{"as_of":"2026-08-14T07:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:47fcc7098124049e7433ab50509affa4834dfffef31a7b4f59ddb61c506f86e5","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":"2026-08-14T06:32:32.682623+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":"2026-08-13T09:41:16.204167Z","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:c352cb724b6dacefbe3ee9c8f8e802eff97b21583baef4c9d072c2252e9087fe","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T04:51:56.031299Z","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":"2026-08-13T09:41:16.204167Z","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:d1b447915c82ba26499b4f778df4fedaa1294fbfb5be5a2a138b38c5001c57a4","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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:f84599af66b50f69e947fe0077164e987bc70fbb9bf1526ada7dd9218c5b1bbe","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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":"sha256:8aec242cf974efefbc2397e6ed403e4cf14471711ca378402abcd07a7bc356b4","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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:ccca0a755da3d4b8afe177af1c462fe724d506c824cec0c2fd2968f15c77e215","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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:a285604935ca3b9ff4b1d06c8d620f62487a7cb1a229bc1423e335a3064d6791","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.04760","last_updated":"2024-10-07T05:34:51Z","snapshot_observed_at":"2026-08-12T22:29:29.451806Z","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":"2026-08-13T09:41:16.204167Z","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":"sha256:750e1619d32f9397e4dea419b5670d8c7509602c84a799afac7aeb09b4901fed","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":"2026-08-13T09:41:16.204167Z","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":"sha256:37a87d279a01d4bffa8bafc86f42918fbd4da976380a16232546657975055787","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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":"sha256:72624eec6afa25b9d979b6254d300e331a2b35adec8e28f7eb5372407d6b87b7","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":"2026-08-13T10:29:38.267801Z","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":"2026-08-13T09:41:16.204167Z","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":"sha256:65b491d9c029c380ad3cc6a144bc455862eb1b58df504c9466669376cec207e9","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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":"sha256:87f36954dac68f660daf88750f7abcf0b4cc454441b8e32eb6408c5f391f9121","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-13T09:41:16.204167Z","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":"sha256:45d88dd7429928070fb232f087d5d7d3240fe35519f00282384f23fabdecea4e","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 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.09906","last_updated":"2021-01-17T19:49:06Z","snapshot_observed_at":"2026-08-14T01:57:51.687002Z","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":"2026-08-13T09:41:16.204167Z","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":"sha256:3e3af11e5ace3d532b65be163bec8053117d62a265fdde7ce80565d141c12c1c","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":"2026-08-13T09:41:16.204167Z","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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2507.12791."}