{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:77GIJ7KHBEAO6CLJGOQWGJ2TPA","short_pith_number":"pith:77GIJ7KH","schema_version":"1.0","canonical_sha256":"ffcc84fd470900ef096933a16327537802f35c9241f3faaf8dc236415719f22c","source":{"kind":"arxiv","id":"2502.19203","version":1},"attestation_state":"computed","paper":{"title":"Polynomial McKean-Vlasov SDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christa Cuchiero, Janka M\\\"oller","submitted_at":"2025-02-26T15:09:42Z","abstract_excerpt":"We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the state variables themselves as well as their conditional moments in a way that mimics the standard polynomial structure. Our approach leads to new results on the existence and uniqueness of solutions to such conditional McKean-Vlasov SDEs which are, to the best of our knowledge, not obtainable using standard methods. Moreover, we show in the case without common"},"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":"2502.19203","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-02-26T15:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"96cc0eeff787ca27838d15aa9f8f788e64491b5de2fd3e7c42a5342afaae9f1b","abstract_canon_sha256":"68740e76bcbe4b78e0d7f41f6b5e2e5fd78a0f7a6a4be932667ecdce93212c2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:28.495797Z","signature_b64":"1Xt93aLaacY0xqo9kgFVy4OStgxyBtwz9IS1T3vhWlFZs8KB3Wa6Wu3W4P2vkjIRjgZU50uRDuejxFZdynI8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffcc84fd470900ef096933a16327537802f35c9241f3faaf8dc236415719f22c","last_reissued_at":"2026-07-05T10:20:28.495057Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:28.495057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial McKean-Vlasov SDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christa Cuchiero, Janka M\\\"oller","submitted_at":"2025-02-26T15:09:42Z","abstract_excerpt":"We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the state variables themselves as well as their conditional moments in a way that mimics the standard polynomial structure. Our approach leads to new results on the existence and uniqueness of solutions to such conditional McKean-Vlasov SDEs which are, to the best of our knowledge, not obtainable using standard methods. Moreover, we show in the case without common"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19203","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/2502.19203/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":"2502.19203","created_at":"2026-07-05T10:20:28.495122+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.19203v1","created_at":"2026-07-05T10:20:28.495122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19203","created_at":"2026-07-05T10:20:28.495122+00:00"},{"alias_kind":"pith_short_12","alias_value":"77GIJ7KHBEAO","created_at":"2026-07-05T10:20:28.495122+00:00"},{"alias_kind":"pith_short_16","alias_value":"77GIJ7KHBEAO6CLJ","created_at":"2026-07-05T10:20:28.495122+00:00"},{"alias_kind":"pith_short_8","alias_value":"77GIJ7KH","created_at":"2026-07-05T10:20:28.495122+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22964","citing_title":"Signature McKean-Vlasov stochastic differential equations","ref_index":22,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA","json":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA.json","graph_json":"https://pith.science/api/pith-number/77GIJ7KHBEAO6CLJGOQWGJ2TPA/graph.json","events_json":"https://pith.science/api/pith-number/77GIJ7KHBEAO6CLJGOQWGJ2TPA/events.json","paper":"https://pith.science/paper/77GIJ7KH"},"agent_actions":{"view_html":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA","download_json":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA.json","view_paper":"https://pith.science/paper/77GIJ7KH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.19203&json=true","fetch_graph":"https://pith.science/api/pith-number/77GIJ7KHBEAO6CLJGOQWGJ2TPA/graph.json","fetch_events":"https://pith.science/api/pith-number/77GIJ7KHBEAO6CLJGOQWGJ2TPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA/action/storage_attestation","attest_author":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA/action/author_attestation","sign_citation":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA/action/citation_signature","submit_replication":"https://pith.science/pith/77GIJ7KHBEAO6CLJGOQWGJ2TPA/action/replication_record"}},"created_at":"2026-07-05T10:20:28.495122+00:00","updated_at":"2026-07-05T10:20:28.495122+00:00"}