{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I5SA74RCHFCUNHAAGVMIS5QQXS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fd28e5ad7fe4326c62da821b7c5ea7a3917f712d5779abbea68c51623bda9f9a","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-12-29T14:36:27Z","title_canon_sha256":"09a39ce3aea23e8e0db857f059ff0238f32c77924655d26a6579dc4674059940"},"schema_version":"1.0","source":{"id":"2012.14772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.14772","created_at":"2026-07-05T05:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"2012.14772v2","created_at":"2026-07-05T05:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.14772","created_at":"2026-07-05T05:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"I5SA74RCHFCU","created_at":"2026-07-05T05:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"I5SA74RCHFCUNHAA","created_at":"2026-07-05T05:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"I5SA74RC","created_at":"2026-07-05T05:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:a3d5b54dc0213797d111fa44f4b34c2878100306fc2de6ca3cfc1c42a736b4b8","target":"graph","created_at":"2026-07-05T05:26:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.14772/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we prove the dynamic programming principle (DPP) in such a general framework. The crucial law invariance property of the value function V is rigorously obtained, which means that V can be viewed as a function on the Wasserstein space of probability measures on the set of continuous functions valued in Hilbert space. We then define a notion of pathwise measure ","authors_text":"Andrea Cosso, Fausto Gozzi, Huy\\^en Pham (LPSM (UMR\\_8001)), Idris Kharroubi, Mauro Rosestolato","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-12-29T14:36:27Z","title":"Optimal control of path-dependent McKean-Vlasov SDEs in infinite dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.14772","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cf651eeb1578cbfd7c19758c3dcdde81c4fc823477182e84625a0681eef4367c","target":"record","created_at":"2026-07-05T05:26:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fd28e5ad7fe4326c62da821b7c5ea7a3917f712d5779abbea68c51623bda9f9a","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-12-29T14:36:27Z","title_canon_sha256":"09a39ce3aea23e8e0db857f059ff0238f32c77924655d26a6579dc4674059940"},"schema_version":"1.0","source":{"id":"2012.14772","kind":"arxiv","version":2}},"canonical_sha256":"47640ff2223945469c003558897610bc9c27ef852d1635c2c1cea9f7d147f595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47640ff2223945469c003558897610bc9c27ef852d1635c2c1cea9f7d147f595","first_computed_at":"2026-07-05T05:26:32.294765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:26:32.294765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KegsezVl8RRuEbjQQbajSejm6jXkBOrTlbYFjulCt0OnoingT8vlMzI5zjHxPDVsMLKkA9sNl4lKbMY1Jx/PAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:26:32.295130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.14772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf651eeb1578cbfd7c19758c3dcdde81c4fc823477182e84625a0681eef4367c","sha256:a3d5b54dc0213797d111fa44f4b34c2878100306fc2de6ca3cfc1c42a736b4b8"],"state_sha256":"63d9e5c1c39273e3a4cb4cc6fefd4ce007b1dd893a33b491b819be0fae46176f"}