{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DBMZAA3EAUR6THD653BJ5DPPZD","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":"a60dddf8221228d211294c0e2b52b27910a08d98e7819ed50adac99a9695566f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-08-02T10:03:02Z","title_canon_sha256":"c1005f9d712e8e513875d9dc3e1838bd17419ada05e0fa4a992400f584c0a60a"},"schema_version":"1.0","source":{"id":"2108.00755","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.00755","created_at":"2026-07-05T04:00:55Z"},{"alias_kind":"arxiv_version","alias_value":"2108.00755v2","created_at":"2026-07-05T04:00:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.00755","created_at":"2026-07-05T04:00:55Z"},{"alias_kind":"pith_short_12","alias_value":"DBMZAA3EAUR6","created_at":"2026-07-05T04:00:55Z"},{"alias_kind":"pith_short_16","alias_value":"DBMZAA3EAUR6THD6","created_at":"2026-07-05T04:00:55Z"},{"alias_kind":"pith_short_8","alias_value":"DBMZAA3E","created_at":"2026-07-05T04:00:55Z"}],"graph_snapshots":[{"event_id":"sha256:140ee1ce7218b4427d4d553d49df8c2e61e1f274c5f8c0afe04011eefba8c923","target":"graph","created_at":"2026-07-05T04:00:55Z","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/2108.00755/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm. For Mean Field Games, convergence of the policy iteration method has been recently proved in [9]. Here, we provide an estimate of its rate of convergence.","authors_text":"Fabio Camilli, Qing Tang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-08-02T10:03:02Z","title":"Rates of convergence for the policy iteration method for Mean Field Games systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.00755","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":"sha256:606a1602bb3fe22a0f4932bcf7a34cf8fb3f8b17bc7827769e2935493df2a5c3","target":"record","created_at":"2026-07-05T04:00:55Z","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":"a60dddf8221228d211294c0e2b52b27910a08d98e7819ed50adac99a9695566f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-08-02T10:03:02Z","title_canon_sha256":"c1005f9d712e8e513875d9dc3e1838bd17419ada05e0fa4a992400f584c0a60a"},"schema_version":"1.0","source":{"id":"2108.00755","kind":"arxiv","version":2}},"canonical_sha256":"18599003640523e99c7eeec29e8defc8f2f9dfb3d33a8a4d2e96d4b2aa08c5e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18599003640523e99c7eeec29e8defc8f2f9dfb3d33a8a4d2e96d4b2aa08c5e3","first_computed_at":"2026-07-05T04:00:55.064989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:00:55.064989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBqCbWh0iLcU2i9TWVW4T1v4LvqduA/XcIyOuQA80JogRtmfQiE5tGHpZc2EQEqYAVce4jLideD7ZUPtcvdUBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:00:55.065349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.00755","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:606a1602bb3fe22a0f4932bcf7a34cf8fb3f8b17bc7827769e2935493df2a5c3","sha256:140ee1ce7218b4427d4d553d49df8c2e61e1f274c5f8c0afe04011eefba8c923"],"state_sha256":"7109df00e7bf798aa05bb9c56e43369d71fc5e3e51969aae05528436c0fb204c"}