{"as_of":"2026-08-21T14:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bb6aad02523d9264a11a099fad0cdcc9327387d97e9070d5a39e2fab6ee1eed8","coverage":[{"denominator":53,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":53,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:56:20.103050Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:14:08.458160Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T06:22:27.534325Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.14939","snapshot_observed_at":"2026-08-06T18:14:08.458160Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.09413","last_updated":"2026-06-17T14:48:33Z","snapshot_observed_at":"2026-08-17T04:42:11.933758Z","submitted_at":"2025-07-12T22:34:37Z","title":"Model Reduction of Multivariate Geometric Brownian Motions and Localization in a Two-State Quantum System","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:14:08.458160Z"},"links":{"cited_paper":"/paper/2506.14939","citing_paper":"/paper/2507.09413"},"observation_digest":"sha256:fe4b0535f9ad7000a5adc153d53c61955a6bcfdb9f7179d4a7423199fc6d8d37","observation_id":"9c6a08fb-3f1e-4c31-8103-4388070fb463","resolution":{"observed_at":"2026-08-06T18:14:08.458160Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"cited_work":{"arxiv_id":"2506.14939","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.14939","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","venue":null,"work_id":"13cf3534-b7fa-46eb-9cdc-bb9a916802b8","year":2025},"citing_paper":{"arxiv_id":"2602.08318","last_updated":"2026-05-07T12:57:02Z","snapshot_observed_at":"2026-08-15T00:53:08.639821Z","submitted_at":"2026-02-09T06:48:45Z","title":"Is Flow Matching Just Trajectory Replay for Sequential Data?","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-16T06:22:23.161815Z"},"links":{"cited_paper":"/paper/2506.14939","citing_paper":"/paper/2602.08318"},"observation_digest":"sha256:066e31124db4f5a3c0f50627b729c29eee9fefab1210538edfb4308d4a844388","observation_id":"dda73381-6bfe-4d7a-a52c-1e1f30ec2305","resolution":{"observed_at":"2026-05-16T06:22:27.537042Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.14939/citation-record","integrity":"/paper/2506.14939/integrity","json":"/paper/2506.14939/citation-record.json","paper":"/paper/2506.14939"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T19:56:20.664073Z","title":"Hypercontractivity and asymptotic behavior in nonautonomous kolmogorov equations","venue":null,"work_id":"203baec8-6350-4ce1-b601-082ff4998285","year":2013},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.917105Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:eeeab808f1ef2536cc4e510e2f11c9615acb2b99bd27929b0d2af074bd738806","observation_id":"d251e10c-53cc-48e5-93d4-31edaef1d5be","resolution":{"observed_at":"2026-08-15T19:56:20.667700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.654389Z","title":"Linear algebra done right","venue":null,"work_id":"fd55e314-919c-44cf-869d-05d0fb64966a","year":1997},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.920976Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:49d0c9bc8ec8b5218e4b77409433833af9f21693570165feb736420d5e27cacf","observation_id":"3a47ce27-caa7-413f-8b75-f7044eec567a","resolution":{"observed_at":"2026-08-15T19:56:20.657880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.01247","last_updated":"2019-01-16T14:17:51Z","snapshot_observed_at":"2026-08-21T02:47:17.679522Z","submitted_at":"2018-04-04T06:12:58Z","title":"A non-linear kinetic model of self-propelled particles with multiple equilibria","version":2},"cited_work":{"arxiv_id":"1804.01247","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.01247","snapshot_observed_at":"2026-08-15T19:56:20.151979Z","title":"A non-linear kinetic model of self-propelled particles with multiple equilibria","venue":"math-ph","work_id":"557ad942-d5fe-436c-b96a-e4ac47223ee9","year":2018},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.924596Z"},"links":{"cited_paper":"/paper/1804.01247","citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:0bbecb245d4cbed99bab4eb372d71c4f5a2e059793e827692823bd8cd7daeae6","observation_id":"74a9aa3d-8842-4f0a-abc8-f25a16ae42ca","resolution":{"observed_at":"2026-08-15T19:56:20.157518Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.644269Z","title":"Global regularity and bounds for solutions of parabolic equations for probability measures","venue":null,"work_id":"4e042b64-4303-4ea7-984a-2bce748cbe97","year":2006},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.928734Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:8ea08ea4072cd9140ed0fc99ae40fbef390ffeaff216f6c4a59d6ac4c4af5404","observation_id":"553871fc-1243-4725-b9b7-051cf127661e","resolution":{"observed_at":"2026-08-15T19:56:20.647706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.633575Z","title":"Mimicking an it\\^ o process by a solution of a stochastic differential equation","venue":null,"work_id":"21db91db-ed60-4fa6-bb5a-8dd285577497","year":2010},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.931938Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:cfc8e7c6bfdce3a7767703b724a4511222d00bc8840df132ff1a03facdd9e64e","observation_id":"5b3cd4e9-3a1c-4cdd-8ff7-e9b435a09519","resolution":{"observed_at":"2026-08-15T19:56:20.637066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.623728Z","title":"Long-time behaviour of degenerate diffusions: Ufg-type sdes and time-inhomogeneous hypoelliptic processes","venue":null,"work_id":"a692e6fb-7d7d-4f07-a4c0-cfcb6d8e9074","year":2021},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.935435Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:6cac01ed5328ba4ff1675e6105b81af07678629003aa346899f7990da51d5806","observation_id":"767ec52e-885e-4a96-b571-8297e8c5dcfc","resolution":{"observed_at":"2026-08-15T19:56:20.627288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.02679","last_updated":"2024-04-05T16:56:35Z","snapshot_observed_at":"2026-08-21T07:51:23.371493Z","submitted_at":"2022-04-06T09:01:09Z","title":"Poisson Equations with locally-Lipschitz coefficients and Uniform in Time Averaging for Stochastic Differential Equations via Strong Exponential Stability","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.02679","snapshot_observed_at":"2026-08-15T19:56:19.938957Z","title":"Poisson equations with locally-lipschitz coefficients and uniform in time averaging for stochastic differential equations via strong exponential stability","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.938957Z"},"links":{"cited_paper":"/paper/2204.02679","citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:eb9d35c6e64befff67309dd87e6d989ee86b1999c97a46bb9c3a0079418c6829","observation_id":"dec6ec76-cb95-45be-ba46-d1ddfc983701","resolution":{"observed_at":"2026-08-15T19:56:19.938957Z","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":"2026-08-15T19:56:20.613923Z","title":"Uniform in time estimates for the weak error of the euler method for sdes and a pathwise approach to derivative estimates for diffusion semigroups","venue":null,"work_id":"5474d997-fcae-4847-a78c-0ccf527aa41e","year":2021},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.942668Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:7880f32c289e409323108837b731eaa6f6da7434cedc80ef92f6c5af78d7e73d","observation_id":"6eddae4b-dd4c-4a75-b728-fab4817732dc","resolution":{"observed_at":"2026-08-15T19:56:20.617253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.604175Z","title":"Optimal prediction and the mori--zwanzig representation of irreversible processes","venue":null,"work_id":"7c7ea7c4-da50-4894-ab9b-1ae4e0ec77e8","year":2000},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.945835Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:fd47c1cf3c3e2734f24aec7bd62c400987a720aa471ffaf57b46d5873e7eb0ce","observation_id":"3f2452c6-9609-453a-88b2-c070120bfc10","resolution":{"observed_at":"2026-08-15T19:56:20.607732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.594578Z","title":"Optimal prediction with memory","venue":null,"work_id":"2b26d782-538b-4bc6-bef3-017dd5753fad","year":2002},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.949096Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:c9a8fa0cfeb6b228a04680abd63bb9ed715fc7ef0316a3c4648d796190d5d92d","observation_id":"711a033b-8736-43ff-91a9-b47b0542f804","resolution":{"observed_at":"2026-08-15T19:56:20.598265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.584774Z","title":"Prediction from partial data, renormalization, and averaging","venue":null,"work_id":"2e40f3ab-9f56-47e4-92ea-c48dfa172098","year":2006},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.952419Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:a1c37edefb55c32eee6df04a01e00b18629e93644348280fdc19068e3fbc907e","observation_id":"284646ae-60b5-4345-9993-e11eefedf155","resolution":{"observed_at":"2026-08-15T19:56:20.588116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.575050Z","title":"Optimal prediction for hamiltonian partial differential equations","venue":null,"work_id":"3f12c64a-b886-4d4d-806e-d732c9ca984b","year":2000},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.955791Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:d268930b26ad92af16b04152da9dc657ff202af7e94e25f4f8de5e9dd2b760a8","observation_id":"86d6f302-5a6e-493d-9f0f-7012a30361ee","resolution":{"observed_at":"2026-08-15T19:56:20.578464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.564899Z","title":"Pointwise gradient bounds for degenerate semigroups (of ufg type)","venue":null,"work_id":"fffc2e5e-dab7-4934-8751-cabb925d911b","year":2016},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.959126Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:32834fedbec80b17fcfc88874fd7e6881bb8f3a697936f277e261f3b6d08095a","observation_id":"31af655b-c20d-453a-9def-da8c110d4e73","resolution":{"observed_at":"2026-08-15T19:56:20.568422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.554753Z","title":"Global existence of smooth solutions for the vlasov-fokker-planck equation in 1 and 2 space dimensions","venue":null,"work_id":"fb179c5c-6d88-4781-8c75-987b8b573073","year":1986},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.962794Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:8f361a2d24181b0fc67fd4a6f3af520fcba14266a2d8f74d5e088f1df9d32940","observation_id":"ca15ae91-f8ac-468e-8a20-ebda1249117a","resolution":{"observed_at":"2026-08-15T19:56:20.558646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.544550Z","title":"Quantification of coarse-graining error in langevin and overdamped langevin dynamics","venue":null,"work_id":"ad4a620b-0e92-4546-b3e6-99d8933b673c","year":2018},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.965877Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:26f678fbdc1f795fd5d89df4389cf9c9e01028b4a75b97e2c57d60c720496bda","observation_id":"1cc074d4-b104-4096-949c-ed6ea8728d5c","resolution":{"observed_at":"2026-08-15T19:56:20.547923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.533719Z","title":"Ornstein--uhlenbeck operators with time periodic coefficients","venue":null,"work_id":"704cae43-7a27-4768-8a34-8476236e4f03","year":2007},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.968985Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:0c6f84d7a7bd49505cc8ca33c8fc9c45ac1e2d617a63033130cd3c1a0c0b428d","observation_id":"6b11ec74-135b-4d81-bdee-88a3dffcdcc5","resolution":{"observed_at":"2026-08-15T19:56:20.537579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.521946Z","title":"Analysis of multiscale methods for stochastic differential equations","venue":null,"work_id":"cc122ff7-3c33-4fe5-9d28-66b01a165e0b","year":2005},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.972602Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:c38315e8cda440c2b387e1e48e69524b967e23b9961c5bb21593ccf1dfe2d43f","observation_id":"6bae7e9a-39f5-4d59-942e-d891246bd86c","resolution":{"observed_at":"2026-08-15T19:56:20.525499Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.511700Z","title":"Extracting macroscopic dynamics: model problems and algorithms","venue":null,"work_id":"dda2054d-b1a4-4a23-b5a9-1820f2398643","year":2004},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.975821Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:ec209288c02c509f0c5e9aab66b58e26200ce4863f222868a7698f956a592f8d","observation_id":"4fb520e9-4e38-4721-b11f-51dbc0e1bd95","resolution":{"observed_at":"2026-08-15T19:56:20.515469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.501016Z","title":"Mimicking the one-dimensional marginal distributions of processes having an It \\^o differential","venue":null,"work_id":"48b23760-0389-4584-a13a-1581ce0a8086","year":1986},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.978875Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:4acc3e5d8bd8ba8008b4f3b0af9cc7cef4f0b06196a5f83dd15b15d12db0fb21","observation_id":"6f85cdfb-6adf-426f-b207-8fa6571321fb","resolution":{"observed_at":"2026-08-15T19:56:20.504818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.490724Z","title":"Accelerating diffusions","venue":null,"work_id":"731639cd-ecb5-4d27-8ed6-d65be7f0b079","year":2005},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.982616Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:855a274bd7ba2ae839dc4653c44a08de4f2af305d0577007bbf0d048871a3ca0","observation_id":"8e3d8d01-be6b-4a3f-a90a-2c84ec7569f2","resolution":{"observed_at":"2026-08-15T19:56:20.493915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.479815Z","title":"Coarse graining of nonreversible stochastic differential equations: Quantitative results and connections to averaging","venue":null,"work_id":"22cb603d-3822-4837-8b60-5c53d227ff89","year":2020},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.986581Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:fcb153d78d72657f1d9f8539c46587c4075d369e1d238a07604a8d83545175c2","observation_id":"b658856f-e074-4a7d-a0dd-bceb61ea01e4","resolution":{"observed_at":"2026-08-15T19:56:20.483504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.469504Z","title":"Adaptive dimensionality reduction of stochastic differential equations for protein dynamics","venue":null,"work_id":"12b37d45-e6c5-426d-8a08-04175288a0c4","year":2009},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.989613Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:8598a98a737eae4e8dfb54e6a325d850afc9dcc577b146e4d358fda9c7213b95","observation_id":"1f508bac-c451-447f-af29-39767ca640a0","resolution":{"observed_at":"2026-08-15T19:56:20.473070Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.459152Z","title":"Stochastic modelling: replacing fast degrees of freedom by noise","venue":null,"work_id":"2924f1b2-cb21-478f-8350-9665e74112e7","year":2001},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.993331Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:63ca95ace65fbac477f2ab9f0b355eb31f87dee698ea2211f9645117df401b30","observation_id":"b37a5b30-056e-44bd-bced-f648547c8474","resolution":{"observed_at":"2026-08-15T19:56:20.462649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.448381Z","title":null,"venue":null,"work_id":"d6525122-8670-42eb-b8c4-00ede4145ba9","year":1968},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.996295Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:a24291c3ef039751a69756c54cd0f7bd80015a5e33d81379d1ef573f48d7d996","observation_id":"823a9b60-5269-4c9e-830f-89caffa89f67","resolution":{"observed_at":"2026-08-15T19:56:20.452318Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:19.999699Z","title":"Statistical mechanics of fluid mixtures","venue":null,"work_id":null,"year":1935},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:19.999699Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:d7c65ffc6e1b8923855bb8d4ce9cfe9ca279bbd2d6514e442575ea706edb8cc8","observation_id":"815da13e-aadc-424f-ac43-37e53c2bab4b","resolution":{"observed_at":"2026-08-15T19:56:19.999699Z","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":"2026-08-15T19:56:20.431568Z","title":"Fast chaos versus white noise: entropy analysis and a fokker--planck model for the slow dynamics","venue":null,"work_id":"68751f9d-1f44-40c2-b7ab-4a488ffc7482","year":2004},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.003241Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:9b9b6e4c103bebe0809626c4e66db14a9bff183738426f156595701c3e3fd554","observation_id":"a4dca7b7-7d90-4038-8568-f309414a34c8","resolution":{"observed_at":"2026-08-15T19:56:20.435800Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.420656Z","title":"Nonautonomous kolmogorov parabolic equations with unbounded coefficients","venue":null,"work_id":"d1a4feb5-562d-44cf-9c52-a1907936817d","year":2010},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.006466Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:b610c1a1a3bb7bddad73c07a860422762436dfd64e63f1a8fed1b7452fe2cbbf","observation_id":"10fd4187-98a6-4df3-9abd-76535cd045b9","resolution":{"observed_at":"2026-08-15T19:56:20.425191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.411010Z","title":"Brownian motion and stochastic calculus , volume 113","venue":null,"work_id":"1682b79e-f370-4ddb-9082-8c04c7c27e55","year":2014},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.010870Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:3bd2d0ef168071b7084ceb0efb0db22fcff3e1d912231e31a61cb7e50baf0886","observation_id":"046688be-b834-47e7-9662-8b68f3b8ff95","resolution":{"observed_at":"2026-08-15T19:56:20.414567Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.401216Z","title":"Fractional kinetics in kac--zwanzig heat bath models","venue":null,"work_id":"b32d4d42-39de-4b52-871b-9ce14cc0c5e7","year":2004},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.014266Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:e8ce79f89aad2dd8e546a1b840e6e22b9cf24d6c88c42a7ff8efc2e89f54b552","observation_id":"c6f3015d-c55a-464f-87b6-61dc3642825e","resolution":{"observed_at":"2026-08-15T19:56:20.404547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.391004Z","title":"Analytical methods for Markov semigroups","venue":null,"work_id":"1caa212c-2eea-4f53-9d7f-91854e88ad15","year":2006},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.017543Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:b3c1338714bffb06034e5920fd1d6189cd5c01a69abfbd765b2d2a2592ace60f","observation_id":"39ac44eb-44e9-4a6b-b0a5-25788fdbff3a","resolution":{"observed_at":"2026-08-15T19:56:20.395134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.380997Z","title":"Effective dynamics using conditional expectations","venue":null,"work_id":"3852fd5a-c46e-46e6-8a3b-2c99e6114e62","year":2010},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.020676Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:8522668195376a93fa1ea4a24baf2b660ed32f6a321034dda6bd68e6aebb6947","observation_id":"67c37aa1-0704-4b3c-b85c-6e28dec556a4","resolution":{"observed_at":"2026-08-15T19:56:20.384559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.370799Z","title":"Some remarks on free energy and coarse-graining","venue":null,"work_id":"30875ebd-6076-4c1f-8028-1ba6e16cfa1c","year":2009},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.024028Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:0f042a2eea3f97f9a472b0251254b6363bec113e1ad5d7097f1611e66a613bbf","observation_id":"98fe7dc4-f0b6-4074-8a7e-979d01694fa5","resolution":{"observed_at":"2026-08-15T19:56:20.374567Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.361844Z","title":"Pathwise estimates for an effective dynamics","venue":null,"work_id":"6d8b69ad-a014-4963-a36d-e9475c593e46","year":2017},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.027469Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:1f44c8a74c18a901118cfc896606519ea05ea014adedf00f7e61c3d480904290","observation_id":"2d594165-abf5-44e2-99a9-fe76ca5c8438","resolution":{"observed_at":"2026-08-15T19:56:20.365033Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.352398Z","title":"Effective dynamics for non-reversible stochastic differential equations: a quantitative study","venue":null,"work_id":"06e10991-7723-401d-81eb-37d3fa8b1154","year":2019},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.030667Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:d3dda3423ed014c2e7ee583c28f68fa402fc8960515b931dbd190aac7410406a","observation_id":"0ee93619-e57a-4fab-879d-24c50f514e86","resolution":{"observed_at":"2026-08-15T19:56:20.356088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.342871Z","title":"A mathematical theory of optimal milestoning (with a detour via exact milestoning)","venue":null,"work_id":"bf9c71e1-5f77-45b8-b499-4425617eaedf","year":2018},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.034144Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:dd0c3cb0273b3ff87ea75875ef2ebbc5226a1e8555a8ef5fc8a23015a98a39c2","observation_id":"c0275787-4a70-4022-9a19-0f7fc056f042","resolution":{"observed_at":"2026-08-15T19:56:20.346302Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.333050Z","title":"Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion","venue":null,"work_id":"39ab109a-d2bf-491c-a44e-63fa7f74e309","year":2013},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.037870Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:7e27e81b9e83bcc32098b4129465cdc743a12cc472d5cf582b80565db2f4cbf6","observation_id":"e327d107-c34f-4b1a-879d-5cc1fc811822","resolution":{"observed_at":"2026-08-15T19:56:20.336727Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.322555Z","title":"Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates","venue":null,"work_id":"270f2696-ea24-4113-b796-0123fbfaa4b4","year":2019},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.042253Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:e45159f6fad34da0058b9eee56aa5a46f9492fba9d2585ced92366448ff64314","observation_id":"ca6ff3c7-b2d0-4ade-8ecf-267ef6970e33","resolution":{"observed_at":"2026-08-15T19:56:20.325979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.312563Z","title":null,"venue":null,"work_id":"2ca8dbcd-99f6-4c69-b8df-cface2e8e507","year":1999},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.046600Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:c69b0af9ac396f7e45776a89b61b630e068047de8f258ea08c58aeb158bc0962","observation_id":"e06b639d-6486-4aed-82e6-313fae172ec2","resolution":{"observed_at":"2026-08-15T19:56:20.316483Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.302110Z","title":"A continued-fraction representation of the time-correlation functions","venue":null,"work_id":"df1b1e6b-efe4-4fab-a21b-58b4564182d0","year":1965},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.050897Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:9fc1d012cefea43d04b271c03f9790ba2fca74af4aa813dc8d3a337e2a2c77b6","observation_id":"622974dc-3be3-4486-af4b-f6bb8f28f879","resolution":{"observed_at":"2026-08-15T19:56:20.305862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.291380Z","title":"A mathematical framework for stochastic climate models","venue":null,"work_id":"6751e251-9e06-4124-baf0-6b22515b7a22","year":2001},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.055623Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:b2cd8a49655affa3280af1bb76638b009866206312514fbc49ab98e45859a9ff","observation_id":"aaf172a3-f19f-4d8e-ab69-b0962871d4d8","resolution":{"observed_at":"2026-08-15T19:56:20.294963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.280305Z","title":"Spectral properties of effective dynamics from conditional expectations","venue":null,"work_id":"ff079c32-9542-46c1-b24b-15239956e99a","year":2021},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.059614Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:d9f6594691716d61d1a104bdebbc5b9883c0d8ef3bf33770b837c3caa21b48c8","observation_id":"7318cb47-7fca-4540-9716-20b91f93f264","resolution":{"observed_at":"2026-08-15T19:56:20.284946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.269457Z","title":"Asymptotic analysis for the generalized langevin equation","venue":null,"work_id":"123661a1-aa1f-4348-90e3-1280924cfccd","year":2011},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.063233Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:7a845b164b2cf448962875798a575032adebcee47d826cb911bafd26877667aa","observation_id":"2b6e4f69-ca4f-4cca-99c3-fe08ea217a9f","resolution":{"observed_at":"2026-08-15T19:56:20.273394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.259029Z","title":"Stochastic processes and applications","venue":null,"work_id":"bf03d683-3495-4afa-88a1-631b0441f98f","year":2014},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.066854Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:4e0c12022bbac3e33de4ce5826bc8b29f345adacd2eabcedd0a5aa5ce771da04","observation_id":"0f43a716-089c-44b6-b1fb-a555d1af28cc","resolution":{"observed_at":"2026-08-15T19:56:20.262616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.247246Z","title":null,"venue":null,"work_id":"e1ba2a14-e9e1-4b44-b163-bdb3c2fec9b6","year":2012},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.070328Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:789899a15d1a3e32b1d24aa7c0cc5c4a07023987445f81d1b037bd76a06748b7","observation_id":"9c1dc02d-c510-428c-9f4f-0a5aca4e6c57","resolution":{"observed_at":"2026-08-15T19:56:20.251196Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.074531Z","title":"Multiscale methods: averaging and homogenization , volume 53","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.074531Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:5d864be78d3c465e4855c56e463c485eb83ebca552e58f06c54bc8f74775c8d8","observation_id":"10166f8a-6920-40f3-921c-ecba3050f0a5","resolution":{"observed_at":"2026-08-15T19:56:20.074531Z","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":"2026-08-15T19:56:20.230065Z","title":"The time-dependent born-oppenheimer approximation","venue":null,"work_id":"d9448477-dd40-42a3-8af1-47ab8ea2c80f","year":2007},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.077799Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:fd34c6162f382822e19c6f0d3bab1a9abb6a589525867cb38cc0aed8c74f7bdf","observation_id":"da48ba27-d816-42e2-bc72-733be311de7d","resolution":{"observed_at":"2026-08-15T19:56:20.234019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.219027Z","title":"On poisson equation and diffusion approximation 2","venue":null,"work_id":"19081100-4543-4858-a99d-6ddea868b6df","year":2003},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.080897Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:a11b8c9bcf43c9c6fa6b10842385c8fc97c97be352a9f9b5f48a4e697d0b5ee1","observation_id":"1442056b-6cf9-44dc-b6c5-c948d7a5a584","resolution":{"observed_at":"2026-08-15T19:56:20.223256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05239","last_updated":"2024-12-06T18:16:00Z","snapshot_observed_at":"2026-08-13T14:05:43.514373Z","submitted_at":"2024-12-06T18:16:00Z","title":"Conditions for uniform in time convergence: applications to averaging, numerical discretisations and mean-field systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05239","snapshot_observed_at":"2026-08-15T19:56:20.084260Z","title":"Conditions for uniform in time convergence: applications to averaging, numerical discretisations and mean-field systems","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.084260Z"},"links":{"cited_paper":"/paper/2412.05239","citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:21bbff8891c2aaa233f3375343ef9c9320bdfa1b9c9b59349d38afec91842b12","observation_id":"922ff0bb-a608-4e99-a10d-b07f92fb7e4c","resolution":{"observed_at":"2026-08-15T19:56:20.084260Z","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":"2026-08-15T19:56:20.207335Z","title":"Longtime convergence of the temperature-accelerated molecular dynamics method","venue":null,"work_id":"0b02a5cf-deb7-46d7-8d86-3640c244e7cf","year":2018},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.088688Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:55585d049367b87559a10b201466ad7aa788780e827c4271882d22f39dbc94b5","observation_id":"63c8286b-2d91-4cc3-ba8e-5803c2e5be66","resolution":{"observed_at":"2026-08-15T19:56:20.211745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.196562Z","title":"Topics in propagation of chaos","venue":null,"work_id":"433f555c-0b40-458d-b97f-87d0a9d6c252","year":1989},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.092475Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:d2d3f1f2b3a3ab1991434518edc4d2983d7a74eb57aa9cbd3b81604f6c91dc17","observation_id":"e642ab6e-0bee-4a95-bbd7-333065d57f17","resolution":{"observed_at":"2026-08-15T19:56:20.200178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.185133Z","title":null,"venue":null,"work_id":"b38589b2-a0c2-4a7c-bde5-931c21d075d6","year":1991},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.095823Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:66aeb143132c1a148d304fcd056fd87edcf35d3175f97d9362f312cf7834a221","observation_id":"e2cac268-f17b-4723-a0b9-0b3fe47b91ea","resolution":{"observed_at":"2026-08-15T19:56:20.189454Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.174481Z","title":"Numerically optimal runge--kutta pairs with interpolants","venue":null,"work_id":"17a9dc22-fb88-457d-9874-ff1fc31fcf0e","year":2010},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.099251Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:ead5269e27f924b8e5aea9fbb294a184eb35de12022e8cd987b8baf8d9a9061a","observation_id":"9b6139fa-a79a-4cd8-9a67-2ff3e15f52b2","resolution":{"observed_at":"2026-08-15T19:56:20.178275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T19:56:20.164650Z","title":"Effective dynamics along given reaction coordinates, and reaction rate theory","venue":null,"work_id":"86a2d7b8-d4a0-42d3-b5f9-569e1d852fed","year":2016},"citing_paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-15T19:56:20.103050Z"},"links":{"citing_paper":"/paper/2506.14939"},"observation_digest":"sha256:913417423af31ccaf48040ba5fc5258f95b6492d82676af44449e6ef8e6cc0d3","observation_id":"bfc47c84-c9e4-4b89-ad53-b472e09867ea","resolution":{"observed_at":"2026-08-15T19:56:20.168259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.14939","last_updated":"2025-06-17T19:46:46Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-18T09:18:26.159126Z","submitted_at":"2025-06-17T19:46:46Z","title":"Coarse graining of stochastic differential equations: averaging and projection method"},"reference_resolution":{"displayed":53,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":44},"total_outbound_references":53},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 2 inbound Pith citation observations for arXiv:2506.14939."}