{"as_of":"2026-08-16T03:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9cb37abe15703cd21baadc953597f09175ae3e85dce30c2ecfa3fdbb58ace14e","coverage":[{"denominator":69,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":69,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T21:51:17.447751Z","state":"measured"},{"denominator":69,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":69,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/2411.08518/citation-record","integrity":"/paper/2411.08518/integrity","json":"/paper/2411.08518/citation-record.json","paper":"/paper/2411.08518"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:18.944408Z","title":"Random Dynamical Systems","venue":null,"work_id":"b074dc68-f74f-4bde-9423-cb19702b94eb","year":1998},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.114217Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:8247aeb2e5d2bd67ab22080d818ac592677fefe867989242b72d15f3adbe1526","observation_id":"59cb51ff-97cb-43ac-bb6c-ab00eb7b80c8","resolution":{"observed_at":"2026-08-12T21:51:18.948392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1201.3207","last_updated":"2012-01-16T10:54:01Z","snapshot_observed_at":"2026-08-15T04:22:22.727139Z","submitted_at":"2012-01-16T10:54:01Z","title":"Refined Second Law of Thermodynamics for fast random processes","version":1},"cited_work":{"arxiv_id":"1201.3207","doi":null,"metadata_source":"pith","pith_arxiv_id":"1201.3207","snapshot_observed_at":"2026-08-12T21:51:18.702952Z","title":"Refined Second Law of Thermodynamics for fast random processes","venue":"cond-mat.stat-mech","work_id":"5ac3aedc-31fa-476b-8783-d4f1a7b222bd","year":2012},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.119503Z"},"links":{"cited_paper":"/paper/1201.3207","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:2e7d2b6729685447858e6eed5f0c13e00fa394974c0ecacf94e14e8b09eaf6a6","observation_id":"04f25a3c-7486-40ff-a6bd-565b80a26bae","resolution":{"observed_at":"2026-08-12T21:51:18.707904Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/16-aihp801","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.716012Z","title":"The Bismut–Elworthy–Li formula for mean-field stochastic differential equations","venue":null,"work_id":"c09c5eb7-4e32-45fe-ad94-972d0a417caa","year":2018},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.125160Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:aca01610f73c12f14a15f2ecb783fd2173317b9dc012ea46700b8e128ed5bc5f","observation_id":"d8bbad24-0a0a-402f-801c-d071558de7e4","resolution":{"observed_at":"2026-08-12T21:51:17.721274Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.130541Z","title":"Control Theory for Physicists","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.130541Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:cd344c843adf11a4fc79ac5e8cc768491be1a437273d011bb4bbd140d7fb0592","observation_id":"8bbd3cec-225e-4ef9-a182-aa9166e78539","resolution":{"observed_at":"2026-08-12T21:51:17.130541Z","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":"2026-08-12T21:51:18.932221Z","title":"Large Deviations and the Malliavin Calculus","venue":null,"work_id":"dd72e50b-ec7f-45e6-835b-3c0d649935a3","year":1984},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.135638Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:e0d03a5de30f83dc36947b2803091e29d7d7995d65fd2274b0bd6a918ccec2ec","observation_id":"a2c68947-28e1-46be-b502-3d61816458d5","resolution":{"observed_at":"2026-08-12T21:51:18.936572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.04642","last_updated":"2023-02-15T22:53:47Z","snapshot_observed_at":"2026-08-16T01:41:24.442089Z","submitted_at":"2022-06-09T17:37:09Z","title":"Probability flow solution of the Fokker-Planck equation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.04642","snapshot_observed_at":"2026-08-12T21:51:17.140148Z","title":"Probability flow solution of the Fokker-Planck equa- tion","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.140148Z"},"links":{"cited_paper":"/paper/2206.04642","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:4a39ff50e2dcc78736fe372a1de9717f8a53b33b9c8ddf8ebf619dcb9d922329","observation_id":"ff3a5877-3c1c-4b7c-a23b-b977e6668d11","resolution":{"observed_at":"2026-08-12T21:51:17.140148Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.06628","last_updated":"2023-10-03T18:32:26Z","snapshot_observed_at":"2026-08-13T15:24:21.989471Z","submitted_at":"2022-06-14T06:38:55Z","title":"Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics","version":3},"cited_work":{"arxiv_id":"2206.06628","doi":null,"metadata_source":"pith","pith_arxiv_id":"2206.06628","snapshot_observed_at":"2026-08-12T21:51:18.671149Z","title":"Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics","venue":"math.OC","work_id":"04b5a21c-db6c-49cd-b4ce-85608c30906f","year":2022},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.145367Z"},"links":{"cited_paper":"/paper/2206.06628","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:9450bc6867c830cef7d7a2ecfdb565e25203844e0102528541c5c440f1c5e6a2","observation_id":"74cca6ff-b18a-4d33-9811-643c5aa59d73","resolution":{"observed_at":"2026-08-12T21:51:18.676279Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.150076Z","title":"Gradient Flow Algorithms for Density Propagation in Stochastic Systems","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.150076Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:401783e10b3fbcaaebb3849dca999b6a75fb2addae91d4f16803086657531456","observation_id":"c68cdab8-d11c-4a5d-8177-1c45b9621b73","resolution":{"observed_at":"2026-08-12T21:51:17.150076Z","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":"2026-08-12T21:51:17.155196Z","title":"Wasserstein Proximal Algorithms for the Schrödinger Bridge Problem: Density Control with Nonlinear Drift","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.155196Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:6b3ebbad25da373b439b212f5d7fe6a8e0a3ad930435f467a1938ee47b7e9cbb","observation_id":"59280d11-3aec-4131-918e-4a898843b0a8","resolution":{"observed_at":"2026-08-12T21:51:17.155196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"nlin/0009014","last_updated":"2000-09-06T14:42:57Z","snapshot_observed_at":"2026-08-03T08:59:02.570244Z","submitted_at":"2000-09-06T14:42:57Z","title":"Fronts in passive scalar turbulence","version":1},"cited_work":{"arxiv_id":"nlin/0009014","doi":null,"metadata_source":"pith","pith_arxiv_id":"nlin/0009014","snapshot_observed_at":"2026-08-12T21:51:18.502590Z","title":"Fronts in passive scalar turbulence","venue":"nlin.CD","work_id":"03ad1454-2d06-441e-9048-42fcd3e26132","year":2000},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.159550Z"},"links":{"cited_paper":"/paper/nlin/0009014","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:753e76d195c4abdae0396874367132ee18de292a432f6b42a4e6fc7fe483cd84","observation_id":"b795df78-7258-4503-b93f-909a030b639e","resolution":{"observed_at":"2026-08-12T21:51:18.509813Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.166462Z","title":"Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.166462Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:15b7d27a2ae9a791483cad767ec8cab76a64ee0272cd7d2afa4d545ffb8caa78","observation_id":"6e9ba453-59c8-4e8f-9334-719878ea28c7","resolution":{"observed_at":"2026-08-12T21:51:17.166462Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.12617","last_updated":"2021-08-30T15:08:19Z","snapshot_observed_at":"2026-07-06T11:13:00.529731Z","submitted_at":"2021-05-26T15:17:17Z","title":"E. Schr\\\"odinger's 1931 paper \"On the Reversal of the Laws of Nature\" [\"\\\"Uber die Umkehrung der Naturgesetze\",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]","version":2},"cited_work":{"arxiv_id":"2105.12617","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.12617","snapshot_observed_at":"2026-08-12T21:51:18.480541Z","title":"E. Schr\\\"odinger's 1931 paper \"On the Reversal of the Laws of Nature\" [\"\\\"Uber die Umkehrung der Naturgesetze\",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]","venue":"physics.hist-ph","work_id":"0b453018-e3ce-4023-bf32-6ce8b43b7c20","year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.172248Z"},"links":{"cited_paper":"/paper/2105.12617","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:d0afb3a2fc641f708ea9fb1eceb27a8165ed718f0591ccdb364ac156c8e2e345","observation_id":"f00aba3c-9fd1-4894-aea1-5dcd6d1f62b1","resolution":{"observed_at":"2026-08-12T21:51:18.485972Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0707.2725","last_updated":"2007-07-18T14:13:29Z","snapshot_observed_at":"2026-08-15T10:35:50.203817Z","submitted_at":"2007-07-18T14:13:29Z","title":"Fluctuation Relations for Diffusion Processes","version":1},"cited_work":{"arxiv_id":"0707.2725","doi":null,"metadata_source":"pith","pith_arxiv_id":"0707.2725","snapshot_observed_at":"2026-08-12T21:51:18.460458Z","title":"Fluctuation Relations for Diffusion Processes","venue":"math-ph","work_id":"1e5b498f-948a-4157-94f6-6cfdc841b07c","year":2007},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.179444Z"},"links":{"cited_paper":"/paper/0707.2725","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:2b49d9fea78cb7c78bf352bbc6ed02a76f936677ec212fe298be6615ef2caa88","observation_id":"442f23b8-b514-47c1-ba6c-b04da9ef0c08","resolution":{"observed_at":"2026-08-12T21:51:18.466266Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.09161","last_updated":"2022-09-08T11:58:05Z","snapshot_observed_at":"2026-08-13T18:25:24.857127Z","submitted_at":"2021-08-20T13:15:40Z","title":"Entropic turnpike estimates for the kinetic Schr\\\"odinger problem","version":2},"cited_work":{"arxiv_id":"2108.09161","doi":null,"metadata_source":"pith","pith_arxiv_id":"2108.09161","snapshot_observed_at":"2026-08-12T21:51:18.443284Z","title":"Entropic turnpike estimates for the kinetic Schr\\\"odinger problem","venue":"math.PR","work_id":"0016b01e-d891-40b7-9ab8-2df613efd7c3","year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.184428Z"},"links":{"cited_paper":"/paper/2108.09161","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:2cedb2b7c1c75a03420e2232e8eb9f7918b3d736de112089e810d51920b2d97e","observation_id":"07153828-7314-4c9e-96e5-1fcd0b8444d5","resolution":{"observed_at":"2026-08-12T21:51:18.447824Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.01357","last_updated":"2023-04-05T09:40:05Z","snapshot_observed_at":"2026-08-06T11:05:16.118576Z","submitted_at":"2021-06-01T17:34:27Z","title":"Diffusion Schr\\\"odinger Bridge with Applications to Score-Based Generative Modeling","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.01357","snapshot_observed_at":"2026-08-12T21:51:17.189092Z","title":"Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.189092Z"},"links":{"cited_paper":"/paper/2106.01357","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:342fc534136abd63a295be50c931a8eab39d4ce95457e999bede709e854601ad","observation_id":"fbfc800e-30f9-45ef-84ff-e3299ba7fef3","resolution":{"observed_at":"2026-08-12T21:51:17.189092Z","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":"2026-08-12T21:51:18.920342Z","title":"Quantum trajectory framework for general time- local master equations","venue":null,"work_id":"e689c321-9406-41b6-a3e2-51c0ab97827a","year":2022},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.193329Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:f427f1032656c1bc491ef185c724fd9e8b3df621ce5a76954512449a8db11312","observation_id":"ec32d718-4a85-4b86-b0c1-223227c0e579","resolution":{"observed_at":"2026-08-12T21:51:18.924689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1706.04702","last_updated":"2017-06-15T00:28:58Z","snapshot_observed_at":"2026-08-14T20:53:58.184322Z","submitted_at":"2017-06-15T00:28:58Z","title":"Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1706.04702","snapshot_observed_at":"2026-08-12T21:51:17.197800Z","title":"Deep learning-based numerical methods for high- dimensional parabolic partial differential equations and backward stochastic differential equations","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.197800Z"},"links":{"cited_paper":"/paper/1706.04702","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:8a1ee62e8ac4faad95115672ccb747442c5bf41858d13e90591a50435fa2b0eb","observation_id":"1a47dd74-f10b-4124-8158-6aeacc7a4c14","resolution":{"observed_at":"2026-08-12T21:51:17.197800Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:18.908624Z","title":"Multilevel Picard itera- tions for solving smooth semilinear parabolic heat equations","venue":null,"work_id":"9ab18de8-2c6d-40be-a833-08cb370b0b22","year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.203642Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:82a2759cfb530039af2c102785d68fcdae9bb09c0f11c0eb496db4c7b347b733","observation_id":"924d715e-485a-4bf6-a3e6-10d4f8533c84","resolution":{"observed_at":"2026-08-12T21:51:18.912768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.896682Z","title":"Differentiation of heat semigroups and applications","venue":null,"work_id":"d1847040-eced-4879-9408-df849aa91c6c","year":1993},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.208323Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:238cc154fd7f30b9dda5679f1e3ddfc20df8e4aca3dcf16e1d3b41e395c71c12","observation_id":"83aae094-ff82-4d6f-9093-fcb7f63e106b","resolution":{"observed_at":"2026-08-12T21:51:18.900898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.214520Z","title":"Formulae for the Derivatives of Heat Semigroups","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.214520Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:97631475282448fba79d7e6de068cd2b433ce013c32a087dc410318b353cafd1","observation_id":"1defc553-7a89-4be4-84e5-000aa09bdadb","resolution":{"observed_at":"2026-08-12T21:51:17.214520Z","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":"2026-08-12T21:51:18.885146Z","title":"2nd, revised","venue":null,"work_id":"f1d962a3-7442-45c1-b8c8-da241b0e33c7","year":2006},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.219335Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:637604f9c52f921827e3584b6cba7dd8851d2f811957df97fd8a50dcffdb6127","observation_id":"1cfb14ef-7682-45b6-9378-d2bb58579e7d","resolution":{"observed_at":"2026-08-12T21:51:18.888926Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.06634","last_updated":"2022-03-12T14:32:58Z","snapshot_observed_at":"2026-08-13T19:40:12.259237Z","submitted_at":"2021-04-14T05:41:13Z","title":"Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.06634","snapshot_observed_at":"2026-08-12T21:51:17.224980Z","title":"Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.224980Z"},"links":{"cited_paper":"/paper/2104.06634","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:39db8f538f7ed27a33b1e68ee43f3e19a807f2e423c153a32fb4cd6cd67371a8","observation_id":"a4644ad1-e896-464a-9255-7f30d5de063a","resolution":{"observed_at":"2026-08-12T21:51:17.224980Z","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":"10.1007/pl00013529","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.680576Z","title":"ApplicationsofMalli- avin calculus to Monte-Carlo methods in finance. II","venue":null,"work_id":"f84c6cd0-364e-4dcf-a41f-24c9b4538344","year":2001},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.229821Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:d5dfcd1aa95082ee60c2ec3c4d19b09b3bcfa56b52e5acf05ea83283e224ddac","observation_id":"3a5b70a4-8dd6-481e-8b93-956d6e992dfe","resolution":{"observed_at":"2026-08-12T21:51:17.686093Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s007800050068","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.657703Z","title":"Ap- plications of Malliavin calculus to Monte Carlo methods in finance","venue":null,"work_id":"a2f6a271-5ffd-483b-90bd-00a431b05bb5","year":1999},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.234057Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:604127749fc916a7a97b18c0349a59758d48440fd52384a39b79dc47eda62f4a","observation_id":"fb8d8957-35be-470c-b4aa-a79fd2bcda41","resolution":{"observed_at":"2026-08-12T21:51:17.663757Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.238351Z","title":"The geometry of physics: an introduction","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.238351Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:4bfd740f67e5b6fb81bbdd4f44e3550ada5eb41b896665d3ee993171d2248823","observation_id":"afb8b1d6-1052-49ff-9f9c-24eeb277704d","resolution":{"observed_at":"2026-08-12T21:51:17.238351Z","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":"2026-08-12T21:51:18.873242Z","title":"Solvinghigh-dimensionalpartialdifferentialequations using deep learning","venue":null,"work_id":"43e14271-faec-4f5b-b35f-4586be77c243","year":2018},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.242635Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:27ef767028afb103aef8901a316d5f835b21c06e26a1efa2d867c941d6b22bb9","observation_id":"767c8167-42f3-4200-9779-82c0a1b0fc73","resolution":{"observed_at":"2026-08-12T21:51:18.877591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.246937Z","title":"Horn and Charles R","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.246937Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:1176c00ce5aaf3e986c3caf45b27175d671c67c21069d642ec851b3f0f2f02f0","observation_id":"d9a4c244-7f4c-4c8c-8ff2-187245d1ae9f","resolution":{"observed_at":"2026-08-12T21:51:17.246937Z","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":"6920.10886","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:18.182689Z","title":"Estimation of Non-Normalized Statistical Models by Score Matching","venue":null,"work_id":"8a02b0ec-0ace-48bb-a5af-d89147355d50","year":null},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.250941Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:fd350aafb9b7392a1773d497e162e5ea1592edce763d90632c0b09daf685604c","observation_id":"705e98ab-4a15-4963-8160-28aec8a547f0","resolution":{"observed_at":"2026-08-12T21:51:18.192407Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.01457","last_updated":"2018-11-10T18:49:35Z","snapshot_observed_at":"2026-08-14T18:06:01.247142Z","submitted_at":"2018-11-01T00:32:27Z","title":"Fashionable Modelling with Flux","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.01457","snapshot_observed_at":"2026-08-12T21:51:17.255125Z","title":"Fashionable Modelling with Flux","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.255125Z"},"links":{"cited_paper":"/paper/1811.01457","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:b8fc57fd88760f21873a4876d878356514d15cf1c9910fe5d9f8f9606e8733f6","observation_id":"44a92b8a-2b12-45b4-af60-8eb703e0b545","resolution":{"observed_at":"2026-08-12T21:51:17.255125Z","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":"2026-08-12T21:51:17.259610Z","title":"Flux: Elegant Machine Learning with Julia","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.259610Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:e629ef22d6b8cecc625eac2f83054c4a21d1ec48a61e5975206a4139ab755bb7","observation_id":"35b44581-182e-44f2-999c-aebd99f95736","resolution":{"observed_at":"2026-08-12T21:51:17.259610Z","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":"10.1002/anie.200504313","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Synthetic Molecular Motors and Mechan- ical Machines","venue":"Angewandte Chemie International Edition","work_id":"ad91a001-cd52-4ec9-84bc-c174a766dbe9","year":2007},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.264902Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:9ba7ffd98a13ec44b1e75e06f7bae4bec69d34d064629912234826eb768eab8a","observation_id":"e6f1e33e-32dc-422b-93da-43fd809a1fe0","resolution":{"observed_at":"2026-08-12T21:51:17.631212Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.861077Z","title":"Adam: A Method for Stochastic Optimization","venue":null,"work_id":"3b4c295f-5c0b-4b8a-87b2-ab10f5b3107f","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.269352Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:69339d342cf34475c14a2a413cd76ae9a8829a08f7f84ff7fcc5475c17be5997","observation_id":"e5779a7a-8cf3-466a-baec-a88aaaf91125","resolution":{"observed_at":"2026-08-12T21:51:18.865623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/p386","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.609019Z","title":"Klebaner","venue":null,"work_id":"3a5397e9-884d-4fea-802e-dedfb2f60e58","year":2005},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.273466Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:88eb3f0dbecce4fc0c2713bb5913b7ac7e273f38375d0caef185f649226507df","observation_id":"bb2c93fe-87b0-45a6-86cb-7ff0ca2bc2ff","resolution":{"observed_at":"2026-08-12T21:51:17.613584Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s004400050085","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.594812Z","title":"Reciprocal diffusions in flat space","venue":null,"work_id":"19ee4114-45c0-49e5-80d8-3cc93ca35b27","year":1997},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.278190Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:3a77032d094dd78f6d176a6463ca69f0e8321584dbe43a41e780c77dc1a5e30e","observation_id":"fa9dfa6e-a894-4983-9584-1ba0544b877b","resolution":{"observed_at":"2026-08-12T21:51:17.599689Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.849224Z","title":"Lectures on Stochastic Flows And Applications","venue":null,"work_id":"5b9dff16-74f6-436e-b893-6f111bcf56d7","year":1986},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.282315Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:ad0730716f7425336a7c8dc76c06a903e6997e2d52c44608041668d8222731c1","observation_id":"1ed24dd3-ee77-4253-a0e7-bf23c7c39ccb","resolution":{"observed_at":"2026-08-12T21:51:18.853808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/17442508208833209","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.580560Z","title":"On backward stochastic differential equations","venue":null,"work_id":"a969ed66-8d7c-4383-b12a-d587c1e7e838","year":1982},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.286398Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:2f53515f2dac9e8e4e7ab6b64731a5397812c6a068797d6bfbf3e05ba8a2f20e","observation_id":"6ff76327-b671-44bb-8df3-6ccf363233de","resolution":{"observed_at":"2026-08-12T21:51:17.585988Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.290640Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.290640Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:c201369001bd6c06e475220ce1e9d682e08b85538de5bf34997f4cd3f2d7fca9","observation_id":"ccd31cfd-697e-4e7a-97af-3fab6045db65","resolution":{"observed_at":"2026-08-12T21:51:17.290640Z","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":"2026-08-12T21:51:18.837539Z","title":"A survey of the Schrödinger problem and some of its connections with optimal transport","venue":null,"work_id":"4e032f54-577e-4c96-91fb-a907430f22b0","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.295171Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:8daf8138b1fbb0319ec6281e4efc0f18fe2aaf47a9374ffdbd369356958e80b2","observation_id":"a896f164-8eb0-4bd0-8d74-845856d60d4d","resolution":{"observed_at":"2026-08-12T21:51:18.841693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.00702","last_updated":"2020-06-01T04:06:38Z","snapshot_observed_at":"2026-08-16T00:29:46.292504Z","submitted_at":"2020-06-01T04:06:38Z","title":"Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.00702","snapshot_observed_at":"2026-08-12T21:51:17.304127Z","title":"InteractingParticleSolutionsofFokker–Planck Equations Through Gradient–Log–Density Estimation","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.304127Z"},"links":{"cited_paper":"/paper/2006.00702","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:01d1f7300161b3c513e80f7ee998e5be851d54bdad8ef99abd1b045c5d7259e4","observation_id":"991e92ff-4130-4e8a-bd31-e63a7d763ae0","resolution":{"observed_at":"2026-08-12T21:51:17.304127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.1282","last_updated":"2015-07-30T15:13:16Z","snapshot_observed_at":"2026-08-14T23:09:09.115797Z","submitted_at":"2014-12-03T11:43:06Z","title":"Brownian Carnot engine","version":4},"cited_work":{"arxiv_id":"1412.1282","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.1282","snapshot_observed_at":"2026-08-12T21:51:18.053682Z","title":"Brownian Carnot engine","venue":"cond-mat.stat-mech","work_id":"4bf2ba01-2906-45da-80d7-e2dc1d4aecf4","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.308720Z"},"links":{"cited_paper":"/paper/1412.1282","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:af1bdb4dbcfbc15c38b0d57b04d83bfa22b3e3b4f1370266db831553f5b13646","observation_id":"157e7a52-4907-4779-ac23-92c69c41694f","resolution":{"observed_at":"2026-08-12T21:51:18.059245Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"nlin/0010042","last_updated":"2000-10-26T10:06:57Z","snapshot_observed_at":"2026-08-02T09:08:35.498534Z","submitted_at":"2000-10-26T10:06:57Z","title":"Passive scalar turbulence in high dimensions","version":1},"cited_work":{"arxiv_id":"nlin/0010042","doi":null,"metadata_source":"pith","pith_arxiv_id":"nlin/0010042","snapshot_observed_at":"2026-08-12T21:51:18.033007Z","title":"Passive scalar turbulence in high dimensions","venue":"nlin.CD","work_id":"9ec5be4e-0551-4116-94d5-39a45da4f642","year":2000},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.314373Z"},"links":{"cited_paper":"/paper/nlin/0010042","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:da66e6624b461f44990a1bfe6e5c97a690dfd2ed032c82b5d5029c494a8d257f","observation_id":"d02d2adf-b772-44a6-8a0c-eb4c7cd7fe63","resolution":{"observed_at":"2026-08-12T21:51:18.038907Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.825298Z","title":"Géométriedifférentiellestochastique,II","venue":null,"work_id":"f3424cc0-fb2f-46a6-aafe-fda1f25ad597","year":1982},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.318992Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:d6d12f3080443f250574597b62fdd4a11580fb106638a85c5231d74612bd47db","observation_id":"1311ae19-52fc-4289-b9f3-81828fa506fd","resolution":{"observed_at":"2026-08-12T21:51:18.829588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.323463Z","title":"Diffusion processes and Riemannian geometry","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.323463Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:03b0d631c292570b615a0ca0175b78440172f587ba8ebcb68c00a17df1f8c854","observation_id":"3669c8f0-78e2-4d2d-9d97-488bb0232ddf","resolution":{"observed_at":"2026-08-12T21:51:17.323463Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1401.3394","last_updated":"2014-01-15T00:14:15Z","snapshot_observed_at":"2026-08-14T23:48:26.282828Z","submitted_at":"2014-01-15T00:14:15Z","title":"On extremals of the entropy production by \"Langevin-Kramers\" dynamics","version":1},"cited_work":{"arxiv_id":"1401.3394","doi":null,"metadata_source":"pith","pith_arxiv_id":"1401.3394","snapshot_observed_at":"2026-08-12T21:51:18.013583Z","title":"On extremals of the entropy production by \"Langevin-Kramers\" dynamics","venue":"cond-mat.stat-mech","work_id":"c29e4bf4-fe62-43fb-b82e-a8fcddc7dd8d","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.327963Z"},"links":{"cited_paper":"/paper/1401.3394","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:98e2e2381d50b4e401a0d108254a3e2872e6434af43653fe960a0510b344af4d","observation_id":"a53afb22-de3e-463b-8b42-d764cbc019cd","resolution":{"observed_at":"2026-08-12T21:51:18.018302Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1503.05788","last_updated":"2015-06-08T10:49:34Z","snapshot_observed_at":"2026-08-14T22:55:40.670225Z","submitted_at":"2015-03-19T14:56:56Z","title":"On the efficiency of heat engines at the micro-scale and below","version":2},"cited_work":{"arxiv_id":"1503.05788","doi":null,"metadata_source":"pith","pith_arxiv_id":"1503.05788","snapshot_observed_at":"2026-08-12T21:51:17.991091Z","title":"On the efficiency of heat engines at the micro-scale and below","venue":"cond-mat.stat-mech","work_id":"f363f619-e5e5-4947-883f-c2dfa5e5b6b7","year":2015},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.333024Z"},"links":{"cited_paper":"/paper/1503.05788","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:cf4eb39fe42605f47f992f9688aa37f97ca284e2acbc72e0006085cdd3616976","observation_id":"c3ca24eb-b1db-4ca7-aadb-8ecf439492d0","resolution":{"observed_at":"2026-08-12T21:51:17.996346Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.5298","last_updated":"2014-11-26T09:33:14Z","snapshot_observed_at":"2026-08-14T23:22:14.618285Z","submitted_at":"2014-08-22T14:11:37Z","title":"On how nanomechanical systems can minimize dissipation","version":2},"cited_work":{"arxiv_id":"1408.5298","doi":null,"metadata_source":"pith","pith_arxiv_id":"1408.5298","snapshot_observed_at":"2026-08-12T21:51:17.969417Z","title":"On how nanomechanical systems can minimize dissipation","venue":"cond-mat.stat-mech","work_id":"cf58add3-40c0-4257-b8e7-d9658f1dd1ea","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.338272Z"},"links":{"cited_paper":"/paper/1408.5298","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:335f283cac0fe27a86ceb5c955e9edfb73e7c63c01654ddb398d812e12f85c14","observation_id":"71aa37a3-005e-46ac-bf89-368fe726ab51","resolution":{"observed_at":"2026-08-12T21:51:17.975142Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.811546Z","title":"Dynamical Theories of Brownian Motion","venue":null,"work_id":"b2ab9596-2e60-4d83-ac4b-94c56e6fd93f","year":2001},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.342789Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:241b3fa2e68ff78bcbdd53ca8fde85782821a5b94b02a47c2b6e248054225fa7","observation_id":"c84eabc0-fac0-4566-b96e-862d4ba3f800","resolution":{"observed_at":"2026-08-12T21:51:18.816842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.795380Z","title":"The Malliavin calculus and related topics","venue":null,"work_id":"1e5c3ac1-20bb-412c-bd9e-60aa91c66294","year":1995},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.348304Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:4c8502b53af083ca422efed0c110c551f7405c568a1ab2c05d330ced530251a4","observation_id":"f6e3a4c0-82d2-4962-b492-9a281d8bf45c","resolution":{"observed_at":"2026-08-12T21:51:18.799598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.781247Z","title":"Pavliotis","venue":null,"work_id":"7557619f-1dc0-416a-9df2-1cc719fba1b7","year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.352746Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:1f7fd9603fff3993fae4d48dacdd8b090f2ab57da7da5671b4f5f9e8302b48db","observation_id":"22e2f081-f25e-4667-871a-e311a8b7d094","resolution":{"observed_at":"2026-08-12T21:51:18.785658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.363827Z","title":"Stochastic Thermodynamics","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.363827Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:3b706fb2940708b7ff7ba4755d59af6f4262f44a7d54f8ce1b424fa03944f2e8","observation_id":"0fe83dc5-7218-400f-a97b-51dcd394e962","resolution":{"observed_at":"2026-08-12T21:51:17.363827Z","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":"2026-08-12T21:51:17.358202Z","title":"url: https://link.springer.com/book/10.1007/978- 1-4939-1323-7","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.358202Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:fe948dd035bb5d20227a8410bfd3b872c35ea88d75cc2f70433648e2a0947f6e","observation_id":"7c257101-088f-4394-ace1-e051d65f84ec","resolution":{"observed_at":"2026-08-12T21:51:17.358202Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.03242","last_updated":"2020-06-05T05:40:22Z","snapshot_observed_at":"2026-08-03T23:33:49.991881Z","submitted_at":"2020-06-05T05:40:22Z","title":"Finite-time Landauer principle","version":1},"cited_work":{"arxiv_id":"2006.03242","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.03242","snapshot_observed_at":"2026-08-12T21:51:17.888984Z","title":"Finite-time Landauer principle","venue":"cond-mat.stat-mech","work_id":"b1d6e453-5826-4e10-b22a-64da00b44a70","year":2020},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.375185Z"},"links":{"cited_paper":"/paper/2006.03242","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:62dfaff427e8b9af38f63453e316cf7291dbbbc9e56d0e14e3c070f5ebd1b751","observation_id":"e3b6d116-0e46-44ad-b6ff-9637d94956ca","resolution":{"observed_at":"2026-08-12T21:51:17.893776Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.767654Z","title":"Constrained Differential Optimization","venue":null,"work_id":"058d4b58-7072-41d8-bbc9-94ee9e8c0911","year":1987},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.368952Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:4f3eb14ebb07962035f417325f1a648b427712ae13ffc546716ab8262f17eba3","observation_id":"379f8c27-5f1f-4ffd-a497-03abec8461e6","resolution":{"observed_at":"2026-08-12T21:51:18.772843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.15678","last_updated":"2025-02-03T14:17:09Z","snapshot_observed_at":"2026-08-12T23:17:15.240334Z","submitted_at":"2024-07-22T14:47:08Z","title":"Minimal work protocols for inertial particles in non-harmonic traps","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.15678","snapshot_observed_at":"2026-08-12T21:51:17.386506Z","title":"Minimal-work protocols for inertial particles in non-harmonic traps","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.386506Z"},"links":{"cited_paper":"/paper/2407.15678","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:89319f436066b45e9ac1efe313d1bd62d7caa7279b237125e87780672fa4915c","observation_id":"549c72ac-565f-4c50-94c9-9292629cacd9","resolution":{"observed_at":"2026-08-12T21:51:17.386506Z","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":"2026-08-12T21:51:18.754918Z","title":"DifferentialEquations.jl–a performant and feature-rich ecosystem for solving differential equations in Julia","venue":null,"work_id":"d264cd77-ef53-4136-9111-085a049b8cbb","year":2017},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.381582Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:caac66d660525690ef3f3d52cdd0ad35148aadcca935e7573c332aecac79aa58","observation_id":"e62d4838-3a12-4b0f-9922-3c18e5e8b237","resolution":{"observed_at":"2026-08-12T21:51:18.759378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0710.4097","last_updated":"2007-10-22T16:55:14Z","snapshot_observed_at":"2026-08-15T10:29:25.931422Z","submitted_at":"2007-10-22T16:55:14Z","title":"Efficiency at maximum power: An analytically solvable model for stochastic heat engines","version":1},"cited_work":{"arxiv_id":"0710.4097","doi":null,"metadata_source":"pith","pith_arxiv_id":"0710.4097","snapshot_observed_at":"2026-08-12T21:51:17.842158Z","title":"Efficiency at maximum power: An analytically solvable model for stochastic heat engines","venue":"cond-mat.stat-mech","work_id":"42463e15-3a59-4fee-8502-24567b6bf038","year":2007},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.397152Z"},"links":{"cited_paper":"/paper/0710.4097","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:3254c96561700773985ddc490189f807a92fec094d1aea76996cce2c8d354652","observation_id":"c017e752-a9e7-4cc1-a047-04da4cb08d1c","resolution":{"observed_at":"2026-08-12T21:51:17.847165Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.00679","last_updated":"2024-08-05T10:23:35Z","snapshot_observed_at":"2026-08-15T21:53:11.086015Z","submitted_at":"2024-03-01T17:10:51Z","title":"Optimal Control of Underdamped Systems: An Analytic Approach","version":2},"cited_work":{"arxiv_id":"2403.00679","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.00679","snapshot_observed_at":"2026-08-12T21:51:17.866593Z","title":"Optimal Control of Underdamped Systems: An Analytic Approach","venue":"cond-mat.stat-mech","work_id":"57f66810-4276-4027-b4c5-2212ea6bd51e","year":2024},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.391929Z"},"links":{"cited_paper":"/paper/2403.00679","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:37a21b4b6c71ce8756578c30dcff5d2d743227ba17bbaa0bdfbc71e021d8241d","observation_id":"2860b6ed-2f42-40f6-a7e9-7c5628790593","resolution":{"observed_at":"2026-08-12T21:51:17.873106Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.406751Z","title":"Über die Umkehrung der Naturgesetze","venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.406751Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:5c7e5e9e283552f7521cee60fffacd8b3c20d05695a3f70c018365f305b38e8f","observation_id":"79854a39-dfa6-4bcf-8b6f-5d20a8444634","resolution":{"observed_at":"2026-08-12T21:51:17.406751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0801.3743","last_updated":"2008-07-23T10:00:43Z","snapshot_observed_at":"2026-08-15T10:23:01.883198Z","submitted_at":"2008-01-24T12:46:42Z","title":"Efficiency of molecular motors at maximum power","version":2},"cited_work":{"arxiv_id":"0801.3743","doi":null,"metadata_source":"pith","pith_arxiv_id":"0801.3743","snapshot_observed_at":"2026-08-12T21:51:17.820418Z","title":"Efficiency of molecular motors at maximum power","venue":"cond-mat.stat-mech","work_id":"1adb5a36-4091-49b0-94cb-6ecc7a94010a","year":2008},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.402082Z"},"links":{"cited_paper":"/paper/0801.3743","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:acc0f139e3111b166c3296268b1ce0b917ea6b78ff1db8c062fe96538a913503","observation_id":"c0610734-2f79-4672-88d5-a7d98b3ae5c5","resolution":{"observed_at":"2026-08-12T21:51:17.826569Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:17.414991Z","title":"Stochastic Energetics","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.414991Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:ea9be6e8daa3e25590d8923b97c7850fe28d6fb7a132ff446242bfa1268a6a01","observation_id":"cd3ef233-4b4d-451e-a0c1-169e34f68723","resolution":{"observed_at":"2026-08-12T21:51:17.414991Z","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":"2026-08-12T21:51:18.743482Z","title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","venue":null,"work_id":"d214ef9a-9b0d-4b8a-80f5-083f70348d98","year":2012},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.411009Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:7bcad5bd6488ca300b4fe905f0c8bd3908fd6cb33da10f1994ecb34c35ab743b","observation_id":"4a19943b-f1be-4f1d-8d67-0c799557d0e1","resolution":{"observed_at":"2026-08-12T21:51:18.747605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.729932Z","title":"Efficient computation of optimal actions","venue":null,"work_id":"46681bc1-505b-478c-ab07-c91acb46b2a1","year":2009},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.423937Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:31400098b6871690bedbc56b7a940d039bd298a80eac33fc40c8715413dc4b4e","observation_id":"377d9685-0cb3-47c5-92d3-d959d90bd13b","resolution":{"observed_at":"2026-08-12T21:51:18.735038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1201/b12126","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.505450Z","title":"Estimating functions for diffusion-type processes","venue":null,"work_id":"f0eb091d-69ee-43cf-9748-4345422848c5","year":2012},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.419688Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:f25c99cc6db0c61ec85a6ccb9d8c2a5b5aec20ccba28694431ecd4aa15f5e98d","observation_id":"d8145a94-98b0-4a43-8d89-9bbb2b7d6c74","resolution":{"observed_at":"2026-08-12T21:51:17.513824Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:51:18.716813Z","title":"Solving Schrödinger Bridges via Maximum Likelihood","venue":null,"work_id":"ce994a8a-5012-49b4-81df-7055af3bce03","year":2021},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.434328Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:4ac5ac83cdada8481e6a2c53f64e0e162264170bd8ffeedcf8e47b063dbf6dce","observation_id":"168c0cf8-d7cf-4a79-832e-6aa2a5356979","resolution":{"observed_at":"2026-08-12T21:51:18.721030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.01608","last_updated":"2019-05-31T15:23:24Z","snapshot_observed_at":"2026-08-14T17:07:28.464755Z","submitted_at":"2019-03-05T00:38:49Z","title":"Theoretical guarantees for sampling and inference in generative models with latent diffusions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.01608","snapshot_observed_at":"2026-08-12T21:51:17.429160Z","title":"Theoretical guarantees for sampling and inference in gen- erative models with latent diffusions","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.429160Z"},"links":{"cited_paper":"/paper/1903.01608","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:ed36b595bf8bf593af0a76365ca4cc310aea709e2043e58e7d080fe783923cad","observation_id":"c5557bad-6feb-4c0d-bcc1-a678c14d5721","resolution":{"observed_at":"2026-08-12T21:51:17.429160Z","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":"2026-08-12T21:51:17.443257Z","title":"Stochastic flows and Bismut formulas for stochastic Hamiltonian systems","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.443257Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:de3c4a4890907b435fff6672e30260c34c22fbf1b4e10fc57d102881cf467edc","observation_id":"835eded8-ad2c-41c7-b2d8-50898954d941","resolution":{"observed_at":"2026-08-12T21:51:17.443257Z","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":"2026-08-12T21:51:17.438717Z","title":"Optimal transport: old and new","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.438717Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:6eeec08e5e1216fc88dce3e96e00b8f5c76fca7ea81a95c7f67a4a5edb5e9047","observation_id":"d2de28ac-2ca8-483f-bb99-0356e7906add","resolution":{"observed_at":"2026-08-12T21:51:17.438717Z","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":"product/9780195","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:51:17.783709Z","title":"Nonequilibrium statistical mechanics","venue":null,"work_id":"5cf58041-6fda-48c9-8ff5-cad18f64d2de","year":2001},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.447751Z"},"links":{"citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:3065ee057044aa6578801f83e23cc41b6d04a87ddda514a5f2ad4731464d01e2","observation_id":"302852ee-7f4c-4ca7-a8b8-1a1988500171","resolution":{"observed_at":"2026-08-12T21:51:17.789757Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1308.0215","last_updated":"2013-08-01T14:16:38Z","snapshot_observed_at":"2026-08-15T00:36:12.054599Z","submitted_at":"2013-08-01T14:16:38Z","title":"A survey of the Schr\\\"odinger problem and some of its connections with optimal transport","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.0215","snapshot_observed_at":"2026-08-12T21:51:17.299576Z","title":"doi: 10.3934/dcds.2014.34.1533","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula","version":2},"reference_index":1574,"source":"pdf_text","source_observed_at":"2026-08-12T21:51:17.299576Z"},"links":{"cited_paper":"/paper/1308.0215","citing_paper":"/paper/2411.08518"},"observation_digest":"sha256:48634988c0bae273538935eab4137ceeb1c9f9b8fce5e203c2d4a5d7a58973f0","observation_id":"b0238c9f-a5b7-4281-a6fd-27fa17cb8101","resolution":{"observed_at":"2026-08-12T21:51:17.299576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.08518","last_updated":"2025-02-01T08:38:26Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-15T00:11:48.015280Z","submitted_at":"2024-11-13T11:03:40Z","title":"On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula"},"reference_resolution":{"displayed":69,"state_counts":{"malformed_identifier":12,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":20,"verified_exact":17,"verified_fuzzy":19},"total_outbound_references":69},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 0 inbound Pith citation observations for arXiv:2411.08518."}