{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HQWWHCABLXVPZZWH2UFRRU2UFM","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":"2e7fadd891ea8a6b25c9fe1aac4fcb52fdf91a919bb001aef4dab92ede4a5d19","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-15T01:22:55Z","title_canon_sha256":"40412aa5dd60a921114b044e08d4a067f6e544e3c02cb834891bb99f08acc793"},"schema_version":"1.0","source":{"id":"1304.3964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3964","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3964v2","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3964","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"HQWWHCABLXVP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HQWWHCABLXVPZZWH","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HQWWHCAB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:22adde4d113a58d461f05c1f4bc0070379f5b0dc847b6945a6a20034b8bf63f6","target":"graph","created_at":"2026-05-18T03:26:31Z","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":"Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kind of problems. Open-loop solutions are presented by means of variational method with decoupling of forward-backward stochastic differential equations, which lead to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which lea","authors_text":"Jiongmin Yong","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-15T01:22:55Z","title":"Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3964","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:d725fc83f3a9c6b63a49db9e6a3251efec63b44df0fdc7235f1257c606ee2bea","target":"record","created_at":"2026-05-18T03:26:31Z","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":"2e7fadd891ea8a6b25c9fe1aac4fcb52fdf91a919bb001aef4dab92ede4a5d19","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-15T01:22:55Z","title_canon_sha256":"40412aa5dd60a921114b044e08d4a067f6e544e3c02cb834891bb99f08acc793"},"schema_version":"1.0","source":{"id":"1304.3964","kind":"arxiv","version":2}},"canonical_sha256":"3c2d6388015deafce6c7d50b18d3542b14da54fbb9e8a123ce367215cb246f04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c2d6388015deafce6c7d50b18d3542b14da54fbb9e8a123ce367215cb246f04","first_computed_at":"2026-05-18T03:26:31.781812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:31.781812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGyBQqQRd6O/bjkFO51c45X3Is3o0p/qbiJtEjUyKoMEYiuH3wJ98VUD5RKl5oU/Gg65jAZMq/9hgSOCdF84AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:31.782530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d725fc83f3a9c6b63a49db9e6a3251efec63b44df0fdc7235f1257c606ee2bea","sha256:22adde4d113a58d461f05c1f4bc0070379f5b0dc847b6945a6a20034b8bf63f6"],"state_sha256":"e111ef1e8f666c3c29b7df3f4d55852ffd567608a7c0086d7f7e55dde35955cb"}