{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NRKN42X7LRN4DBFFUXDUPJXJK5","short_pith_number":"pith:NRKN42X7","canonical_record":{"source":{"id":"1207.2982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-12T14:27:28Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e176d59ef8e28191257e55170719e7fa9a93f62970ec05bd800957d3a3423a88","abstract_canon_sha256":"8cf25223ff5afac56f3d5107c121eae35ccc16a96932a786910bd8550bee22f2"},"schema_version":"1.0"},"canonical_sha256":"6c54de6aff5c5bc184a5a5c747a6e9575b20e069ebdc1efe4ea2003328d2748b","source":{"kind":"arxiv","id":"1207.2982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2982","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2982v1","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2982","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"pith_short_12","alias_value":"NRKN42X7LRN4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NRKN42X7LRN4DBFF","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NRKN42X7","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NRKN42X7LRN4DBFFUXDUPJXJK5","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-12T14:27:28Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e176d59ef8e28191257e55170719e7fa9a93f62970ec05bd800957d3a3423a88","abstract_canon_sha256":"8cf25223ff5afac56f3d5107c121eae35ccc16a96932a786910bd8550bee22f2"},"schema_version":"1.0"},"canonical_sha256":"6c54de6aff5c5bc184a5a5c747a6e9575b20e069ebdc1efe4ea2003328d2748b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:13.346916Z","signature_b64":"pqPLALJQac0AvI9VyOYV2TUnMvYkFxf1s3zi0xdW7giQoSbC6IEp9YFoko8qYA3FsvHIks+jB6ywMCtgObpICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c54de6aff5c5bc184a5a5c747a6e9575b20e069ebdc1efe4ea2003328d2748b","last_reissued_at":"2026-05-18T03:51:13.346367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:13.346367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2982","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqZFNvKl1ALyrI56WnJwrQTWPGIZNf++kqqLTKnhjyMXWwm2FJ53Hplqw1PVxA0icrGeV18AAVkHnUOaku+FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:32:39.676060Z"},"content_sha256":"f0e198062d12a52c6adb094d55e6b1dc1da80c428bf52a68d67c2fa94df959df","schema_version":"1.0","event_id":"sha256:f0e198062d12a52c6adb094d55e6b1dc1da80c428bf52a68d67c2fa94df959df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NRKN42X7LRN4DBFFUXDUPJXJK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean field games: convergence of a finite difference method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Fabio Camilli, Italo Capuzzo Dolcetta, Yves Achdou","submitted_at":"2012-07-12T14:27:28Z","abstract_excerpt":"Mean field type models describing the limiting behavior, as the number of players tends to $+\\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works . Convergence theorems for these methods are proved under various assumptions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2982","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGBK6ggbMbO66Zn0WbMEp/OaavsEcrEtyiyNHDezVq8UmlS4gOFsUwySI5h4V1pmLDYLtQ2nN0zRu0t+Gsr5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:32:39.676424Z"},"content_sha256":"9a62c4e083558d5290f8818c27bb3bbfe1ca3cb28b19cb6a2d90fa6c4126f799","schema_version":"1.0","event_id":"sha256:9a62c4e083558d5290f8818c27bb3bbfe1ca3cb28b19cb6a2d90fa6c4126f799"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/bundle.json","state_url":"https://pith.science/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T19:32:39Z","links":{"resolver":"https://pith.science/pith/NRKN42X7LRN4DBFFUXDUPJXJK5","bundle":"https://pith.science/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/bundle.json","state":"https://pith.science/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRKN42X7LRN4DBFFUXDUPJXJK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NRKN42X7LRN4DBFFUXDUPJXJK5","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":"8cf25223ff5afac56f3d5107c121eae35ccc16a96932a786910bd8550bee22f2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-12T14:27:28Z","title_canon_sha256":"e176d59ef8e28191257e55170719e7fa9a93f62970ec05bd800957d3a3423a88"},"schema_version":"1.0","source":{"id":"1207.2982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2982","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2982v1","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2982","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"pith_short_12","alias_value":"NRKN42X7LRN4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NRKN42X7LRN4DBFF","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NRKN42X7","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:9a62c4e083558d5290f8818c27bb3bbfe1ca3cb28b19cb6a2d90fa6c4126f799","target":"graph","created_at":"2026-05-18T03:51:13Z","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":"Mean field type models describing the limiting behavior, as the number of players tends to $+\\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works . Convergence theorems for these methods are proved under various assumptions","authors_text":"Fabio Camilli, Italo Capuzzo Dolcetta, Yves Achdou","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-12T14:27:28Z","title":"Mean field games: convergence of a finite difference method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2982","kind":"arxiv","version":1},"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:f0e198062d12a52c6adb094d55e6b1dc1da80c428bf52a68d67c2fa94df959df","target":"record","created_at":"2026-05-18T03:51:13Z","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":"8cf25223ff5afac56f3d5107c121eae35ccc16a96932a786910bd8550bee22f2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-07-12T14:27:28Z","title_canon_sha256":"e176d59ef8e28191257e55170719e7fa9a93f62970ec05bd800957d3a3423a88"},"schema_version":"1.0","source":{"id":"1207.2982","kind":"arxiv","version":1}},"canonical_sha256":"6c54de6aff5c5bc184a5a5c747a6e9575b20e069ebdc1efe4ea2003328d2748b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c54de6aff5c5bc184a5a5c747a6e9575b20e069ebdc1efe4ea2003328d2748b","first_computed_at":"2026-05-18T03:51:13.346367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:13.346367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqPLALJQac0AvI9VyOYV2TUnMvYkFxf1s3zi0xdW7giQoSbC6IEp9YFoko8qYA3FsvHIks+jB6ywMCtgObpICg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:13.346916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0e198062d12a52c6adb094d55e6b1dc1da80c428bf52a68d67c2fa94df959df","sha256:9a62c4e083558d5290f8818c27bb3bbfe1ca3cb28b19cb6a2d90fa6c4126f799"],"state_sha256":"fb40ad81c4fe08deda441fb604d86e33f4fea1501ab5212f51daf555b69e62e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZ8XP1JN7/BfPn/QBOvvBopuj8jf0Y5WBlDv0jJu4XkLYBjrxLKDvojnLAX6y5p0kJFiQKDpcz7ARlLRlsQrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:32:39.678490Z","bundle_sha256":"fe62d6a70da523b4ef2e2473fc89799c72ce499f4d3a76d7bc7252c09859835e"}}