{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E57Q7OT6QQ3AFYBQVSID6KJWE5","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":"a2d9fea7218ca706c98782c5bb85f1ce89fb8e58329c02f77d1dff5dd1712f92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-14T01:55:30Z","title_canon_sha256":"974ff31977759d2c6d4b91460bf8c676d2f7b56b7ec6c51845dc10635fdefea5"},"schema_version":"1.0","source":{"id":"1903.05788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05788","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05788v2","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05788","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"E57Q7OT6QQ3A","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E57Q7OT6QQ3AFYBQ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E57Q7OT6","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:56ef9d95df432c1c12dc3d5c04d3160d2339660a0c4f9fb78274c811ccd99e40","target":"graph","created_at":"2026-05-17T23:51:04Z","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":"The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium. However, in some situations, typically involving symmetry breaking, non-uniqueness of solutions is an essential feature. To investigate the nature of non-unique solutions, this paper focuses on the technically simple setting where players have one of two states, with continuous time dynamics, and the game is symmetric in the players, and players are restricted t","authors_text":"Bruce Hajek, Michael Livesay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-14T01:55:30Z","title":"On non-unique solutions in mean field games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05788","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":"sha256:0c49d90d8ff6a656315776538d533beb57325a21fc981f541e7f303829b95287","target":"record","created_at":"2026-05-17T23:51:04Z","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":"a2d9fea7218ca706c98782c5bb85f1ce89fb8e58329c02f77d1dff5dd1712f92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-14T01:55:30Z","title_canon_sha256":"974ff31977759d2c6d4b91460bf8c676d2f7b56b7ec6c51845dc10635fdefea5"},"schema_version":"1.0","source":{"id":"1903.05788","kind":"arxiv","version":2}},"canonical_sha256":"277f0fba7e843602e030ac903f293627519e50287004677300a66c70119ad6c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"277f0fba7e843602e030ac903f293627519e50287004677300a66c70119ad6c5","first_computed_at":"2026-05-17T23:51:04.757231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:04.757231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"olrBrHK9gb/jfJaOIfkzHmsq7CUNf5NgWYkmD2CS331KrvSvVe76VCF0I80qxo4zf0n1+mR28eV8D9dL8r8ZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:04.757717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c49d90d8ff6a656315776538d533beb57325a21fc981f541e7f303829b95287","sha256:56ef9d95df432c1c12dc3d5c04d3160d2339660a0c4f9fb78274c811ccd99e40"],"state_sha256":"0eb634847ad87914645aa928bb616cc56f26d19033e78ede1b56d019bc9ec6ed"}