{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6QI6YPX7ZOD73U33MQMHUFFJLC","short_pith_number":"pith:6QI6YPX7","canonical_record":{"source":{"id":"1303.1064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2013-03-05T15:25:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"21834bfc3475a1c728708f04325d57c0da68256219027d5a0a9f24ec66f0d8a5","abstract_canon_sha256":"483a9be75335b79eb0f452c461557c1b288d5e6966ff43cb8d230e0bc73f6ded"},"schema_version":"1.0"},"canonical_sha256":"f411ec3effcb87fdd37b64187a14a95897fac4e3c3b4124372a2b5d5c1380c67","source":{"kind":"arxiv","id":"1303.1064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1064","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1064v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1064","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"6QI6YPX7ZOD7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6QI6YPX7ZOD73U33","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6QI6YPX7","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6QI6YPX7ZOD73U33MQMHUFFJLC","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2013-03-05T15:25:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"21834bfc3475a1c728708f04325d57c0da68256219027d5a0a9f24ec66f0d8a5","abstract_canon_sha256":"483a9be75335b79eb0f452c461557c1b288d5e6966ff43cb8d230e0bc73f6ded"},"schema_version":"1.0"},"canonical_sha256":"f411ec3effcb87fdd37b64187a14a95897fac4e3c3b4124372a2b5d5c1380c67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:45.647393Z","signature_b64":"/zh+H6g4pcTR5mn38iVYy6SSA5QBJN0HJo44vll/riED1Uv234MynLCybalAbCu4ChSI4BkqY4vIgFTuZ61TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f411ec3effcb87fdd37b64187a14a95897fac4e3c3b4124372a2b5d5c1380c67","last_reissued_at":"2026-05-18T03:31:45.646778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:45.646778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1064","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":"2026-05-18T03:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c9tJeP6KuYuxZ1fVq+oAJmWiRq4yKxTJJEZi1c+PBFz1WJO4ysBV/2FNR436Cc07QEbPDR0psJtlMziDi8q4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:54:42.797822Z"},"content_sha256":"8b420c36b1d816fb740fe0931b4aa4450542fa95ab0de2e94aa92bff50203467","schema_version":"1.0","event_id":"sha256:8b420c36b1d816fb740fe0931b4aa4450542fa95ab0de2e94aa92bff50203467"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6QI6YPX7ZOD73U33MQMHUFFJLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"q-fin.PM","authors_text":"Duan Li, Xiangyu Cui, Xun Li","submitted_at":"2013-03-05T15:25:09Z","abstract_excerpt":"The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1064","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":"2026-05-18T03:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcfhhUiauMswmM+LnGRjQPYVbcZqC8eAe7yu0W2YHU6hgRvyOxeLb/1LmTuz20x3p2wPPu1bKtFXR4q6ecp/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:54:42.798265Z"},"content_sha256":"b952e9442b56a4a5da39cbc22ac48ce2e87fd4856669e1b3f3c9eb70af45169e","schema_version":"1.0","event_id":"sha256:b952e9442b56a4a5da39cbc22ac48ce2e87fd4856669e1b3f3c9eb70af45169e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/bundle.json","state_url":"https://pith.science/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/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":"2026-08-17T08:54:42Z","links":{"resolver":"https://pith.science/pith/6QI6YPX7ZOD73U33MQMHUFFJLC","bundle":"https://pith.science/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/bundle.json","state":"https://pith.science/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QI6YPX7ZOD73U33MQMHUFFJLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6QI6YPX7ZOD73U33MQMHUFFJLC","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":"483a9be75335b79eb0f452c461557c1b288d5e6966ff43cb8d230e0bc73f6ded","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2013-03-05T15:25:09Z","title_canon_sha256":"21834bfc3475a1c728708f04325d57c0da68256219027d5a0a9f24ec66f0d8a5"},"schema_version":"1.0","source":{"id":"1303.1064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1064","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1064v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1064","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"6QI6YPX7ZOD7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6QI6YPX7ZOD73U33","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6QI6YPX7","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:b952e9442b56a4a5da39cbc22ac48ce2e87fd4856669e1b3f3c9eb70af45169e","target":"graph","created_at":"2026-05-18T03:31:45Z","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 classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field f","authors_text":"Duan Li, Xiangyu Cui, Xun Li","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2013-03-05T15:25:09Z","title":"Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1064","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":"sha256:8b420c36b1d816fb740fe0931b4aa4450542fa95ab0de2e94aa92bff50203467","target":"record","created_at":"2026-05-18T03:31:45Z","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":"483a9be75335b79eb0f452c461557c1b288d5e6966ff43cb8d230e0bc73f6ded","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2013-03-05T15:25:09Z","title_canon_sha256":"21834bfc3475a1c728708f04325d57c0da68256219027d5a0a9f24ec66f0d8a5"},"schema_version":"1.0","source":{"id":"1303.1064","kind":"arxiv","version":1}},"canonical_sha256":"f411ec3effcb87fdd37b64187a14a95897fac4e3c3b4124372a2b5d5c1380c67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f411ec3effcb87fdd37b64187a14a95897fac4e3c3b4124372a2b5d5c1380c67","first_computed_at":"2026-05-18T03:31:45.646778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:45.646778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/zh+H6g4pcTR5mn38iVYy6SSA5QBJN0HJo44vll/riED1Uv234MynLCybalAbCu4ChSI4BkqY4vIgFTuZ61TAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:45.647393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b420c36b1d816fb740fe0931b4aa4450542fa95ab0de2e94aa92bff50203467","sha256:b952e9442b56a4a5da39cbc22ac48ce2e87fd4856669e1b3f3c9eb70af45169e"],"state_sha256":"bd305f8e28d9621ade41b009848eeac788d6bf6f61f703dcdbdc82d8a279a208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndviw9VR3CBT6BplvtZDMCvCqZjnJuev+HQY21FHuZWdF4KZi6JvQwvg12ToJQpFDel9UPiMlqFG8OlGwr1bAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T08:54:42.803373Z","bundle_sha256":"5130c0d6d0f85960b9bf86cac6bcce6f46a156f036273bd48f2bcd65606005c3"}}