{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC","short_pith_number":"pith:NZ2Q7UUU","canonical_record":{"source":{"id":"1902.09758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T06:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"6dfdefd76dac48c7cd4d3d3d38e9011c3b94f495467b8935fabddb12750947ee","abstract_canon_sha256":"9a7d1e17906c40c5bbaad126b3b75193f49a0f177b0b0b06119a91771c608a5f"},"schema_version":"1.0"},"canonical_sha256":"6e750fd294c6b3d334a13bb3f708b8c899c798e19d1a50e471d4ae20649d613a","source":{"kind":"arxiv","id":"1902.09758","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09758","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09758v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09758","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"NZ2Q7UUUY2Z5","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NZ2Q7UUUY2Z5GNFB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NZ2Q7UUU","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T06:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"6dfdefd76dac48c7cd4d3d3d38e9011c3b94f495467b8935fabddb12750947ee","abstract_canon_sha256":"9a7d1e17906c40c5bbaad126b3b75193f49a0f177b0b0b06119a91771c608a5f"},"schema_version":"1.0"},"canonical_sha256":"6e750fd294c6b3d334a13bb3f708b8c899c798e19d1a50e471d4ae20649d613a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:35.444622Z","signature_b64":"9gRrt/rPiB/BdSnu4SR5CPt9plycJd2JJD3r+2HAaEe7KT+kB5kNd+NuwgYY8C5dcgJaHLJiuaeV/ANDYecBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e750fd294c6b3d334a13bb3f708b8c899c798e19d1a50e471d4ae20649d613a","last_reissued_at":"2026-05-17T23:52:35.443986Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:35.443986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09758","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":"2026-05-17T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+6Rxfdmh1/HCbzvN7/5uhYIgD7ROCLubE6HlTmaQiOVN1XdKvV5IxZsA5K2hSDOQK+bm6P9vGseErA7uJTiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:19:44.786220Z"},"content_sha256":"3d39ecdcbc2ff69aa045c8ecdb87d571b487751ae294e73d05ae5acc11ef9b7c","schema_version":"1.0","event_id":"sha256:3d39ecdcbc2ff69aa045c8ecdb87d571b487751ae294e73d05ae5acc11ef9b7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear quadratic problems for fully coupled forward-backward stochastic control systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mingshang Hu, Shaolin Ji, Xiaole Xue","submitted_at":"2019-02-26T06:51:51Z","abstract_excerpt":"This paper is concerned with optimal control of stochastic fully coupled forward-backward linear quadratic (FBLQ) problems with indefinite control weight costs. In order to obtain the state feedback representation of the optimal control, we propose a new decoupling technique and obtain one kind of non-Riccati-type ordinary differential equations (ODEs). By applying the completion-of-squares method, we prove the existence of the solutions for the obtained ODEs under some assumptions and derive the state feedback form of the optimal control. For this FBLQ problem, the optimal control depends on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09758","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":"2026-05-17T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4+E/BshC2VgGgDdOhcyKKnZ24SViMBdgX9alZoX8bi4lvGTlecxZaDSp6Ww9naqE8U9giHhdVq6miOSkCyYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:19:44.786821Z"},"content_sha256":"74a9b5ad1f805eda94a5319cba10dbca5501b6795c52bfb51a0eea768894092e","schema_version":"1.0","event_id":"sha256:74a9b5ad1f805eda94a5319cba10dbca5501b6795c52bfb51a0eea768894092e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/bundle.json","state_url":"https://pith.science/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/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":"2026-05-26T19:19:44Z","links":{"resolver":"https://pith.science/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC","bundle":"https://pith.science/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/bundle.json","state":"https://pith.science/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NZ2Q7UUUY2Z5GNFBHOZ7OCFYZC","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":"9a7d1e17906c40c5bbaad126b3b75193f49a0f177b0b0b06119a91771c608a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T06:51:51Z","title_canon_sha256":"6dfdefd76dac48c7cd4d3d3d38e9011c3b94f495467b8935fabddb12750947ee"},"schema_version":"1.0","source":{"id":"1902.09758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09758","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09758v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09758","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"NZ2Q7UUUY2Z5","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NZ2Q7UUUY2Z5GNFB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NZ2Q7UUU","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:74a9b5ad1f805eda94a5319cba10dbca5501b6795c52bfb51a0eea768894092e","target":"graph","created_at":"2026-05-17T23:52:35Z","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":"This paper is concerned with optimal control of stochastic fully coupled forward-backward linear quadratic (FBLQ) problems with indefinite control weight costs. In order to obtain the state feedback representation of the optimal control, we propose a new decoupling technique and obtain one kind of non-Riccati-type ordinary differential equations (ODEs). By applying the completion-of-squares method, we prove the existence of the solutions for the obtained ODEs under some assumptions and derive the state feedback form of the optimal control. For this FBLQ problem, the optimal control depends on ","authors_text":"Mingshang Hu, Shaolin Ji, Xiaole Xue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T06:51:51Z","title":"Linear quadratic problems for fully coupled forward-backward stochastic control systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09758","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":"sha256:3d39ecdcbc2ff69aa045c8ecdb87d571b487751ae294e73d05ae5acc11ef9b7c","target":"record","created_at":"2026-05-17T23:52:35Z","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":"9a7d1e17906c40c5bbaad126b3b75193f49a0f177b0b0b06119a91771c608a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T06:51:51Z","title_canon_sha256":"6dfdefd76dac48c7cd4d3d3d38e9011c3b94f495467b8935fabddb12750947ee"},"schema_version":"1.0","source":{"id":"1902.09758","kind":"arxiv","version":1}},"canonical_sha256":"6e750fd294c6b3d334a13bb3f708b8c899c798e19d1a50e471d4ae20649d613a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e750fd294c6b3d334a13bb3f708b8c899c798e19d1a50e471d4ae20649d613a","first_computed_at":"2026-05-17T23:52:35.443986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:35.443986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9gRrt/rPiB/BdSnu4SR5CPt9plycJd2JJD3r+2HAaEe7KT+kB5kNd+NuwgYY8C5dcgJaHLJiuaeV/ANDYecBCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:35.444622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d39ecdcbc2ff69aa045c8ecdb87d571b487751ae294e73d05ae5acc11ef9b7c","sha256:74a9b5ad1f805eda94a5319cba10dbca5501b6795c52bfb51a0eea768894092e"],"state_sha256":"8477aa2d75a1fa34944a94e9bbe5fff8637a3c9f3f2e16b3ddf4d8cfcd7415d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7o7u9SSfycLRqJOvFsx+ZSgSCVLfFjidJJ2cqUrNdZKhu4u12YzbrX3UuGtI1O0xJQmvHlwaYgrFNsz9oxbbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:19:44.789886Z","bundle_sha256":"14bd6e8dc6ba5d7134b988d9545a5c8f79343efc3484bd9da99dcc7591a31ab5"}}