{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JEZBJOVPC4NOQTZLSBJ6X3FCYH","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":"0c008574e96ff1622def9261823ecda733930e6aea4a45d3371d68300a00f1ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-16T09:40:49Z","title_canon_sha256":"5d9c0badfaf2555b04e4f329bc409b55da76caea0fab11e2a975718d1604845b"},"schema_version":"1.0","source":{"id":"1112.3744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3744","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3744v2","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3744","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"JEZBJOVPC4NO","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JEZBJOVPC4NOQTZL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JEZBJOVP","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8281ad32c63f30822005a0b202497a01022cffadbe939fea053d0c2d1fdc269c","target":"graph","created_at":"2026-05-18T03:58:26Z","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"},"paper":{"abstract_excerpt":"In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of L\\'evy-Khintchine type (with variable coefficients). We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N","authors_text":"Jiajie Li, Vassili N. Kolokoltsov, Wei Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-16T09:40:49Z","title":"Mean Field Games and Nonlinear Markov Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3744","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":"sha256:3403f6e0bf1a7f3fdd293344f714b6e53fae8ffa2f0f95ab304d8002f4f90735","target":"record","created_at":"2026-05-18T03:58:26Z","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":"0c008574e96ff1622def9261823ecda733930e6aea4a45d3371d68300a00f1ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-16T09:40:49Z","title_canon_sha256":"5d9c0badfaf2555b04e4f329bc409b55da76caea0fab11e2a975718d1604845b"},"schema_version":"1.0","source":{"id":"1112.3744","kind":"arxiv","version":2}},"canonical_sha256":"493214baaf171ae84f2b9053ebeca2c1de756bbf5f89003d028348422dd7b444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"493214baaf171ae84f2b9053ebeca2c1de756bbf5f89003d028348422dd7b444","first_computed_at":"2026-05-18T03:58:26.202889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:26.202889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2SBGIRgXs5Ov2MCD+1hq0Wc5pH1KLdpqnIN8g8PaaEYIatO0+2ZMFg/JIva06lgue/XR2vznBeY0Ugfj+mSQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:26.203636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3403f6e0bf1a7f3fdd293344f714b6e53fae8ffa2f0f95ab304d8002f4f90735","sha256:8281ad32c63f30822005a0b202497a01022cffadbe939fea053d0c2d1fdc269c"],"state_sha256":"2bebe3839e6d30c82408c02900026fbffa3bf2ec7f33cb500d2132a74f390f0d"}