{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TVKYX2WVLEQKJLPPYGLE4LBXUD","short_pith_number":"pith:TVKYX2WV","schema_version":"1.0","canonical_sha256":"9d558bead55920a4adefc1964e2c37a0e28c88ac1b6a6ff5e9369259e8cd55e2","source":{"kind":"arxiv","id":"2507.23553","version":1},"attestation_state":"computed","paper":{"title":"McKean-Vlasov equations with singular coefficients - a review of recent results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elena Issoglio (UNITO), ENSTA), Francesco Russo (ENSTA Paris, Luca Bondi (UNITO, OC, OC)","submitted_at":"2025-07-31T13:41:49Z","abstract_excerpt":"This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of singularities of the coefficients: on the one hand they satisfy some integrability and measurability conditions only, while on the other hand the drift is allowed to be a generalised function. Different types of dependencies on the law of the unknown and different noises will also be considered. McKean-Vlasov SDEs are closely related to non-linear Fokker-Planck equatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.23553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-31T13:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"3526777e820bac9b0ca650a29e254347ea5784a7cdd26a673d9914fac73fd2fd","abstract_canon_sha256":"4c91d2480400118a55a68e69fefe117ad8073b52b5d749e37735617341d30611"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:26.751208Z","signature_b64":"kevXEUrIxFAvzQxFgMsfUYcu3cBJthTSxUMnCknKYsHrwc0bmZLQrAmiKS+bUqvqVTvg9B7X9AQJaV4zKer6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d558bead55920a4adefc1964e2c37a0e28c88ac1b6a6ff5e9369259e8cd55e2","last_reissued_at":"2026-07-05T11:46:26.750580Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:26.750580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"McKean-Vlasov equations with singular coefficients - a review of recent results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elena Issoglio (UNITO), ENSTA), Francesco Russo (ENSTA Paris, Luca Bondi (UNITO, OC, OC)","submitted_at":"2025-07-31T13:41:49Z","abstract_excerpt":"This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of singularities of the coefficients: on the one hand they satisfy some integrability and measurability conditions only, while on the other hand the drift is allowed to be a generalised function. Different types of dependencies on the law of the unknown and different noises will also be considered. McKean-Vlasov SDEs are closely related to non-linear Fokker-Planck equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23553","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.23553/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.23553","created_at":"2026-07-05T11:46:26.750661+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.23553v1","created_at":"2026-07-05T11:46:26.750661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23553","created_at":"2026-07-05T11:46:26.750661+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVKYX2WVLEQK","created_at":"2026-07-05T11:46:26.750661+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVKYX2WVLEQKJLPP","created_at":"2026-07-05T11:46:26.750661+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVKYX2WV","created_at":"2026-07-05T11:46:26.750661+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.18877","citing_title":"Ergodic Properties of Non-Linear Density-Dependent Perturbations of the Ornstein-Uhlenbeck Process","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD","json":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD.json","graph_json":"https://pith.science/api/pith-number/TVKYX2WVLEQKJLPPYGLE4LBXUD/graph.json","events_json":"https://pith.science/api/pith-number/TVKYX2WVLEQKJLPPYGLE4LBXUD/events.json","paper":"https://pith.science/paper/TVKYX2WV"},"agent_actions":{"view_html":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD","download_json":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD.json","view_paper":"https://pith.science/paper/TVKYX2WV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.23553&json=true","fetch_graph":"https://pith.science/api/pith-number/TVKYX2WVLEQKJLPPYGLE4LBXUD/graph.json","fetch_events":"https://pith.science/api/pith-number/TVKYX2WVLEQKJLPPYGLE4LBXUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD/action/storage_attestation","attest_author":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD/action/author_attestation","sign_citation":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD/action/citation_signature","submit_replication":"https://pith.science/pith/TVKYX2WVLEQKJLPPYGLE4LBXUD/action/replication_record"}},"created_at":"2026-07-05T11:46:26.750661+00:00","updated_at":"2026-07-05T11:46:26.750661+00:00"}