{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MTECRBWL4DIOI64CHYLADJEPJQ","short_pith_number":"pith:MTECRBWL","schema_version":"1.0","canonical_sha256":"64c82886cbe0d0e47b823e1601a48f4c24bbcafb9dc616871e09271c80a4124f","source":{"kind":"arxiv","id":"1604.04057","version":2},"attestation_state":"computed","paper":{"title":"Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"CREST), Huy\\^en Pham (LPMA, Xiaoli Wei (LPMA)","submitted_at":"2016-04-14T07:30:55Z","abstract_excerpt":"We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measures, which is proved from a flow property of the conditional law of the controlled state process. Next, by relying on the notion of differentiability with respect to probability measures due to P.L. Lion"},"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":"1604.04057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-14T07:30:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"dfab04a8f0e06b0f7e188a8db6f54007a0b803b6e1ecf68c2b64bb93f990af52","abstract_canon_sha256":"d5a02f7bccdda250db246ffd9bba38fe5ea4f3f371ccbaedc907e29446096280"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:20.916257Z","signature_b64":"MwMg9JBj/fb5fZ1Q7PEx+0EjBvOxyd7xmDN0ehlDz3UJqjYZsmO712Mx+jrumA/9RX/e2KVecmocWzoDBscbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64c82886cbe0d0e47b823e1601a48f4c24bbcafb9dc616871e09271c80a4124f","last_reissued_at":"2026-05-18T00:53:20.915765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:20.915765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"CREST), Huy\\^en Pham (LPMA, Xiaoli Wei (LPMA)","submitted_at":"2016-04-14T07:30:55Z","abstract_excerpt":"We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measures, which is proved from a flow property of the conditional law of the controlled state process. Next, by relying on the notion of differentiability with respect to probability measures due to P.L. Lion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04057","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1604.04057","created_at":"2026-05-18T00:53:20.915853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.04057v2","created_at":"2026-05-18T00:53:20.915853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04057","created_at":"2026-05-18T00:53:20.915853+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTECRBWL4DIO","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTECRBWL4DIOI64C","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTECRBWL","created_at":"2026-05-18T12:30:32.724797+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/MTECRBWL4DIOI64CHYLADJEPJQ","json":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ.json","graph_json":"https://pith.science/api/pith-number/MTECRBWL4DIOI64CHYLADJEPJQ/graph.json","events_json":"https://pith.science/api/pith-number/MTECRBWL4DIOI64CHYLADJEPJQ/events.json","paper":"https://pith.science/paper/MTECRBWL"},"agent_actions":{"view_html":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ","download_json":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ.json","view_paper":"https://pith.science/paper/MTECRBWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.04057&json=true","fetch_graph":"https://pith.science/api/pith-number/MTECRBWL4DIOI64CHYLADJEPJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/MTECRBWL4DIOI64CHYLADJEPJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ/action/storage_attestation","attest_author":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ/action/author_attestation","sign_citation":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ/action/citation_signature","submit_replication":"https://pith.science/pith/MTECRBWL4DIOI64CHYLADJEPJQ/action/replication_record"}},"created_at":"2026-05-18T00:53:20.915853+00:00","updated_at":"2026-05-18T00:53:20.915853+00:00"}