{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2YOMLPC3DHO3KAGSUISFVJED7H","short_pith_number":"pith:2YOMLPC3","schema_version":"1.0","canonical_sha256":"d61cc5bc5b19ddb500d2a2245aa483f9cc2a51b9a8ee5589015e766e8078a72b","source":{"kind":"arxiv","id":"1509.02505","version":1},"attestation_state":"computed","paper":{"title":"The master equation and the convergence problem in mean field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Delarue, Jean-Michel Lasry, Pierre Cardaliaguet, Pierre-Louis Lions","submitted_at":"2015-09-08T19:24:27Z","abstract_excerpt":"The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called \"master equation\", a kind of second order partial differential equation stated on the space of probability measures. Our first main result is the well-posedness of the master equation. To do so, we first show the existence and uniqueness of a solution to the \"mean field game system with common noise\", which consists in a coupled system made of a backward stochas"},"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":"1509.02505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-08T19:24:27Z","cross_cats_sorted":[],"title_canon_sha256":"7c5d68d3a42058bf635c678bb7032af6636eb9edbd90dd4660ceeb70e21c1848","abstract_canon_sha256":"7d6efe40e04fcbb0be352fa35b179fd7b29aaed63a7fa09226219ab008e46aeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:40.759217Z","signature_b64":"1/1Sn8c28/fLxxTZZsEVDfUbCtAwU/b+LbfrsuDodyTR3lM8CEeg5NT5TjMOQryojIeBR+dQ6bKiEs2hnoAqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d61cc5bc5b19ddb500d2a2245aa483f9cc2a51b9a8ee5589015e766e8078a72b","last_reissued_at":"2026-05-18T01:33:40.758798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:40.758798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The master equation and the convergence problem in mean field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Delarue, Jean-Michel Lasry, Pierre Cardaliaguet, Pierre-Louis Lions","submitted_at":"2015-09-08T19:24:27Z","abstract_excerpt":"The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called \"master equation\", a kind of second order partial differential equation stated on the space of probability measures. Our first main result is the well-posedness of the master equation. To do so, we first show the existence and uniqueness of a solution to the \"mean field game system with common noise\", which consists in a coupled system made of a backward stochas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02505","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":""},"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":"1509.02505","created_at":"2026-05-18T01:33:40.758857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02505v1","created_at":"2026-05-18T01:33:40.758857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02505","created_at":"2026-05-18T01:33:40.758857+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YOMLPC3DHO3","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YOMLPC3DHO3KAGS","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YOMLPC3","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2006.15158","citing_title":"Relative Arbitrage Opportunities with Interactions among $N$ Investors","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H","json":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H.json","graph_json":"https://pith.science/api/pith-number/2YOMLPC3DHO3KAGSUISFVJED7H/graph.json","events_json":"https://pith.science/api/pith-number/2YOMLPC3DHO3KAGSUISFVJED7H/events.json","paper":"https://pith.science/paper/2YOMLPC3"},"agent_actions":{"view_html":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H","download_json":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H.json","view_paper":"https://pith.science/paper/2YOMLPC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02505&json=true","fetch_graph":"https://pith.science/api/pith-number/2YOMLPC3DHO3KAGSUISFVJED7H/graph.json","fetch_events":"https://pith.science/api/pith-number/2YOMLPC3DHO3KAGSUISFVJED7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H/action/storage_attestation","attest_author":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H/action/author_attestation","sign_citation":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H/action/citation_signature","submit_replication":"https://pith.science/pith/2YOMLPC3DHO3KAGSUISFVJED7H/action/replication_record"}},"created_at":"2026-05-18T01:33:40.758857+00:00","updated_at":"2026-05-18T01:33:40.758857+00:00"}