{"as_of":"2026-08-22T23:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9b4703eaf286a4f1b6373e6c6b09288c6190b7dde38db9f172a3edc0dcac9189","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T21:59:17.713114Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2508.07867/citation-record","integrity":"/paper/2508.07867/integrity","json":"/paper/2508.07867/citation-record.json","paper":"/paper/2508.07867"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/puqr.2023010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Non-linear affine pro- cesses with jumps","venue":"Probability Uncertainty and Quantitative Risk","work_id":"babaa682-ccc4-41dd-a07e-b843f033457f","year":2023},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:14.646195Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:d90a72a9a89d78f3612f28faf43f4f021d6eef7b18357f12dacb801d9dc331da","observation_id":"1b17daeb-2cb5-4ff8-80ac-5278c4d3c50b","resolution":{"observed_at":"2026-08-05T21:59:21.161688Z","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":"10.3934/puqr.2025011","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Mean-field stochastic differ- ential equations driven by G-Brownian motion","venue":"Probability Uncertainty and Quantitative Risk","work_id":"62657d39-1aa9-4286-ab6c-df10683985cf","year":2025},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:14.721368Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:54e53c71a6e774f2840712a80e45723fda3e02d1ca497d59d725aa58784f158e","observation_id":"8c8c2cd7-23e2-482d-83f2-b406c92baa37","resolution":{"observed_at":"2026-08-05T21:59:20.939841Z","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":{"arxiv_id":"1407.1215","last_updated":"2014-07-04T13:06:25Z","snapshot_observed_at":"2026-08-14T23:27:56.172568Z","submitted_at":"2014-07-04T13:06:25Z","title":"Mean-field stochastic differential equations and associated PDEs","version":1},"cited_work":{"arxiv_id":"1407.1215","doi":null,"metadata_source":"pith","pith_arxiv_id":"1407.1215","snapshot_observed_at":"2026-08-05T21:59:21.723829Z","title":"Mean-field stochastic differential equations and associated PDEs","venue":"math.PR","work_id":"0700dbe5-8cf4-4828-bb2e-187b0870a4d7","year":2014},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:14.805816Z"},"links":{"cited_paper":"/paper/1407.1215","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:e242ac3d31e3c719153c79b025e6b9f1c6b5c6532942f652a23e5bd36de5aecb","observation_id":"378441d2-9603-4279-95c6-dff75d3b6057","resolution":{"observed_at":"2026-08-05T21:59:21.798257Z","resolver_source":"local_arxiv","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":"10.1007/s11579-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T21:59:20.457199Z","title":"Mean field game of controls and an application to trade crowding","venue":null,"work_id":"4737c5a0-9802-437b-9145-52e34e165164","year":2018},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:14.907967Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:6efb064b9b64f4bf482a87715799a0b4e4fe0982f9b9904dfa2bf47e85b0bfa6","observation_id":"474381fc-7ce6-4bac-a5f3-4c3eee2be2b1","resolution":{"observed_at":"2026-08-05T21:59:20.592918Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"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":"2026-08-05T21:59:23.234632Z","title":"Probabilistic theory of mean field games with applications I: Mean field FBSDEs, control, and games","venue":null,"work_id":"9f858fc0-3d91-4fe9-aee4-3335edab8516","year":2018},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:14.986170Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:7fa66786ad7d3d36c2383b38121c9df0bcd0636bf15dfb1e3cb3da5fa1bd171b","observation_id":"de704094-715a-4e2a-82d9-c8a31e13f03a","resolution":{"observed_at":"2026-08-05T21:59:23.287227Z","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":"2026-08-05T21:59:23.120685Z","title":"Probabilistic theory of mean field games with applications II: mean field games with common noise and master equations","venue":null,"work_id":"b74491c4-affe-474b-89ff-378656fccd9e","year":2017},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.114927Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:bd21dd15e1d22027f8878513641ee139f821990682f11e8f1e6a8a5246618ffc","observation_id":"a56afd71-777e-4653-a52e-6d1e2f74cd95","resolution":{"observed_at":"2026-08-05T21:59:23.156270Z","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":"10.1214/ejp.v17-2224","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces","venue":"Electronic Journal of Probability","work_id":"1bd84cf3-f22f-44a9-96df-d40ce766393f","year":2012},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.264217Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:58241b15f3041d5548f2517518055e7069aa27047ffd7667ad66d98c5692db91","observation_id":"a6f8bb80-1b5b-4a66-84a8-5b57f06dbdb3","resolution":{"observed_at":"2026-08-05T21:59:20.361973Z","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":"10.1186/s41546-019-0039-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Affine processes under pa- rameter uncertainty","venue":"Probability Uncertainty and Quantitative Risk","work_id":"2056aefd-e20c-42af-819e-4915e4049db1","year":2019},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.349450Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:594c6d3256408fbd14435db699ba420f9a745e040ef9335d8d133be79a8ca333","observation_id":"149aaef6-68de-4d4d-864a-190e237bdab8","resolution":{"observed_at":"2026-08-05T21:59:20.148183Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[{"edge_observation":{"observed_at":"2026-08-06T00:18:56.953186+00:00","source":"paper_reference_links","state":"open"},"event_date":"2019-08-26","event_type":"correction","notice_doi":"10.1186/s41546-019-0041-7","provenance":{"observed_at":"2026-07-11T02:56:42.644802+00:00","source":"crossref","source_record_id":"10.1186/s41546-019-0041-7->10.1186/s41546-019-0039-1:correction"}}],"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":"2026-08-05T21:59:23.079439Z","title":"Lévy-type processes under uncertainty and related nonlocal equations","venue":null,"work_id":"57064689-3375-4203-a691-11e758637f9f","year":2016},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.438835Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:fac203e775ff4620149767335649f8a1edf546a76231f65c19951eb96678bccf","observation_id":"12709f9c-b7c4-4a6d-b400-7cd6f7f44edf","resolution":{"observed_at":"2026-08-05T21:59:23.114153Z","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":"2205.09164","last_updated":"2022-05-18T18:26:32Z","snapshot_observed_at":"2026-08-20T15:02:31.623714Z","submitted_at":"2022-05-18T18:26:32Z","title":"BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs","version":1},"cited_work":{"arxiv_id":"2205.09164","doi":"10.48550/arxiv.2205.09164","metadata_source":"pith","pith_arxiv_id":"2205.09164","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs","venue":"math.PR","work_id":"dd8b4063-8402-419c-8e1e-6bc7e95ff5a3","year":2022},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.502461Z"},"links":{"cited_paper":"/paper/2205.09164","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:ab4147122dbe6f0e02693d04e09741629a9c796976df42991c8a7ec4c884e1d8","observation_id":"ab6ff3a1-c66f-4015-b7b8-85872bca6196","resolution":{"observed_at":"2026-08-05T21:59:20.008381Z","resolver_source":"local_arxiv","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":"10.3934/puqr","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T21:59:19.698481Z","title":"G-Lévyprocessesundersublinearexpectations","venue":null,"work_id":"08939b60-53d0-4336-81f6-684d600d33ac","year":2021},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.580338Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:4fc02f55c9470c8a780774525447aa9a676f513c957419c934fc79ae1511baa3","observation_id":"8f0f7e39-fd98-42b0-a427-746f24975156","resolution":{"observed_at":"2026-08-05T21:59:19.790109Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"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":"2026-08-05T21:59:22.967654Z","title":"Backward stochastic differential equations driven by G-Brownian motion","venue":null,"work_id":"1f521fd0-c3c2-40f4-9fb4-e20fa8c6dfb1","year":2014},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.629693Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:0947e17d25a2c151d434bb2a68e65c9cbb70291006259592b27afdd8497439ef","observation_id":"8e945f71-ea7c-40a1-a82a-1594150438ec","resolution":{"observed_at":"2026-08-05T21:59:23.025537Z","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":"2026-08-05T21:59:22.874691Z","title":"Foundations of Kinetic Theory","venue":null,"work_id":"141df3a2-f9c4-416a-8d44-dfdc18d3c598","year":1956},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.883963Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:7874f68913d30748062b2bb44a5a2cdf79f2ad2530610d7e7f710c8c8456125e","observation_id":"e1584a5f-360b-4dc6-b949-e4e01ed9b16c","resolution":{"observed_at":"2026-08-05T21:59:22.911287Z","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":"2026-08-05T21:59:15.931664Z","title":"Jeux à champ moyen. I – Le cas station- naire","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.931664Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:82db38f60a85e89da80f97edaac0d0751de58ebfd950c98e43b3bed4781e3c94","observation_id":"e5c62def-6077-42e6-8e1d-7f1326e4ae77","resolution":{"observed_at":"2026-08-05T21:59:15.931664Z","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":"2026-08-05T21:59:22.787062Z","title":"Jeux à champ moyen. II – Horizon fini et contrôle optimal","venue":null,"work_id":"60428caa-e20a-4330-b183-16de524c119e","year":2006},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.987333Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:28e852e90b1483cb6d85662b5a69849868b96a08fec5486f42a7b70e3b3f857c","observation_id":"ca899666-5921-4913-8f74-faaa88bce425","resolution":{"observed_at":"2026-08-05T21:59:22.827213Z","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":"10.1007/s40072-025-00354-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Doubly reflected backward SDEs driven by G-Brownian mo- tions and fully nonlinear PDEs with double obstacles","venue":"Stochastic Partial Differential Equations Analysis and Computations","work_id":"3f6414b8-b2a8-438d-8762-fb18575a1913","year":2025},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.144100Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:198e2ee40baa0149c0a6691557e22a5282d7e8c2cb75fccd69c7c2d5b9ec548a","observation_id":"417fd112-1a34-4fc8-8cee-1a6f2bb4794f","resolution":{"observed_at":"2026-08-05T21:59:19.388463Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T21:59:16.247329Z","title":"A Class of Markov Processes Associated with Nonlinear Parabolic Equations","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.247329Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:d5ba982a4429f1f484d0a83bb25c9f666bce715a4ff3c0ee3df968f74cdc4d9e","observation_id":"dbfbaecf-9345-490a-aad5-f69e8ac9c0ea","resolution":{"observed_at":"2026-08-05T21:59:16.247329Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1401.7253","last_updated":"2015-01-11T19:19:37Z","snapshot_observed_at":"2026-08-20T08:02:29.080293Z","submitted_at":"2014-01-28T16:50:58Z","title":"Nonlinear L\\'evy Processes and their Characteristics","version":2},"cited_work":{"arxiv_id":"1401.7253","doi":null,"metadata_source":"pith","pith_arxiv_id":"1401.7253","snapshot_observed_at":"2026-08-05T21:59:21.585455Z","title":"Nonlinear L\\'evy Processes and their Characteristics","venue":"math.PR","work_id":"4465f2cd-8267-4494-9d78-f894dfbfd98c","year":2014},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.348478Z"},"links":{"cited_paper":"/paper/1401.7253","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:9e46b403bd345861a64773419c6a6aa872f7581cf0a12c5aee139a4cfa5b5547","observation_id":"6d178435-5146-4af6-b0ac-04317874a422","resolution":{"observed_at":"2026-08-05T21:59:21.669453Z","resolver_source":"local_arxiv","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":"2026-08-05T21:59:22.719566Z","title":"Constructing sublinear expectations on path space","venue":null,"work_id":"46c06a86-1219-409a-8d55-5d64a72c2e33","year":2013},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.463217Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:12b51b45ec80d72da997ea1aa294ddd100b8914d2b59d83cbc8bc79e8cd7ed05","observation_id":"ce71431b-3fa4-4e55-bee5-2473bd29ca7c","resolution":{"observed_at":"2026-08-05T21:59:22.755854Z","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":"0803.2656","last_updated":"2008-03-18T15:22:25Z","snapshot_observed_at":"2026-08-16T01:04:06.430805Z","submitted_at":"2008-03-18T15:22:25Z","title":"A New Central Limit Theorem under Sublinear Expectations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0803.2656","snapshot_observed_at":"2026-08-05T21:59:16.688621Z","title":"A New Central Limit Theorem under Sublinear Expectations","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.688621Z"},"links":{"cited_paper":"/paper/0803.2656","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:3cf515b5cde3dea14fa785029f38e513e39e9e0660d6f34fd7b749c28dc91039","observation_id":"2afab20a-655b-4145-af0f-de9e9c415360","resolution":{"observed_at":"2026-08-05T21:59:16.688621Z","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":"10.1007/s10255-004-0161-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Filtration Consistent Nonlinear Expectations and Evaluations of Contin- gent Claims","venue":"Acta Mathematicae Applicatae Sinica English Series","work_id":"153e6853-d185-4e33-854e-5d95ef4ff17a","year":2004},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.871995Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:39efe62b1b9ba931b919183ed8f551ce9855deb0580790410a91838434c7bbba","observation_id":"9fb00717-8224-42c5-9953-04b003675405","resolution":{"observed_at":"2026-08-05T21:59:18.935443Z","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":"10.1007/978-3-540-70847-6_25","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:07:33.414567Z","title":"G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type","venue":"Stochastic Analysis and Applications","work_id":"fc945742-6981-4fe9-a951-c4de3c38f5a6","year":2007},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.062740Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:26efe0b33255003aa724e0666edb429dfb6e0fc9b98d291352ede20a6911d9a3","observation_id":"5fafaec9-ad27-4198-a33b-cf160d565344","resolution":{"observed_at":"2026-08-05T21:59:18.694285Z","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":{"arxiv_id":"math/0601035","last_updated":"2006-12-31T15:27:04Z","snapshot_observed_at":"2026-07-07T05:53:58.072736Z","submitted_at":"2006-01-03T08:20:24Z","title":"G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type","version":2},"cited_work":{"arxiv_id":"math/0601035","doi":"10.48550/arxiv.math/0601035","metadata_source":"pith","pith_arxiv_id":"math/0601035","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type","venue":"math.PR","work_id":"113ef5e4-7c1a-4c80-af3d-69cb7cc5b9b2","year":2006},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.164222Z"},"links":{"cited_paper":"/paper/math/0601035","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:8553ef171bfebfd9a1ecbfa2648fd56ff528b0c9142b8c118997fc45e0e9ebcd","observation_id":"c05389b7-5d5a-469b-8a1d-aafb91db7ae9","resolution":{"observed_at":"2026-08-05T21:59:18.448772Z","resolver_source":"local_arxiv","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":"10.1016/j.spa.2007.10.015","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation","venue":"Stochastic Processes and their Applications","work_id":"6a18d11c-15ff-4589-a891-f7f1b2f8aaaa","year":2008},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.258675Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:944199b786929a79c860ea158cb04c0125ff2f712fa264684068becc9a358f6b","observation_id":"fcdd6f4c-21db-474d-b332-29b99782c082","resolution":{"observed_at":"2026-08-05T21:59:18.111577Z","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":"2026-08-05T21:59:22.451719Z","title":"Nonlinear expectations and stochastic calculus under uncertainty: with Ro- bust CLT and G-Brownian motion","venue":null,"work_id":"06845a35-abe7-479c-942e-52ffddd20c33","year":null},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.310184Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:deb9088abcbfa82c3575906d0ded68d1fcd78e56ab8016bf3a0e97961fb87db7","observation_id":"66eab239-c006-4668-a4eb-53d0338117ca","resolution":{"observed_at":"2026-08-05T21:59:22.639497Z","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":"10.1007/s11425-015-5086-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"BSDE, path-dependent PDE and nonlinear Feynman- Kac formula","venue":"Science China Mathematics","work_id":"8494b9ec-eb4c-4a23-a5d0-38b6c6ebee96","year":2016},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.473636Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:0e593aa46bdd40874bea9d6e429e4f9d534aa9cb415150994c12217bbe54d9f4","observation_id":"3e2f0962-3661-4195-ae83-d76d064259ea","resolution":{"observed_at":"2026-08-05T21:59:17.805361Z","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":{"arxiv_id":"2302.12539","last_updated":"2023-02-24T09:50:35Z","snapshot_observed_at":"2026-08-16T15:53:00.507340Z","submitted_at":"2023-02-24T09:50:35Z","title":"On distribution dependent stochastic differential equations driven by $G$-Brownian motion","version":1},"cited_work":{"arxiv_id":"2302.12539","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.12539","snapshot_observed_at":"2026-08-05T21:59:21.333672Z","title":"On distribution dependent stochastic differential equations driven by $G$-Brownian motion","venue":"math.PR","work_id":"7dbb2260-3623-4bce-b75e-88aae966e426","year":2023},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.552116Z"},"links":{"cited_paper":"/paper/2302.12539","citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:6d31035c864a1588f85ffbc32342b3b6138009cdf70c26679b550d12ce190fbc","observation_id":"46299781-f5ee-4d75-9b68-89e4faddcd35","resolution":{"observed_at":"2026-08-05T21:59:21.466227Z","resolver_source":"local_arxiv","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":"2026-08-05T21:59:22.227627Z","title":"Mean-field backward stochastic differential equations driven by G- Brownian motion and related partial differential equations","venue":null,"work_id":"5aeab27e-ffba-4394-b761-5f5dc40a909c","year":2020},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.617601Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:f5988874d7ead0fa314164871b91ca8a5aebc9c82a8e5072fa8a412d61020f53","observation_id":"ea4550b6-c917-456f-9b3b-ac0c31bbbfe4","resolution":{"observed_at":"2026-08-05T21:59:22.327335Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"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":"2026-08-05T21:59:21.907308Z","title":"Topics in propagation of chaos","venue":null,"work_id":"f01ce45b-9fa0-4924-94f2-acdad9531f39","year":1989},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.677766Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:5f88489a5a86dd0f3248a31bae26f29dc9c9f45c3f50fd0b0b8afdfbd1467571","observation_id":"6dbf9c14-4919-4afb-aed0-90660efc949e","resolution":{"observed_at":"2026-08-05T21:59:22.079800Z","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":"2026-08-05T21:59:17.713114Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.713114Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:887557737db693c07c4fbaf606ced769b309bec3c637b476a403a361c33f2e66","observation_id":"a0106c09-e4cf-4bfa-a95d-0d9109aa19a2","resolution":{"observed_at":"2026-08-05T21:59:17.713114Z","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":"2026-08-05T21:59:17.376758Z","title":"doi: 10.1007/978- 3662-59903-7","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:17.376758Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:0452c7ae61e2cd7bb03abe07a2411552fe39a13a57b50d2c98266968e923bdbe","observation_id":"32186237-09d9-474f-b768-768f2c1e6de7","resolution":{"observed_at":"2026-08-05T21:59:17.376758Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T21:59:16.059650Z","title":"doi: 10.1016/j.crma.2006.09.018","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":684,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.059650Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:5a8538141acb514ad3fef17ec52fc4e68f125f639fd996795b3e773a8ac39be1","observation_id":"1b37db15-91b7-42f3-9505-71ef0d5599a8","resolution":{"observed_at":"2026-08-05T21:59:16.059650Z","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":"10.1016/j.spa.2013.09.010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"doi: 10.1016/j.spa.2013.09.010","venue":"Stochastic Processes and their Applications","work_id":"240d4a31-7dd9-44db-a715-d41915bf9a53","year":2013},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":784,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:15.767928Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:c986bf50fdfb8ae2cca33d7f76be0cef01925afa2c34171b24973304d03d1bb7","observation_id":"c5267fe2-1b5a-483f-9b3d-e58f5552c467","resolution":{"observed_at":"2026-08-05T21:59:19.603835Z","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":"10.1016/j.spa.2013.03.022","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"doi: 10.1016/j.spa.2013.03.022","venue":"Stochastic Processes and their Applications","work_id":"0865ec86-7813-4b72-a35f-f50798fd47ff","year":2013},"citing_paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs","version":1},"reference_index":3121,"source":"pdf_text","source_observed_at":"2026-08-05T21:59:16.570492Z"},"links":{"citing_paper":"/paper/2508.07867"},"observation_digest":"sha256:c95ebe5ba37b7239a3c383595037c1cd53c40c81474c72770cd6c525b2134395","observation_id":"81621339-36ad-4bc8-b399-cf69ee6bf823","resolution":{"observed_at":"2026-08-05T21:59:19.177798Z","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"}}],"paper":{"arxiv_id":"2508.07867","last_updated":"2025-08-11T11:36:11Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-08T17:22:58.799744Z","submitted_at":"2025-08-11T11:36:11Z","title":"Regularity of Solutions of Mean-Field $G$-SDEs"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":16,"verified_fuzzy":9},"total_outbound_references":34},"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 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2508.07867."}