{"as_of":"2026-08-13T07:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:10ace021f34ba2de298795ade34ac97bbc003321f6e8ff7d93cc00306074574c","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T14:49:33.320567Z","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":"2026-07-03T03:07:35.876272Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-08-12T14:49:33.320567Z","title":"Cecchin and F","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.14936","last_updated":"2025-06-08T12:08:08Z","snapshot_observed_at":"2026-08-12T14:39:38.664534Z","submitted_at":"2024-11-22T13:49:02Z","title":"Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T14:49:33.320567Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2411.14936"},"observation_digest":"sha256:c3b761ce7afb355e5ff38d743bf72bc50750d4bf5cc40fbb419a992cb34de9ef","observation_id":"d5095f87-880b-41aa-aca0-595582f2da8f","resolution":{"observed_at":"2026-08-12T14:49:33.320567Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-08-11T14:47:26.589242Z","title":"Cecchin and F","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.11742","last_updated":"2025-04-12T03:12:19Z","snapshot_observed_at":"2026-08-12T06:06:15.792887Z","submitted_at":"2024-12-16T13:02:10Z","title":"A particle system approach towards the global well-posedness of master equations for potential mean field games of control","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:26.589242Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2412.11742"},"observation_digest":"sha256:ddc41c284eb98e7adaf22248239230f84a60cc9200f1887c3d6ce394d5fc24e5","observation_id":"c441ca03-c2c0-4622-8ea1-5662630331c4","resolution":{"observed_at":"2026-08-11T14:47:26.589242Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-08-11T13:55:18.386320Z","title":"Weak solutions to the maste r equation of potential mean ﬁeld games","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.12741","last_updated":"2024-12-17T10:04:50Z","snapshot_observed_at":"2026-08-11T19:53:38.912070Z","submitted_at":"2024-12-17T10:04:50Z","title":"A study of common noise in mean field games","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T13:55:18.386320Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2412.12741"},"observation_digest":"sha256:82f3e13fea8ddc3b26daaed399e9312afb1e5812995bc559c281a7c1958c200f","observation_id":"93c9b263-4d61-42af-9559-9a0acdedf55b","resolution":{"observed_at":"2026-08-11T13:55:18.386320Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-08-07T01:17:46.941745Z","title":"Weak solutions to the master equation of potential mean field games","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.11868","last_updated":"2025-06-13T15:17:56Z","snapshot_observed_at":"2026-08-07T00:59:58.145284Z","submitted_at":"2025-06-13T15:17:56Z","title":"A \"trembling hand perfect\" equilibrium for a certain class of mean field games","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T01:17:46.941745Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2506.11868"},"observation_digest":"sha256:ccd3d80f097475dd07155079b4b1026c1ef410d8b34282b2fae7be3b03198cbc","observation_id":"0b6ee273-41ce-465e-acd9-f6c2c8491f80","resolution":{"observed_at":"2026-08-07T01:17:46.941745Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":"2204.04315","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-07-03T03:07:35.876272Z","title":"Weak solutions to the master equation of potential mean field games.arXiv preprint arXiv:2204.04315, 2022","venue":null,"work_id":"d16783d0-d08e-45ea-8474-9417253900b2","year":2022},"citing_paper":{"arxiv_id":"2606.09815","last_updated":"2026-07-13T10:18:34Z","snapshot_observed_at":"2026-08-08T12:26:47.318036Z","submitted_at":"2026-06-08T17:55:47Z","title":"Limit Theory for $N$-Player $\\alpha$-Potential Games","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T15:26:43.020134Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2606.09815"},"observation_digest":"sha256:dc9c40942520c7fe9c872aba582cee69aa75e1752b9b92b1d97219025f997fec","observation_id":"574376ac-cf00-47ad-9f5b-a56ca92bfa90","resolution":{"observed_at":"2026-07-03T03:07:35.878064Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04315","snapshot_observed_at":"2026-07-14T18:08:39.286851Z","title":"Weak solutions to the master equation of potential mean field games.arXiv preprint arXiv:2204.04315, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.09815","last_updated":"2026-07-13T10:18:34Z","snapshot_observed_at":"2026-08-08T12:26:47.318036Z","submitted_at":"2026-06-08T17:55:47Z","title":"Limit Theory for $N$-Player $\\alpha$-Potential Games","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T18:08:39.286851Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2606.09815"},"observation_digest":"sha256:c1d77dac69f72eef61275e06a93d0d04e6068339497418f66de037a0e4ab291d","observation_id":"f01551d0-e9c2-4735-a51f-658d24996fd1","resolution":{"observed_at":"2026-07-14T18:08:39.286851Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2204.04315/citation-record","integrity":"/paper/2204.04315/integrity","json":"/paper/2204.04315/citation-record.json","paper":"/paper/2204.04315"},"outbound":[],"paper":{"arxiv_id":"2204.04315","last_updated":"2022-06-29T09:14:36Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-07-06T12:58:27.906110Z","submitted_at":"2022-04-08T22:20:35Z","title":"Weak solutions to the master equation of potential mean field games"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2204.04315."}