{"as_of":"2026-08-08T09:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d2b311046927e09dfcbf910177f12ee3d731e2edabff5305157a6772bf15803f","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:49:30.261633Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-25T07:46:49.641026Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-25T07:50:29.490995Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"cited_work":{"arxiv_id":"2507.12791","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.12791","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","venue":null,"work_id":"c95bd26f-af9f-41bd-8cd5-231c5e529558","year":2025},"citing_paper":{"arxiv_id":"2512.18598","last_updated":"2026-05-21T18:21:50Z","snapshot_observed_at":"2026-08-02T10:43:01.782589Z","submitted_at":"2025-12-21T05:10:01Z","title":"Long-time reverse transportation inequalities for non-globally-dissipative Langevin dynamics","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-25T07:46:49.641026Z"},"links":{"cited_paper":"/paper/2507.12791","citing_paper":"/paper/2512.18598"},"observation_digest":"sha256:5900c2cd7bff376a9ba343cddb417bb3d78c0f8e58e3e79866e66ae42f210cfb","observation_id":"0ef97f34-d71b-4940-a509-416dbe1ba25f","resolution":{"observed_at":"2026-05-25T07:50:29.493462Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.12791/citation-record","integrity":"/paper/2507.12791/integrity","json":"/paper/2507.12791/citation-record.json","paper":"/paper/2507.12791"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2401.00071","last_updated":"2023-12-29T20:34:43Z","snapshot_observed_at":"2026-08-06T15:13:22.137950Z","submitted_at":"2023-12-29T20:34:43Z","title":"Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds","version":1},"cited_work":{"arxiv_id":"2401.00071","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.00071","snapshot_observed_at":"2026-08-06T16:49:31.604853Z","title":"Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds","venue":"math.PR","work_id":"a44775f9-6678-4137-93fa-538f26781a74","year":2023},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:28.720562Z"},"links":{"cited_paper":"/paper/2401.00071","citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:05862bcd4e8324ac3dca2ec87acf9ea481e1c8b3df3bbde55157b26bcb950aed","observation_id":"f8823fa6-10b5-4c32-a28f-e17d362f0cd0","resolution":{"observed_at":"2026-08-06T16:49:31.676561Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:32.880485Z","title":"Itˆ o formula and Girsanov theorem for anticipating stochastic integrals","venue":null,"work_id":"5e7403aa-b1d4-4f5d-ac62-a5c846b30b45","year":2013},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.547998Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:e38e95e827f7f8d6f60891eb8b62ed9061e09b85fd26c03348a4df1f1c59e233","observation_id":"470862a1-4caa-40b4-99b2-6af7a32b7fe2","resolution":{"observed_at":"2026-08-06T16:49:32.923625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:32.571715Z","title":"The non-linear transformation of Gaussian measure on Banach spaces and its absolute continuity (1)","venue":null,"work_id":"f9358212-359e-4097-9a43-9d6770bf3cba","year":1974},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.730958Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:4e70db451ae0ef2f4b13e01df966d68d1b460b6f547ab6b29866a1c4e6f200c3","observation_id":"6672fe6d-e308-4f14-95d4-458a17e65adb","resolution":{"observed_at":"2026-08-06T16:49:32.706598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2405.17068","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:31.011521Z","title":"Implicit Langevin algorithms for sampling from log-concave densities","venue":null,"work_id":"b6f5fadf-3e07-46d7-84d7-7c9c90261e0b","year":2021},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.296841Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:cf7d1a2c2adcda24e34100a47f12954ee0a4bc46286537cdf7db6c7b3df05c54","observation_id":"7a5867ac-0b8c-4b7f-a036-52352fe82699","resolution":{"observed_at":"2026-08-06T16:49:31.146472Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2506.07614","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:30.556263Z","title":"Applications of anticipating stochastic calculus to stochastic differential equations","venue":null,"work_id":"d94af786-8611-44a9-86d0-6181d36489f9","year":2024},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.930291Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:e0f2819ddb662a95698621ea727f2da66528d32f8b471b685c284c663bb175df","observation_id":"61b0754b-09a1-4997-9ac9-47a9549dba8a","resolution":{"observed_at":"2026-08-06T16:49:30.773860Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.04760","last_updated":"2024-10-07T05:34:51Z","snapshot_observed_at":"2026-08-06T04:32:12.204479Z","submitted_at":"2024-10-07T05:34:51Z","title":"Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.04760","snapshot_observed_at":"2026-08-06T16:49:30.261633Z","title":"Stochastic Runge–Kutta methods: Provable acceleration of diffusion models","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:30.261633Z"},"links":{"cited_paper":"/paper/2410.04760","citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:92583eab4a644f1ee1ec6c43a252faa0ae63ba40cb2344593093a1661230b35f","observation_id":"230d51b5-a8af-4d55-828c-32e937cf612c","resolution":{"observed_at":"2026-08-06T16:49:30.261633Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:32.195243Z","title":"Stochastic Runge–Kutta accelerates Langevin Monte Carlo and beyond","venue":null,"work_id":"8d3766f7-bf5d-43f8-92cb-08c3c09f585c","year":2019},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":530,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.842640Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:4b1fc64de466139886b2d7815584f34692cb5d65d8455d7b9ca2650e9b1ce3eb","observation_id":"a3189861-4762-4093-a61b-d885e4d089ba","resolution":{"observed_at":"2026-08-06T16:49:32.409735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T16:49:28.986813Z","title":"When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":1994,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:28.986813Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:81db7a702ca22d71251efe286f682382d671acaba9c93ca717729b2496e6a06a","observation_id":"82cde2c7-601d-4734-87b1-edc3d53f69d2","resolution":{"observed_at":"2026-08-06T16:49:28.986813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.11491","last_updated":"2023-08-22T15:12:39Z","snapshot_observed_at":"2026-08-07T18:06:26.097734Z","submitted_at":"2023-08-22T15:12:39Z","title":"Nonlinear Hamiltonian Monte Carlo & its Particle Approximation","version":1},"cited_work":{"arxiv_id":"2308.11491","doi":null,"metadata_source":"pith","pith_arxiv_id":"2308.11491","snapshot_observed_at":"2026-08-06T16:49:31.441814Z","title":"Nonlinear Hamiltonian Monte Carlo & its Particle Approximation","venue":"math.PR","work_id":"fd3c2e52-b4d2-4301-892f-ad212d1ac400","year":2023},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:28.864259Z"},"links":{"cited_paper":"/paper/2308.11491","citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:6d7189cdcc3c8375d7efdc36b31e8246d7f67a1792f94d42b218992e0ca6013f","observation_id":"816bc90c-5c24-4816-92df-fb4f58a70420","resolution":{"observed_at":"2026-08-06T16:49:31.524683Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:32.997675Z","title":"Generalization of the anticipative Girsanov theorem","venue":null,"work_id":"7e52e8ef-58e3-482b-9ab7-b4f06e91c0bd","year":2013},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.418073Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:9070c1cf4b532391e0c8b6e41875a979e182b448e6fec1837dfba0a735595dc9","observation_id":"8dcb90e9-18b8-4971-9de6-48a26749cfad","resolution":{"observed_at":"2026-08-06T16:49:33.117772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:49:31.741584Z","title":"Transformation of Wiener measure under anticipative flows","venue":null,"work_id":"ea3043d0-f97a-4711-a62c-2e01e7f43767","year":1992},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:30.042287Z"},"links":{"citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:91f71cf75234e7fd884026a325a66b84e9e4e00a90c18fde907e0058213dfc66","observation_id":"6f79a1a1-fcf0-416d-9f94-e4587e1aee43","resolution":{"observed_at":"2026-08-06T16:49:31.977707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.09906","last_updated":"2021-01-17T19:49:06Z","snapshot_observed_at":"2026-08-02T20:17:38.632450Z","submitted_at":"2020-03-22T14:22:54Z","title":"Complexity of randomized algorithms for underdamped Langevin dynamics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.09906","snapshot_observed_at":"2026-08-06T16:49:29.190505Z","title":"Complexity of randomized algorithms for underdamped Langevin dynamics","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-06T16:49:29.190505Z"},"links":{"cited_paper":"/paper/2003.09906","citing_paper":"/paper/2507.12791"},"observation_digest":"sha256:1be280953f821e9114c9c89eb187bd720240d41b32023d10c007dd17cacabb56","observation_id":"660b1516-1a73-4669-bb2a-f65393c2a9a5","resolution":{"observed_at":"2026-08-06T16:49:29.190505Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.12791","last_updated":"2025-07-17T05:05:27Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T16:36:05.876844Z","submitted_at":"2025-07-17T05:05:27Z","title":"Analysis of Langevin midpoint methods using an anticipative Girsanov theorem"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":4,"verified_fuzzy":5},"total_outbound_references":12},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2507.12791."}