-a-rank-condition.html#L1302","scope":"read/monographs-large-signal-model/formal-scope.html#p29","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CanonicalCone.lean","url":"read/monographs-large-signal-model/canonicalcone-cc6959fd2823.html","label":"KomorebiLSM/CanonicalCone.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/TestTopology.lean","url":"read/monographs-large-signal-model/testtopology-546889c5bc84.html","label":"KomorebiLSM/TestTopology.lean"}]},{"number":39,"title":"Finite positive-lift certificate","statement":"read/monographs-large-signal-model/43-a-finite-certificate-with-a-positive-lift.html#L1758","proof":"read/monographs-large-signal-model/43-a-finite-certificate-with-a-positive-lift.html#L1774","scope":"read/monographs-large-signal-model/formal-scope.html#p39","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveLift.lean","url":"read/monographs-large-signal-model/positivelift-9495afc6f9bc.html","label":"KomorebiLSM/PositiveLift.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveLiftTopology.lean","url":"read/monographs-large-signal-model/positivelifttopology-5e4998f39e3b.html","label":"KomorebiLSM/PositiveLiftTopology.lean"}]},{"number":40,"title":"Robust finite-domain certificate","statement":"read/monographs-large-signal-model/44-robustness-is-a-quantified-invariance-statement.html#L1794","proof":"read/monographs-large-signal-model/44-robustness-is-a-quantified-invariance-statement.html#L1814","scope":"read/monographs-large-signal-model/formal-scope.html#p40","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/FacetRobustness.lean","url":"read/monographs-large-signal-model/facetrobustness-24260f9e3b69.html","label":"KomorebiLSM/FacetRobustness.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RobustFiniteDomains.lean","url":"read/monographs-large-signal-model/robustfinitedomains-260c1b08d09f.html","label":"KomorebiLSM/RobustFiniteDomains.lean"}]}],"12":[{"number":46,"title":"A rational rank-three model with no polyhedral probability-domain certificate","statement":"read/monographs-large-signal-model/51-why-finite-predictive-rank-need-not-mean-finitely-many-positive-states.html#L2048","proof":"read/monographs-large-signal-model/51-why-finite-predictive-rank-need-not-mean-finitely-many-positive-states.html#L2056","scope":"read/monographs-large-signal-model/formal-scope.html#p46","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RotationConeGeometry.lean","url":"read/monographs-large-signal-model/rotationconegeometry-6f0c628a36b5.html","label":"KomorebiLSM/RotationConeGeometry.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RotationDensity.lean","url":"read/monographs-large-signal-model/rotationdensity-15b287ade9a4.html","label":"KomorebiLSM/RotationDensity.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RotationModel.lean","url":"read/monographs-large-signal-model/rotationmodel-4b5a833e6609.html","label":"KomorebiLSM/RotationModel.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RotationP46.lean","url":"read/monographs-large-signal-model/rotationp46-6267e8edb058.html","label":"KomorebiLSM/RotationP46.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RotationRank.lean","url":"read/monographs-large-signal-model/rotationrank-3d55cf7ac9eb.html","label":"KomorebiLSM/RotationRank.lean"}]},{"number":50,"title":"Matrix-embedding probability certificate","statement":"read/monographs-large-signal-model/56-a-matrix-certificate-for-a-curved-domain.html#L2197","proof":"read/monographs-large-signal-model/56-a-matrix-certificate-for-a-curved-domain.html#L2214","scope":"read/monographs-large-signal-model/formal-scope.html#p50","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MatrixEmbedding.lean","url":"read/monographs-large-signal-model/matrixembedding-221e40cbbd79.html","label":"KomorebiLSM/MatrixEmbedding.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MatrixOrderUnit.lean","url":"read/monographs-large-signal-model/matrixorderunit-908ce089bb2e.html","label":"KomorebiLSM/MatrixOrderUnit.lean"}]},{"number":51,"title":"Exact rational matrix witness for the rotation model","statement":"read/monographs-large-signal-model/57-the-earlier-disk-obstruction-has-an-exact-finite-matrix-witness.html#L2245","proof":"read/monographs-large-signal-model/57-the-earlier-disk-obstruction-has-an-exact-finite-matrix-witness.html#L2264","scope":"read/monographs-large-signal-model/formal-scope.html#p51","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MatrixRotation.lean","url":"read/monographs-large-signal-model/matrixrotation-6abca95a7994.html","label":"KomorebiLSM/MatrixRotation.lean"}]}],"13":[{"number":56,"title":"Exact bin coarsening and its posterior","statement":"read/monographs-large-signal-model/62-exact-observation-bins-preserve-their-own-event-law.html#L2463","proof":"read/monographs-large-signal-model/62-exact-observation-bins-preserve-their-own-event-law.html#L2470","scope":"read/monographs-large-signal-model/formal-scope.html#p56","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ContinuousBinnedRecords.lean","url":"read/monographs-large-signal-model/continuousbinnedrecords-e487b8f80672.html","label":"KomorebiLSM/ContinuousBinnedRecords.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ContinuousBins.lean","url":"read/monographs-large-signal-model/continuousbins-92a9a1c68c3c.html","label":"KomorebiLSM/ContinuousBins.lean"}]},{"number":57,"title":"Exact covariance correction for an averaged congruence","statement":"read/monographs-large-signal-model/63-averaging-transformations-has-a-covariance-defect.html#L2480","proof":"read/monographs-large-signal-model/63-averaging-transformations-has-a-covariance-defect.html#L2492","scope":"read/monographs-large-signal-model/formal-scope.html#p57","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/AveragedCongruence.lean","url":"read/monographs-large-signal-model/averagedcongruence-d11b2d0b3be8.html","label":"KomorebiLSM/AveragedCongruence.lean"}]},{"number":58,"title":"Positive cell-average approximation","statement":"read/monographs-large-signal-model/64-a-valid-density-approximation-with-a-resolution-bound.html#L2514","proof":"read/monographs-large-signal-model/64-a-valid-density-approximation-with-a-resolution-bound.html#L2530","scope":"read/monographs-large-signal-model/formal-scope.html#p58","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CellDistance.lean","url":"read/monographs-large-signal-model/celldistance-43880b6856ee.html","label":"KomorebiLSM/CellDistance.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveCellApproximation.lean","url":"read/monographs-large-signal-model/positivecellapproximation-a209508341d7.html","label":"KomorebiLSM/PositiveCellApproximation.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveCellP58.lean","url":"read/monographs-large-signal-model/positivecellp58-5d742ad3974f.html","label":"KomorebiLSM/PositiveCellP58.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveCellResolution.lean","url":"read/monographs-large-signal-model/positivecellresolution-045416689be5.html","label":"KomorebiLSM/PositiveCellResolution.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PositiveCellUniform.lean","url":"read/monographs-large-signal-model/positivecelluniform-eebf4473dbef.html","label":"KomorebiLSM/PositiveCellUniform.lean"}]},{"number":59,"title":"Continuous-record total-variation bound","statement":"read/monographs-large-signal-model/65-full-continuous-record-laws-inherit-the-stability-argument.html#L2561","proof":"read/monographs-large-signal-model/65-full-continuous-record-laws-inherit-the-stability-argument.html#L2579","scope":"read/monographs-large-signal-model/formal-scope.html#p59","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BaseNormIntegration.lean","url":"read/monographs-large-signal-model/basenormintegration-0e9beabea905.html","label":"KomorebiLSM/BaseNormIntegration.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ConditionalEventTV.lean","url":"read/monographs-large-signal-model/conditionaleventtv-aa50af1ebda5.html","label":"KomorebiLSM/ConditionalEventTV.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ContinuousTV.lean","url":"read/monographs-large-signal-model/continuoustv-533aad8ab177.html","label":"KomorebiLSM/ContinuousTV.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ContinuousTVDensity.lean","url":"read/monographs-large-signal-model/continuoustvdensity-79f9803436a9.html","label":"KomorebiLSM/ContinuousTVDensity.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/TimeRecords.lean","url":"read/monographs-large-signal-model/timerecords-9d1a3d7c5664.html","label":"KomorebiLSM/TimeRecords.lean"}]}],"14":[{"number":72,"title":"Boundary fragility under mass preserving perturbations","statement":"read/monographs-large-signal-model/81-why-exact-boundary-preservation-can-have-zero-noise-radius.html#L3245","proof":"read/monographs-large-signal-model/81-why-exact-boundary-preservation-can-have-zero-noise-radius.html#L3253","scope":"read/monographs-large-signal-model/formal-scope.html#p72","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/LorentzBoundaryFragility.lean","url":"read/monographs-large-signal-model/lorentzboundaryfragility-75b25055bf8c.html","label":"KomorebiLSM/LorentzBoundaryFragility.lean"}]},{"number":83,"title":"Structured curved-domain certificate","statement":"read/monographs-large-signal-model/94-a-nonlinear-observable-state-with-a-curved-moment-domain.html#L3798","proof":"read/monographs-large-signal-model/94-a-nonlinear-observable-state-with-a-curved-moment-domain.html#L3820","scope":"read/monographs-large-signal-model/formal-scope.html#p83","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentGeometry.lean","url":"read/monographs-large-signal-model/curvedmomentgeometry-8f2a1cbaa8e1.html","label":"KomorebiLSM/CurvedMomentGeometry.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentInstrument.lean","url":"read/monographs-large-signal-model/curvedmomentinstrument-2628d5444e79.html","label":"KomorebiLSM/CurvedMomentInstrument.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentMarkov.lean","url":"read/monographs-large-signal-model/curvedmomentmarkov-ecc5e006d959.html","label":"KomorebiLSM/CurvedMomentMarkov.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentPolynomial.lean","url":"read/monographs-large-signal-model/curvedmomentpolynomial-08f6e2a192f7.html","label":"KomorebiLSM/CurvedMomentPolynomial.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentReferences.lean","url":"read/monographs-large-signal-model/curvedmomentreferences-8426d2288c4c.html","label":"KomorebiLSM/CurvedMomentReferences.lean"}]}],"15":[{"number":66,"title":"Time-uniform predictable-residual certificate","statement":"read/monographs-large-signal-model/74-evidence-from-dependent-observations.html#L3057","proof":"read/monographs-large-signal-model/74-evidence-from-dependent-observations.html#L3069","scope":"read/monographs-large-signal-model/formal-scope.html#p66","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ConditionalBernoulli.lean","url":"read/monographs-large-signal-model/conditionalbernoulli-cdf0b651a090.html","label":"KomorebiLSM/ConditionalBernoulli.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ConditionalHoeffding.lean","url":"read/monographs-large-signal-model/conditionalhoeffding-7ad97e1bb541.html","label":"KomorebiLSM/ConditionalHoeffding.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CountableConfidence.lean","url":"read/monographs-large-signal-model/countableconfidence-c5ef0b9dc814.html","label":"KomorebiLSM/CountableConfidence.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictableResidualAffine.lean","url":"read/monographs-large-signal-model/predictableresidualaffine-b303734fb431.html","label":"KomorebiLSM/PredictableResidualAffine.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictableResidualAnytime.lean","url":"read/monographs-large-signal-model/predictableresidualanytime-a13e66d18b88.html","label":"KomorebiLSM/PredictableResidualAnytime.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictableResidualGeneral.lean","url":"read/monographs-large-signal-model/predictableresidualgeneral-6cbad603cbe9.html","label":"KomorebiLSM/PredictableResidualGeneral.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/PredictableResidualP66.lean","url":"read/monographs-large-signal-model/predictableresidualp66-4bde6da51b32.html","label":"KomorebiLSM/PredictableResidualP66.lean"}]},{"number":68,"title":"Sequential evidence gives a lower error certificate","statement":"read/monographs-large-signal-model/76-what-a-residual-can-prove-about-misspecification.html#L3115","proof":"read/monographs-large-signal-model/76-what-a-residual-can-prove-about-misspecification.html#L3126","scope":"read/monographs-large-signal-model/formal-scope.html#p68","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/SequentialLowerCertificate.lean","url":"read/monographs-large-signal-model/sequentiallowercertificate-bab5865da920.html","label":"KomorebiLSM/SequentialLowerCertificate.lean"}]},{"number":81,"title":"Time-uniform regression confidence","statement":"read/monographs-large-signal-model/92-confidence-from-dependent-observations.html#L3675","proof":"read/monographs-large-signal-model/92-confidence-from-dependent-observations.html#L3690","scope":"read/monographs-large-signal-model/formal-scope.html#p81","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ConditionalRandomMultiplier.lean","url":"read/monographs-large-signal-model/conditionalrandommultiplier-490dc54d5e27.html","label":"KomorebiLSM/ConditionalRandomMultiplier.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RegressionConfidence.lean","url":"read/monographs-large-signal-model/regressionconfidence-e74591ddd808.html","label":"KomorebiLSM/RegressionConfidence.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RegressionExponential.lean","url":"read/monographs-large-signal-model/regressionexponential-9670449ee658.html","label":"KomorebiLSM/RegressionExponential.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RegressionGaussian.lean","url":"read/monographs-large-signal-model/regressiongaussian-8def1e340882.html","label":"KomorebiLSM/RegressionGaussian.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RegressionGeometry.lean","url":"read/monographs-large-signal-model/regressiongeometry-a909c0ffdebf.html","label":"KomorebiLSM/RegressionGeometry.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RegressionRadius.lean","url":"read/monographs-large-signal-model/regressionradius-a8bc970754d1.html","label":"KomorebiLSM/RegressionRadius.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ScalarRegressionConfidence.lean","url":"read/monographs-large-signal-model/scalarregressionconfidence-b4e80020ce2a.html","label":"KomorebiLSM/ScalarRegressionConfidence.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/VilleInequality.lean","url":"read/monographs-large-signal-model/villeinequality-bc8b2dbe887c.html","label":"KomorebiLSM/VilleInequality.lean"}]},{"number":82,"title":"Sequential observable-moment operator sets","statement":"read/monographs-large-signal-model/93-from-observable-moment-regression-to-operator-sets.html#L3734","proof":"read/monographs-large-signal-model/93-from-observable-moment-regression-to-operator-sets.html#L3756","scope":"read/monographs-large-signal-model/formal-scope.html#p82","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableMomentAlgebra.lean","url":"read/monographs-large-signal-model/observablemomentalgebra-2eb5574c7d23.html","label":"KomorebiLSM/ObservableMomentAlgebra.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableMomentConditional.lean","url":"read/monographs-large-signal-model/observablemomentconditional-bdfd7c9dfa5b.html","label":"KomorebiLSM/ObservableMomentConditional.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableMomentConfidence.lean","url":"read/monographs-large-signal-model/observablemomentconfidence-9fae869f106b.html","label":"KomorebiLSM/ObservableMomentConfidence.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableMomentProcess.lean","url":"read/monographs-large-signal-model/observablemomentprocess-6e6de13fa124.html","label":"KomorebiLSM/ObservableMomentProcess.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ObservableOperatorSets.lean","url":"read/monographs-large-signal-model/observableoperatorsets-a530c117df98.html","label":"KomorebiLSM/ObservableOperatorSets.lean"}]},{"number":83,"title":"Structured curved-domain certificate","statement":"read/monographs-large-signal-model/94-a-nonlinear-observable-state-with-a-curved-moment-domain.html#L3798","proof":"read/monographs-large-signal-model/94-a-nonlinear-observable-state-with-a-curved-moment-domain.html#L3820","scope":"read/monographs-large-signal-model/formal-scope.html#p83","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentGeometry.lean","url":"read/monographs-large-signal-model/curvedmomentgeometry-8f2a1cbaa8e1.html","label":"KomorebiLSM/CurvedMomentGeometry.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentInstrument.lean","url":"read/monographs-large-signal-model/curvedmomentinstrument-2628d5444e79.html","label":"KomorebiLSM/CurvedMomentInstrument.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentMarkov.lean","url":"read/monographs-large-signal-model/curvedmomentmarkov-ecc5e006d959.html","label":"KomorebiLSM/CurvedMomentMarkov.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentPolynomial.lean","url":"read/monographs-large-signal-model/curvedmomentpolynomial-08f6e2a192f7.html","label":"KomorebiLSM/CurvedMomentPolynomial.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentReferences.lean","url":"read/monographs-large-signal-model/curvedmomentreferences-8426d2288c4c.html","label":"KomorebiLSM/CurvedMomentReferences.lean"}]},{"number":84,"title":"Exact rational outer confidence intervals","statement":"read/monographs-large-signal-model/95-a-fully-rational-dependent-data-reference-experiment.html#L3854","proof":"read/monographs-large-signal-model/95-a-fully-rational-dependent-data-reference-experiment.html#L3862","scope":"read/monographs-large-signal-model/formal-scope.html#p84","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BoundedResponseNoise.lean","url":"read/monographs-large-signal-model/boundedresponsenoise-ae84c6094fef.html","label":"KomorebiLSM/BoundedResponseNoise.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/OutwardConfidenceIntervals.lean","url":"read/monographs-large-signal-model/outwardconfidenceintervals-b6d56de2c27c.html","label":"KomorebiLSM/OutwardConfidenceIntervals.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RationalConfidenceArithmetic.lean","url":"read/monographs-large-signal-model/rationalconfidencearithmetic-c9621368e4f2.html","label":"KomorebiLSM/RationalConfidenceArithmetic.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RationalRegressionConfidence.lean","url":"read/monographs-large-signal-model/rationalregressionconfidence-db427018a07d.html","label":"KomorebiLSM/RationalRegressionConfidence.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/RationalSqrtEnclosure.lean","url":"read/monographs-large-signal-model/rationalsqrtenclosure-bfc166a8d708.html","label":"KomorebiLSM/RationalSqrtEnclosure.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/ScalarRegressionConfidence.lean","url":"read/monographs-large-signal-model/scalarregressionconfidence-b4e80020ce2a.html","label":"KomorebiLSM/ScalarRegressionConfidence.lean"}]},{"number":87,"title":"Observable structured learning with a covered domain","statement":"read/monographs-large-signal-model/98-a-conditional-data-to-domain-theorem.html#L3979","proof":"read/monographs-large-signal-model/98-a-conditional-data-to-domain-theorem.html#L3983","scope":"read/monographs-large-signal-model/formal-scope.html#p87","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredLearning.lean","url":"read/monographs-large-signal-model/structuredlearning-fc14ef0e0d1f.html","label":"KomorebiLSM/StructuredLearning.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredLearningCapstone.lean","url":"read/monographs-large-signal-model/structuredlearningcapstone-71fda8a5abf4.html","label":"KomorebiLSM/StructuredLearningCapstone.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredRectangle.lean","url":"read/monographs-large-signal-model/structuredrectangle-f1b28b65a687.html","label":"KomorebiLSM/StructuredRectangle.lean"}]}],"16":[{"number":85,"title":"Parameter-to-law error without a state-estimation term","statement":"read/monographs-large-signal-model/96-structured-uncertainty-has-an-observable-error-bound.html#L3902","proof":"read/monographs-large-signal-model/96-structured-uncertainty-has-an-observable-error-bound.html#L3926","scope":"read/monographs-large-signal-model/formal-scope.html#p85","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentRecordTV.lean","url":"read/monographs-large-signal-model/curvedmomentrecordtv-a9ed05cfbfc5.html","label":"KomorebiLSM/CurvedMomentRecordTV.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentReferences.lean","url":"read/monographs-large-signal-model/curvedmomentreferences-8426d2288c4c.html","label":"KomorebiLSM/CurvedMomentReferences.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/CurvedMomentTV.lean","url":"read/monographs-large-signal-model/curvedmomenttv-5c3a46d8f048.html","label":"KomorebiLSM/CurvedMomentTV.lean"}]},{"number":86,"title":"Uniform marginal and rolling-window stability","statement":"read/monographs-large-signal-model/97-long-horizon-marginal-control-is-not-full-record-control.html#L3946","proof":"read/monographs-large-signal-model/97-long-horizon-marginal-control-is-not-full-record-control.html#L3958","scope":"read/monographs-large-signal-model/formal-scope.html#p86","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/BernoulliRecordSeparation.lean","url":"read/monographs-large-signal-model/bernoullirecordseparation-8d7ba26f8faa.html","label":"KomorebiLSM/BernoulliRecordSeparation.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MarkovMarginals.lean","url":"read/monographs-large-signal-model/markovmarginals-d64c184c24ce.html","label":"KomorebiLSM/MarkovMarginals.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MarkovMinorization.lean","url":"read/monographs-large-signal-model/markovminorization-b96caffc2d3a.html","label":"KomorebiLSM/MarkovMinorization.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MarkovRecords.lean","url":"read/monographs-large-signal-model/markovrecords-08ffc2fe8342.html","label":"KomorebiLSM/MarkovRecords.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/MarkovWindows.lean","url":"read/monographs-large-signal-model/markovwindows-475bbbea9adf.html","label":"KomorebiLSM/MarkovWindows.lean"}]},{"number":87,"title":"Observable structured learning with a covered domain","statement":"read/monographs-large-signal-model/98-a-conditional-data-to-domain-theorem.html#L3979","proof":"read/monographs-large-signal-model/98-a-conditional-data-to-domain-theorem.html#L3983","scope":"read/monographs-large-signal-model/formal-scope.html#p87","modules":[{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredLearning.lean","url":"read/monographs-large-signal-model/structuredlearning-fc14ef0e0d1f.html","label":"KomorebiLSM/StructuredLearning.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredLearningCapstone.lean","url":"read/monographs-large-signal-model/structuredlearningcapstone-71fda8a5abf4.html","label":"KomorebiLSM/StructuredLearningCapstone.lean"},{"path":"monographs/large-signal-model/Lean/KomorebiLSM/StructuredRectangle.lean","url":"read/monographs-large-signal-model/structuredrectangle-f1b28b65a687.html","label":"KomorebiLSM/StructuredRectangle.lean"}]}]},"math_expressions":194,"new_tex_build":false,"new_lean_execution":false,"new_proof_review":false,"original_figure_generator_executed":false,"interactive_audit":"verification/large-signal-atlas/run/manifest.json"}
