{"as_of":"2026-08-09T07:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ebea9903b1b69023347f574e59b6f967568c7445232c1c2eb17e293213d88de4","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T04:43:51.371895Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2602.04644/citation-record","integrity":"/paper/2602.04644/integrity","json":"/paper/2602.04644/citation-record.json","paper":"/paper/2602.04644"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:47.756042Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:47.756042Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:bb6c800d1f15ee4c3f8c5ef46918f58cdd7ab2278f6035db55d8089d22b53044","observation_id":"fb7f8b6b-7722-4bdd-b288-75f63553bf8d","resolution":{"observed_at":"2026-08-03T04:43:47.756042Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0377-0257(00)00135-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Non-Newtonian Fluid Mechanics","work_id":"b3d0eeb2-8faf-4b55-9c60-1f5ae5953354","year":2001},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:47.878807Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:289301cee09bcd98ac9cc85c780036631f89a6ad9e06762030d4b166606cc203","observation_id":"598c1867-295b-44b8-ac7f-faad34f529f5","resolution":{"observed_at":"2026-08-03T04:48:44.578850Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0378-4371(02)01017-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Physica A Statistical Mechanics and its Applications","work_id":"ed866ba3-7159-4c9e-9c49-c32b62d053c2","year":2002},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.086102Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:fbf384a6c82feb1233832c2c2a1f0076d674ecd528e2ed2dab5eb0ace411dd6a","observation_id":"3fe98513-dee5-40a4-848f-96039adf3e7a","resolution":{"observed_at":"2026-08-03T04:48:44.334948Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:48.229526Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.229526Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:dd918e948cb4d978ac8c82c47d7fc3e00b636d5876b7de2816e5085deeef7685","observation_id":"18fbed52-4c59-48d7-9513-5ce6e7d4c5f9","resolution":{"observed_at":"2026-08-03T04:43:48.229526Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:48.367894Z","title":"Dębiec, E","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.367894Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:e3187b19dfd253b5ab1124f794b109ca5783525fd93317fd1c57eb09fad3e45d","observation_id":"adf06dd9-a2ac-4ad1-94bc-87fd844e19b2","resolution":{"observed_at":"2026-08-03T04:43:48.367894Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/5.0161336","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hetland, E","venue":"Physics of Fluids","work_id":"f75a8bd7-97cb-4711-bdb4-131456cfdab3","year":2023},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.514610Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:0bff60116fc07696a40f76ab37ff433930afd6f15864b1c1b36f8c39d6b258aa","observation_id":"372df235-0c4b-473c-958a-73a70e9db613","resolution":{"observed_at":"2026-08-03T04:48:44.097454Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:48.621990Z","title":"Beddrich, E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.621990Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:fe39e263cd053321bb6530c6ba92ab8ded187f123b9936d96c7ca45905e4a991","observation_id":"6f0c4bc6-bd06-462a-90e6-e0e9537c0a8e","resolution":{"observed_at":"2026-08-03T04:43:48.621990Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:48.700923Z","title":"Beddrich, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.700923Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:6fcfe625843909bdf78977686a2e2e749c837e85d3173e8870e422cd0d8ed229","observation_id":"b76542ea-1990-4eec-91d6-b22799d79c55","resolution":{"observed_at":"2026-08-03T04:43:48.700923Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:48.905157Z","title":"Jordan, D","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:48.905157Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:d07faa297f6c09dee5184df7f29b028ea9405c6e1ef12079358dfd23548dea1b","observation_id":"3744db79-908e-4868-bad9-ee5abd01fc63","resolution":{"observed_at":"2026-08-03T04:43:48.905157Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-08-03T04:43:49.083922Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.083922Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:f2e6e75ce3bfd6718cf173c400ef6f1fbc36ecb0adf3dba8c3c4de16387a7939","observation_id":"36641210-6095-41ca-ac4f-ab5c33d80cf1","resolution":{"observed_at":"2026-08-03T04:43:49.083922Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:49.309903Z","title":"Anderson, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.309903Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:4b4c708d957dd9f892884924409369eace3fdfe2e0fb12b66a452a3f77feb523","observation_id":"73846cf0-7766-4802-860e-9b342cf97ddf","resolution":{"observed_at":"2026-08-03T04:43:49.309903Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:49.508634Z","title":"Bruna, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.508634Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:e751b7b26dfe78bef2ae5c878813381696db614a313046e49405d70be9c62acc","observation_id":"61615a70-fc90-4f23-872b-9af9452e538e","resolution":{"observed_at":"2026-08-03T04:43:49.508634Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.03597","last_updated":"2024-03-09T15:35:46Z","snapshot_observed_at":"2026-07-06T16:28:18.257251Z","submitted_at":"2023-10-05T15:20:35Z","title":"Sampling via Gradient Flows in the Space of Probability Measures","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.03597","snapshot_observed_at":"2026-08-03T04:43:49.664898Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.664898Z"},"links":{"cited_paper":"/paper/2310.03597","citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:2ccdc386360c1b961abef0af409254413daf3c4b2b4d9b691cefc1151427cbbd","observation_id":"9f868d06-a975-4189-9383-1313c2d2089f","resolution":{"observed_at":"2026-08-03T04:43:49.664898Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.1742462","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"The Journal of Chemical Physics","work_id":"b10888b8-6d6d-4bdb-a85a-657cd99a3f62","year":1956},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.808886Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:b8d9fdf2d3073dc6c818488a0471dac50d264f3cadaee0ac6b34df458c2de250","observation_id":"3ac1a4b1-a7dc-4c2c-9307-74c8caf59118","resolution":{"observed_at":"2026-08-03T04:48:43.246864Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:49.992060Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.992060Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:3cddcdc1eacdc758350c0cd3f0c67d96ba0bcbfaf513abc8337d16cb78ddf2c0","observation_id":"9c272e2b-1cd9-43bb-baaa-aa052577546c","resolution":{"observed_at":"2026-08-03T04:43:49.992060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00397-014-0802-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Jedynak, Approximation of the inverse Langevin function revisited, Rheol","venue":"Rheologica Acta","work_id":"b512e3e9-59b6-4a48-bbca-71e2645151c5","year":2015},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.157657Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:4aa28073482979374eb7bb0720bba1ccbfd72485565073a2a59f93d9bc46d9fd","observation_id":"b51f70cc-025a-48cb-998d-96113e6796c1","resolution":{"observed_at":"2026-08-03T04:48:42.996573Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:50.288496Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.288496Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:a059ace8cae6214ed771efa3089e527849e07dee0cd1ad205125640a9e3db6a6","observation_id":"55dede6e-06b7-4f00-9d9d-471612b19fab","resolution":{"observed_at":"2026-08-03T04:43:50.288496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0025-5718-04-01685-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lubich, On variational approximations in quantum molecular dynamics, Math","venue":"Mathematics of Computation","work_id":"9bbbe994-4937-4b86-bba2-0d8bbbfcd874","year":2005},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.466693Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:a7f6e8572ed245232bd776bcc65ef1c5c1c594aa4fb843452ed00d1c85c4cf3d","observation_id":"08e878e8-c4aa-4af2-835a-f78cb3bd6aa6","resolution":{"observed_at":"2026-08-03T04:48:42.700396Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:50.594958Z","title":"Lasser, C","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.594958Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:51affdf805ae60b4a9ccba5a75430e6b81e5058011a997bd5d289e65edcab9e6","observation_id":"c4fe07e0-3862-4bfe-9265-f2855e583cbb","resolution":{"observed_at":"2026-08-03T04:43:50.594958Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:50.783628Z","title":"Lasser, C","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.783628Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:e49c6cd61a870c50bbb79cfbe6df03be31ea79cdfdf0740a62d2e176df9d8e69","observation_id":"1674e7dc-f8a3-4b4c-bd83-50688f1c75f7","resolution":{"observed_at":"2026-08-03T04:43:50.783628Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:50.932228Z","title":"Arendt, Chp","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:50.932228Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:4086ccd8dbbe852dbe15e7d632f93649caddd4e25b2d9092175db575fb5857a6","observation_id":"ca6bcac3-62e3-4b74-8266-468211ef9a81","resolution":{"observed_at":"2026-08-03T04:43:50.932228Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:51.012204Z","title":"Gilbarg, N","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:51.012204Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:83632913590334ca561cd91a49116ef0addc4c923cfe6ea8ae1f7d82011dff3f","observation_id":"cd5cbaa3-1cdc-4e3b-bbd1-576f9aa87439","resolution":{"observed_at":"2026-08-03T04:43:51.012204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:51.154430Z","title":"Engel, R","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:51.154430Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:e368a747792969e1b29267b1df3a6ed88cedb77cc8cfc1278805456bbce2f2a2","observation_id":"743c3f47-6901-4b05-bc68-53718fe434ea","resolution":{"observed_at":"2026-08-03T04:43:51.154430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T04:43:51.371895Z","title":"Pazy, Semigroups of linear operators and applications to partial differential equations, Vol","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:51.371895Z"},"links":{"citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:868ba047c21141bd18048a87beacccf03f925a602cb105959a9dc22365f7e83b","observation_id":"99481e9a-9802-4598-9021-aea4649b156a","resolution":{"observed_at":"2026-08-03T04:43:51.371895Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","latest_version":2,"primary_category":"math.SP","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":6,"verified_fuzzy":0},"total_outbound_references":24},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2602.04644."}