{"as_of":"2026-08-13T01:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2bba4b455df8167943fee764ee6f47e99b99a48ae7140359f3e0c5719d9f8cd4","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T06:57:45.221520Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T00:12:47.017139Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-12T00:12:49.196822Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"cited_work":{"arxiv_id":"2606.23433","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.23433","snapshot_observed_at":"2026-08-12T00:12:49.196822Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","venue":"math.PR","work_id":"a1a98731-3d6c-400e-bcc4-e51bdee1c5ce","year":2026},"citing_paper":{"arxiv_id":"2608.08358","last_updated":"2026-08-08T22:53:03Z","snapshot_observed_at":"2026-08-13T01:14:01.265179Z","submitted_at":"2026-08-08T22:53:03Z","title":"A Shared Observation Shields Collective Fluctuations while Preserving Local Independence","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T00:12:47.017139Z"},"links":{"cited_paper":"/paper/2606.23433","citing_paper":"/paper/2608.08358"},"observation_digest":"sha256:dafe029077be7702551434e8bcdf12e3a3549ff3283764b9a6bb2f97bdfd1c7a","observation_id":"61035feb-3822-460f-9207-6b2553bff21f","resolution":{"observed_at":"2026-08-12T00:12:49.201750Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2606.23433/citation-record","integrity":"/paper/2606.23433/integrity","json":"/paper/2606.23433/citation-record.json","paper":"/paper/2606.23433"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T06:57:45.221520Z","title":"and Caramellino, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:283c312f440e3bb92534564b3d1535bd08fa45b2924a9d9394e83a348c765064","observation_id":"43b06d88-2473-48ce-aca2-22af0c3f3958","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Stein's method for normal approximation in W asserstein distances with application to the multivariate central limit theorem","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:9338dd2412e466b1779e0a44c6c3f10ac52a3d14633ff5233150bfb9da05831c","observation_id":"2d67c2b4-34ef-409e-ad4e-813a1f5371ec","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:6b212d4221b19dddd8855c603340270f6b23ea2a742b02e2782ee49014d48181","observation_id":"fed6cbc6-d83a-4846-b63b-0819fda2da9c","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Hydrodynamic limit for interacting neurons","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:dfc8807df1a9652393865c930bd7f63d945e1ee33ab13540eb7e0dc8c40d2128","observation_id":"ece0ff49-9d54-4aec-83b7-b73cfa0cc72d","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"and L \\\" o cherbach, E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:60d224135419bd67a842e7cfec6e097ffd242d93751346d49351d097d4e72b47","observation_id":"be9c525c-5875-46f3-9512-d0c7a77000f6","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Lipschitz functions of self-adjoint operators in perturbation theory","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:1ec919115fca244402beb91cec707be14db7a33b321f91e1ade7cc45b1714a35","observation_id":"bc2f99c3-f89a-478a-a46f-da7b514c0361","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Feyel and A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:37bb27785d17618cd0dc2dd92a39d0fb4b8a1ed9b7913eb5075bbfcad52d3b55","observation_id":"3d2c28ba-b312-4596-ae98-741714fefaaa","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"A toy model of interacting neurons","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:312e394021c56232fbfd4ba5cf7d74e6fa7a4da9d642f2c78306063bec76b630","observation_id":"4e0fc075-faaa-4165-99e5-16d17c60f7ed","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:c6681d076e97cc81e016f6a0f1dac4a753be198de6fa09c02021d85a6f61b196","observation_id":"232f177b-049a-473a-a363-313bfe1ea167","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Mckean- V lasov I to- S korokhod equations, and nonlinear diffusions with discrete jump sets","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:dbce5d7c05bc6dd92f922f7f1f8ecaa96a04af80772fda825a785c2893bb8b4a","observation_id":"47382b74-f782-49f5-9248-98a476bb8677","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Controlling rough paths","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:68c7d860b5e631c586f391b7eed198ddfe47940db421eb3baf5ed2c402a1cb89","observation_id":"74901e6d-d04b-49d8-8ae3-ef6fbbc09046","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"and Watanabe, S","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:a99eeb86a95a60c2756ca531a1837827be4658afb0f63990877e4de5517bd7e2","observation_id":"7c5b47ae-7df0-459c-a3d6-7b0f923504c9","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"and Major, P","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:393975f210f12448d20c1cf8bbeff756a53cee892ffc57ae59326b1cb9e9fab0","observation_id":"cca2f4d5-ab5e-440b-8633-f4c199b40371","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"L\\^ e A stochastic sewing lemma and applications","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:725d47ab16c22c1a2a4e5a13c88bd77481fcc3974b58ac6a259f9db024433b51","observation_id":"079c520a-d5e8-40f0-be26-106ca77652d7","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Upper bounds for minimal distances in the central limit theorem Annales de l'I.H.P","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:bb18500c2d0402c132b728da55b3dd1bc9772fbdbcf7efe9e1fcf6e27641bb22","observation_id":"ffd56e2e-2f24-4110-a7b8-e4b7d0be3f25","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","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":"2026-06-26T06:57:45.221520Z","title":"Optimal transport, old and new","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-26T06:57:45.221520Z"},"links":{"citing_paper":"/paper/2606.23433"},"observation_digest":"sha256:268856c01b7ba4c45161d25bd09e67dd29a6e24fe28256c24a1b9be36acd8e98","observation_id":"9298ecdb-eb09-4067-ad7f-406d8579e1df","resolution":{"observed_at":"2026-06-26T06:57:45.221520Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.23433","last_updated":"2026-06-22T14:51:18Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-08T06:11:58.078948Z","submitted_at":"2026-06-22T14:51:18Z","title":"Emergence of Common Noise: Quantitative Conditional Propagation of Chaos"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":16},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2606.23433."}