{"as_of":"2026-08-22T15:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:309151b351fd40a3de6594c4d1c7be7dc24c12e0e5b674c1f4886459e3f17030","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T21:27:26.564743Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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":"2026-08-01T11:27:30.759356Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.10045","snapshot_observed_at":"2026-08-01T11:27:30.759356Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting.arXiv preprint arXiv:2505.10045, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.19939","last_updated":"2026-07-22T09:13:09Z","snapshot_observed_at":"2026-08-17T23:05:24.943464Z","submitted_at":"2026-07-22T09:13:09Z","title":"Analysis on spaces of measures","version":1},"reference_index":105,"source":"pdf_text","source_observed_at":"2026-08-01T11:27:30.759356Z"},"links":{"cited_paper":"/paper/2505.10045","citing_paper":"/paper/2607.19939"},"observation_digest":"sha256:60455657ba22f247ebc4bc14bdb0a1a2d682e26b85f8a2eaf0e7867c7f82bab8","observation_id":"42aa8763-62e6-40ad-b60f-e073e68f3b2e","resolution":{"observed_at":"2026-08-01T11:27:30.759356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.10045/citation-record","integrity":"/paper/2505.10045/integrity","json":"/paper/2505.10045/citation-record.json","paper":"/paper/2505.10045"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.439116Z","title":"Hidden monotonicity and canonical transformations for mea n ﬁeld games and master equations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.439116Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:b2a296630d12642300f68b90060087be01a950bcacd9da7241e125117850e1e4","observation_id":"ecd0f8b5-f372-42ab-bf06-f12683a56e6c","resolution":{"observed_at":"2026-08-15T21:27:26.439116Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.443584Z","title":"The Master equation in mean ﬁeld theory","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.443584Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:9d1fa92354d3a569aca16542205f17db15f87c6045481eed5b1d9c3365583ea0","observation_id":"d00bbc3e-8179-4556-8797-287926788d94","resolution":{"observed_at":"2026-08-15T21:27:26.443584Z","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":"2026-08-15T21:27:27.051051Z","title":"Jeux à champ moyen et contrôle stochastiqu e dans l’espace de Wasserstein","venue":null,"work_id":"01569810-76e6-4f1e-a291-6cccb503b22a","year":2023},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.447335Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:b75980c3d57a8bf4a77389d9830004518421418fecf175bcc5cf099f9d8eb223","observation_id":"25355c9a-95fc-4306-a509-804a9bb4bc89","resolution":{"observed_at":"2026-08-15T21:27:27.055268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:27.040186Z","title":"Monotone solutions for mean ﬁeld games mas ter equations: continuous state space and common noise","venue":null,"work_id":"a03c14f2-4361-4793-b593-aa140d2a1c30","year":2023},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.451103Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:258cf040bf2a85c59c7508097a9020e60e160aad1f0f50b2d287350e594109e1","observation_id":"7629c461-f0f3-4f3a-9c20-45470788c1a6","resolution":{"observed_at":"2026-08-15T21:27:27.043985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:27.028706Z","title":"A two spaces extension of C auchy-Lipschitz theorem","venue":null,"work_id":"85d91626-705a-4e87-9a60-3a28ec993d05","year":2025},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.454639Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:0bdef573b5baeba5f1495818019b8047e976256e970f59b413318733b6cc4586","observation_id":"567f3463-c526-47fd-adf3-61bcd815b404","resolution":{"observed_at":"2026-08-15T21:27:27.032832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.05635","last_updated":"2024-03-05T09:00:42Z","snapshot_observed_at":"2026-08-21T16:16:49.874218Z","submitted_at":"2024-02-08T12:46:37Z","title":"Noise through an additional variable for mean field games master equation on finite state space","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.05635","snapshot_observed_at":"2026-08-15T21:27:26.458185Z","title":"Noise through on additionn al variable for mean ﬁeld games master equation on ﬁnite state space","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.458185Z"},"links":{"cited_paper":"/paper/2402.05635","citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:d9c2d67a3c7777584b1551d14e02e662bb4892627207e5f8c9063f381dfa8cd0","observation_id":"4594c05f-505f-41ad-a999-b75f7c91d515","resolution":{"observed_at":"2026-08-15T21:27:26.458185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/jep.167","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.606052Z","title":"Monotone solutions for mean ﬁeld ga mes master equations: ﬁnite state space and optimal stopping","venue":null,"work_id":"5bded766-94dc-4c27-bfd1-412721ba8c44","year":2021},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.462260Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:5f2d9d571a51c8020bf9f00d2a3da7f4dbfe0bc4ffddd5b396a0f8894cffac50","observation_id":"6b653971-f7e5-4939-aac7-98bdd806eb67","resolution":{"observed_at":"2026-08-15T21:27:26.610024Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/slsedp.153","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.591299Z","title":"On monotone solutions of mean ﬁeld g ames master equations","venue":null,"work_id":"9b756872-d1db-4c6d-bc85-7ba6024765fc","year":2021},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.465568Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:e53a9df5504fdfb24560c26d644af85644052b4b572f101f9498b60177cc979c","observation_id":"82736bfb-a4dc-4424-8873-f6c929347d08","resolution":{"observed_at":"2026-08-15T21:27:26.597314Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:27.017529Z","title":"Mean Field Game s Master Equations: From Discrete to Continuous State Space","venue":null,"work_id":"557f1e71-fa2c-414c-a842-e62020d50617","year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.469044Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:c6c78e06e2be893df02741b12cea87ab20b7a79682961e46c9c3bf816184af5d","observation_id":"f6444d52-6e18-4699-84de-3e96c7a9c909","resolution":{"observed_at":"2026-08-15T21:27:27.021701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:27.006909Z","title":"On Lipschitz solutions of mean ﬁeld games master equations","venue":null,"work_id":"64eb642e-5d16-415d-bf91-ff4d11ca6c0c","year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.472246Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:54f74b8fbed16cff1b077d6dab29cbc420d364e7592d1bda5d60a1270aa56b60","observation_id":"34c48d26-ea0c-49b3-a5c1-86b07e61c6f9","resolution":{"observed_at":"2026-08-15T21:27:27.010787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.11793","last_updated":"2024-09-18T08:20:38Z","snapshot_observed_at":"2026-08-21T16:16:01.134298Z","submitted_at":"2024-09-18T08:20:38Z","title":"An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.11793","snapshot_observed_at":"2026-08-15T21:27:26.475609Z","title":"An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.475609Z"},"links":{"cited_paper":"/paper/2409.11793","citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:dfc84e6d155bfa5d82412fe18dbecba51bd23a256888b506d350d4cd76bbb241","observation_id":"0b398550-6bd3-4368-8479-1f4920fed876","resolution":{"observed_at":"2026-08-15T21:27:26.475609Z","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":"2026-08-15T21:27:26.995352Z","title":"Weak Solutions for First Order Mean F ield Games with Local Coupling","venue":null,"work_id":"46da557b-e0b9-4d30-82ab-fa2826572bd9","year":2015},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.479336Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:27c6f7c51b9bdc7860f6d6c108b7df502045acabc6c401378cddfbc61c55562c","observation_id":"4e5aa57a-b7b9-44b8-ae4b-b3272295a774","resolution":{"observed_at":"2026-08-15T21:27:26.998900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.482626Z","title":"The master equation and the convergence problem in mean ﬁeld games","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.482626Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:f93859ac82ed2245b5f012ba283faad256e8fdaaa8b46cd5ad11f696c88de559","observation_id":"ada56d2c-d9a2-4685-a94f-8f50ce64b7f7","resolution":{"observed_at":"2026-08-15T21:27:26.482626Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.485843Z","title":"Mean ﬁeld forwar d-backward stochastic diﬀerential equations","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.485843Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:dd5cd07aa254fa3a257945dcbfe97e05cdaf2b917d7e58eba966bb0ffb98a098","observation_id":"cc6dbdfc-b1a4-468a-9135-b8f35e6f65ce","resolution":{"observed_at":"2026-08-15T21:27:26.485843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.488948Z","title":"Probabilistic Theory of Mean Field Games with Applications II","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.488948Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:f92b2e10925c08edc89674a3f7588b23b7905d785b237b8b29b0d3f08b58b59b","observation_id":"af4828f0-621c-4954-b271-837c7738c95e","resolution":{"observed_at":"2026-08-15T21:27:26.488948Z","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":"2026-08-18T04:10:28.933132Z","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":"2026-08-15T21:27:26.492302Z","title":"Weak solutions to the maste r equation of potential mean ﬁeld games","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.492302Z"},"links":{"cited_paper":"/paper/2204.04315","citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:3e7d9f6113b3888da4af44d2460c359c7e6b018b4db9a39218106704933f6ba8","observation_id":"e1ce6a4e-79a0-465f-a426-f67bb3d0a84c","resolution":{"observed_at":"2026-08-15T21:27:26.492302Z","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":"2026-08-15T21:27:26.964353Z","title":"On smooth approxim ations in the Wasserstein space","venue":null,"work_id":"addc41bb-6686-455a-845d-6a702f8f3317","year":2023},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.495926Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:6dab8b66ee51aa5205a6fd1544efeb2d999f9826017b274f06a4ee5012d43184","observation_id":"221e629a-c169-438a-bd82-27feb7f869fa","resolution":{"observed_at":"2026-08-15T21:27:26.968386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.953347Z","title":"user’s guide to viscosity solutions of second order partial diﬀerential equations","venue":null,"work_id":"e93ed232-ed0e-4bfc-b21e-12f2c57987be","year":1992},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.499433Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:93232ccd1c1193065e85726ddfac55a38cf981fb57c5db4e671339648b966c47","observation_id":"7007107a-05a4-4da0-9a75-d8e1efb37026","resolution":{"observed_at":"2026-08-15T21:27:26.957674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.943248Z","title":"A comparison principle for se milinear Hamilton–Jacobi–Bellman equations in the Wasserstein space","venue":null,"work_id":"d5247eb6-fa88-4c7e-84bc-a787470920ad","year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.503302Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:f3f39b332dd1abb21289022db056a08e656daa76323a8492c56a71b19457c2ba","observation_id":"f7d38429-4494-4504-b2f0-d613acfb7ae6","resolution":{"observed_at":"2026-08-15T21:27:26.946964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.932661Z","title":"Fatou’s Lemma in Its Classical Form and Lebesgue’s Convergence Theorems for Varying Measures with Applicatio ns to Markov Decision Processes","venue":null,"work_id":"0693eb95-f6bf-4d9a-843a-26e58ad5fc6c","year":2020},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.506782Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:28dc1517d2d6a5a82962d4cac889d918e27c9daeaf27d7b391d830cc0c5abea4","observation_id":"6012991c-ca5c-4be2-8feb-833cb523ae27","resolution":{"observed_at":"2026-08-15T21:27:26.936472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.922370Z","title":null,"venue":null,"work_id":"41d2705e-d403-47e9-a1ed-622ea71827d0","year":2006},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.509980Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:fcff20d050ab9b41cfcbca4790b5075038ca9db6660fcac8f0c5083ee3b25b7b","observation_id":"49e78c0b-441c-49db-8d63-fc53fcc11f99","resolution":{"observed_at":"2026-08-15T21:27:26.925755Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.513384Z","title":"Mean Fi eld Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.513384Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:4731dbc96bca8044ed8c387b65ad19b62543ce7dcdd4f6982f44430f5139633a","observation_id":"c182742c-a3f8-40ca-92c2-d4194ecf18a7","resolution":{"observed_at":"2026-08-15T21:27:26.513384Z","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":"2026-08-15T21:27:26.905163Z","title":"and Mandrekar, V","venue":null,"work_id":"cb7243ff-922a-469f-9419-f26d706d2820","year":2011},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.516575Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:afa9af97dc257a2971f33fc8ec044dd3c727d8c3a9309fa2bc1ee3c158e826e4","observation_id":"0197776b-70f1-4adb-a001-b6c9ac87da73","resolution":{"observed_at":"2026-08-15T21:27:26.908872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.893716Z","title":null,"venue":null,"work_id":"f3f11264-4535-4a8b-bd78-e15c8683d87f","year":1996},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.519697Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:633ed00f01142e59d4f28a3d457a0299929de6ce2c149728e3c3c7357b0803d8","observation_id":"8d10f8c8-ebb5-41be-9610-693a06c9a6e6","resolution":{"observed_at":"2026-08-15T21:27:26.897169Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.523330Z","title":"Mean ﬁel d games","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.523330Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:d32689ad0db6ea03d492473d2f41474eb9d6e996765fd7a4954b618a4bdc677f","observation_id":"7e228ca4-1c47-4c9c-bfdd-547026733676","resolution":{"observed_at":"2026-08-15T21:27:26.523330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.526670Z","title":"Lectures at Collège de France","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.526670Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:c9219edbc1b48b361240226657c2371800b228b1ca0dd59b75754280463f5fdc","observation_id":"c5a9c496-2ab2-4aa7-a9bc-bd4f4c6d9f07","resolution":{"observed_at":"2026-08-15T21:27:26.526670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.530151Z","title":"“Viscosity solutions of fully nonlinear s econd-order equations and optimal stochastic control in inﬁnite dimensions","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.530151Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:73e025e454459ebe7278b87bc206cdeca3b9c8cbd5ea2769db41115330a13051","observation_id":"f7419011-1102-46c7-be44-abdd4eb56e6c","resolution":{"observed_at":"2026-08-15T21:27:26.530151Z","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":"2026-08-15T21:27:26.863006Z","title":"Transport Equations and Flows with One-Sided Lipschitz Velocity Fields","venue":null,"work_id":"66829805-5c19-4f63-a406-a545ddd511e3","year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.533546Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:750490fdca383a3109cbe644b9198d5d42b6b6f187e3e713cb8d625819052564","observation_id":"bbf73d0b-dbbb-4a43-9664-c69a9b01e79b","resolution":{"observed_at":"2026-08-15T21:27:26.867400Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.851884Z","title":"“Viscosity solutions of fully nonlinear se cond-order equations and optimal stochastic control in inﬁnite dimensions","venue":null,"work_id":"3c019d98-3b33-430f-ab5f-0431ab263abd","year":1989},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.536794Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:31aa5e5ffdf293c812dca79c84a63176f42a66e6a74d7eaa253902b5c6ff7c4f","observation_id":"28d748a7-3977-426e-b53a-5c4d175724fb","resolution":{"observed_at":"2026-08-15T21:27:26.855418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.16167","last_updated":"2024-11-30T17:26:03Z","snapshot_observed_at":"2026-08-21T16:16:41.940403Z","submitted_at":"2023-08-30T17:41:11Z","title":"Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.16167","snapshot_observed_at":"2026-08-15T21:27:26.540326Z","title":"Bansil, Alpár R","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.540326Z"},"links":{"cited_paper":"/paper/2308.16167","citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:7e1dcb7b1354353117bbb3f48611256399a0db47f054d78d8dda1a117c6a297b","observation_id":"dc76e84a-3f89-49bc-9eae-975c50253b30","resolution":{"observed_at":"2026-08-15T21:27:26.540326Z","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":"2026-08-15T21:27:26.840431Z","title":"A study of common noise in mean ﬁeld games","venue":null,"work_id":"307d5a8c-bf8b-4041-9da1-ed4c61978cf7","year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.543919Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:286bde7700525f67a153b7382f0c1962a781bab31fe16dd1105756ae4039f0e6","observation_id":"b8533e87-7020-4315-ace1-6e3f00833cab","resolution":{"observed_at":"2026-08-15T21:27:26.844480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.547644Z","title":"Wellposedness of S econd Order Master Equations for Mean Field Games with Nonsmooth Data","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.547644Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:cec1c35462819316a923ca21b29b9189fb43c70b04f9ad72fdd4cdddc2491dc1","observation_id":"c8de496f-3294-46f7-8322-a4455c72e0ec","resolution":{"observed_at":"2026-08-15T21:27:26.547644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.551015Z","title":"Mean Field Games Systems under Displacement Monotonicity","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.551015Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:11fb846a6193203ece0e8ba3d97a9cf2a1f64134898677cdfbb9b595e605c399","observation_id":"66fea998-61d5-4d6d-8c5e-7f19d838a3f3","resolution":{"observed_at":"2026-08-15T21:27:26.551015Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.554364Z","title":"Fully Coupled Forward-Backward Sto chastic Diﬀerential Equations and Applications to Optimal Control","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.554364Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:749ff1dac19bc8afb5b59e1e5b58aa55d4cb9eddc3e50e4706b6709b5ed0fd46","observation_id":"97483744-23eb-41eb-945f-3f5b8a779c40","resolution":{"observed_at":"2026-08-15T21:27:26.554364Z","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":"2026-08-15T21:27:26.808717Z","title":"Weak Solutions to Fokker–Planck E quations and Mean Field Games","venue":null,"work_id":"22a39a58-a1dd-4f4e-8134-18b363fe19a2","year":2015},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.557629Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:23542a63b688b04672e9429a345ac0ea0c89a5c821ae5c2ba33819f4bdadd9c0","observation_id":"edd928d4-acc3-4886-965a-df5342846f86","resolution":{"observed_at":"2026-08-15T21:27:26.812641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"proc/2011005","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T21:27:26.685775Z","title":"Existence and uniqueness to the Cauch y problem for linear and semilinear parabolic equations with local conditions","venue":null,"work_id":"4d5fb53d-88d9-4d77-ba9c-26c30510125f","year":2011},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.561300Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:311f905d37462f9a018ec994aba02a3f67d995965ab552dcd42daa39f412d898","observation_id":"004a6adb-f6c9-43ba-8fc9-c23605bc0639","resolution":{"observed_at":"2026-08-15T21:27:26.691505Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-15T21:27:26.797325Z","title":"Optimization of functions on certa in subsets of Banach spaces","venue":null,"work_id":"6fd53bd3-3362-4708-9e97-d3d6a2d9127f","year":1978},"citing_paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T21:27:26.564743Z"},"links":{"citing_paper":"/paper/2505.10045"},"observation_digest":"sha256:10c064edbc787a2048dac514eaddb02c5f0a0eb2e0242996fd03133e75aec229","observation_id":"021d6d45-7c87-4ad6-8bfe-7088d6805206","resolution":{"observed_at":"2026-08-15T21:27:26.801483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.10045","last_updated":"2025-09-05T08:32:59Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-21T16:16:10.034667Z","submitted_at":"2025-05-15T07:43:13Z","title":"Monotone solutions to mean field games master equation in the L2-monotone setting"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":3,"verified_fuzzy":16},"total_outbound_references":37},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2505.10045."}