{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YMAQ77RARWFD6OJMSJYWBHDC3T","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":"3a7382e1a7f7256769df76e0a918a737a95e9322c972e5687c80ece13cff4e41","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-14T06:27:16Z","title_canon_sha256":"fb59e0f19029a185b9088f860546c38980cc9b20c7a5f31a502464853f324783"},"schema_version":"1.0","source":{"id":"1507.03731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03731","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03731v2","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03731","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"pith_short_12","alias_value":"YMAQ77RARWFD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YMAQ77RARWFD6OJM","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YMAQ77RA","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:86b692e1d646760388c08377c34d5b15d371d928645ccddcc48acce58efaa848","target":"graph","created_at":"2026-05-18T01:26:25Z","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":"We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out.","authors_text":"Claudio Marchi, Fabio Camilli, Simone Cacace","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-14T06:27:16Z","title":"A numerical method for Mean Field Games on networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03731","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":"sha256:7aa85678652951ca7bba77a2b5ac7898823d50274d47368ddfce16cbcb1af314","target":"record","created_at":"2026-05-18T01:26:25Z","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":"3a7382e1a7f7256769df76e0a918a737a95e9322c972e5687c80ece13cff4e41","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-14T06:27:16Z","title_canon_sha256":"fb59e0f19029a185b9088f860546c38980cc9b20c7a5f31a502464853f324783"},"schema_version":"1.0","source":{"id":"1507.03731","kind":"arxiv","version":2}},"canonical_sha256":"c3010ffe208d8a3f392c9271609c62dccd85f7e282c6133532756fe8023f600a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3010ffe208d8a3f392c9271609c62dccd85f7e282c6133532756fe8023f600a","first_computed_at":"2026-05-18T01:26:25.129221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:25.129221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khsroqE+d9sEp14i7+9XFUjJbZgUs4E3f1ahQiS25jzY4RNADXR8EZ/g4/i+AapD3Tgybkq564YVjNGnu8OqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:25.129809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa85678652951ca7bba77a2b5ac7898823d50274d47368ddfce16cbcb1af314","sha256:86b692e1d646760388c08377c34d5b15d371d928645ccddcc48acce58efaa848"],"state_sha256":"bae80c7fa1bd73778a63110fcd693d179773ba9ad14e559ddfdb2688009379ba"}