{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IK6AKPXN6IFRZGLZUV3GTQ36H5","short_pith_number":"pith:IK6AKPXN","schema_version":"1.0","canonical_sha256":"42bc053eedf20b1c9979a57669c37e3f7328998afba73ba32bc9f5a813082786","source":{"kind":"arxiv","id":"2606.22964","version":1},"attestation_state":"computed","paper":{"title":"Signature McKean-Vlasov stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fred Espen Benth, Leonardo Tarquini, Salvador Ortiz-Latorre","submitted_at":"2026-06-22T07:44:53Z","abstract_excerpt":"McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric $p$-rough path lift of its solution, with $p\\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chao"},"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":"2606.22964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-22T07:44:53Z","cross_cats_sorted":[],"title_canon_sha256":"c0b53f84888c2a3696de1ec0bada5d68958d401c4a8341171ca846b09f7eb55a","abstract_canon_sha256":"2b4417fec78043b6ebb4d50f5a6780faa3b7d31c09167c8f58b9305d56bf982b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:05.420394Z","signature_b64":"nV8iAMgcxO3oC7V5YqOc3bmmQa55ZIYzEPqI82hyWxJ4e9VaAe4Y17NtgTi3dbD+520Zo359ty45rfB4Tal6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42bc053eedf20b1c9979a57669c37e3f7328998afba73ba32bc9f5a813082786","last_reissued_at":"2026-06-23T03:14:05.420038Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:05.420038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signature McKean-Vlasov stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fred Espen Benth, Leonardo Tarquini, Salvador Ortiz-Latorre","submitted_at":"2026-06-22T07:44:53Z","abstract_excerpt":"McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric $p$-rough path lift of its solution, with $p\\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chao"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22964","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/2606.22964/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":"2606.22964","created_at":"2026-06-23T03:14:05.420097+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22964v1","created_at":"2026-06-23T03:14:05.420097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22964","created_at":"2026-06-23T03:14:05.420097+00:00"},{"alias_kind":"pith_short_12","alias_value":"IK6AKPXN6IFR","created_at":"2026-06-23T03:14:05.420097+00:00"},{"alias_kind":"pith_short_16","alias_value":"IK6AKPXN6IFRZGLZ","created_at":"2026-06-23T03:14:05.420097+00:00"},{"alias_kind":"pith_short_8","alias_value":"IK6AKPXN","created_at":"2026-06-23T03:14:05.420097+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5","json":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5.json","graph_json":"https://pith.science/api/pith-number/IK6AKPXN6IFRZGLZUV3GTQ36H5/graph.json","events_json":"https://pith.science/api/pith-number/IK6AKPXN6IFRZGLZUV3GTQ36H5/events.json","paper":"https://pith.science/paper/IK6AKPXN"},"agent_actions":{"view_html":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5","download_json":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5.json","view_paper":"https://pith.science/paper/IK6AKPXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22964&json=true","fetch_graph":"https://pith.science/api/pith-number/IK6AKPXN6IFRZGLZUV3GTQ36H5/graph.json","fetch_events":"https://pith.science/api/pith-number/IK6AKPXN6IFRZGLZUV3GTQ36H5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5/action/storage_attestation","attest_author":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5/action/author_attestation","sign_citation":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5/action/citation_signature","submit_replication":"https://pith.science/pith/IK6AKPXN6IFRZGLZUV3GTQ36H5/action/replication_record"}},"created_at":"2026-06-23T03:14:05.420097+00:00","updated_at":"2026-06-23T03:14:05.420097+00:00"}