{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LQV6K3KOHYXCRFCIC7IKP3CLMR","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":"31ab3b95c98c8ffdcfa958248e85221872220e417b884d3dab29db5b262e5c6e","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-25T14:41:51Z","title_canon_sha256":"70267d3e92e47e64eb3e7d8c1c5b8763158e366f94db2adf4dbdc195261b4fd9"},"schema_version":"1.0","source":{"id":"1104.4725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4725","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4725v2","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4725","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"LQV6K3KOHYXC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LQV6K3KOHYXCRFCI","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LQV6K3KO","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:c80c79e71dbccdd2d15e29e6cd38e17096abce7ab72d2dbed37ba3995289ad02","target":"graph","created_at":"2026-05-18T04:18:52Z","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 backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted M-solutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. As applications, a multi-dimensional comparison theorem is proved for adapted M-solutions of MF-BSVIEs and a maximum principle is established for an optimal control of MF-FSVIEs.","authors_text":"Jiongmin Yong, Tianxiao Wang, Yufeng Shi","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-25T14:41:51Z","title":"Mean-Field Backward Stochastic Volterra Integral Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4725","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":"sha256:85ace6864f9f391155f6126e767de632690256e46333e646d6d0eb0fa4dd4c0c","target":"record","created_at":"2026-05-18T04:18:52Z","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":"31ab3b95c98c8ffdcfa958248e85221872220e417b884d3dab29db5b262e5c6e","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-25T14:41:51Z","title_canon_sha256":"70267d3e92e47e64eb3e7d8c1c5b8763158e366f94db2adf4dbdc195261b4fd9"},"schema_version":"1.0","source":{"id":"1104.4725","kind":"arxiv","version":2}},"canonical_sha256":"5c2be56d4e3e2e28944817d0a7ec4b647efaf642635e82e0e06c6444cb3a930a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c2be56d4e3e2e28944817d0a7ec4b647efaf642635e82e0e06c6444cb3a930a","first_computed_at":"2026-05-18T04:18:52.910768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:52.910768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZBvTZC7iVdoy5ZodiBtO5vGhGDa6y3U0XXjls5Diut1fJXydhCEiD07XuiBNa3uC7DAv5MH9H/UlxOj3NwjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:52.911251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85ace6864f9f391155f6126e767de632690256e46333e646d6d0eb0fa4dd4c0c","sha256:c80c79e71dbccdd2d15e29e6cd38e17096abce7ab72d2dbed37ba3995289ad02"],"state_sha256":"c21c62a0723ce1c4ff9dec8b6c33c6e19eb301340f3cf528a5b262dba7174205"}