{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NQT4B4UQFTH6BN55UV3R7QOLIE","short_pith_number":"pith:NQT4B4UQ","canonical_record":{"source":{"id":"1203.1774","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T12:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"31edbc61e3e8e3914dafd11c180b98e23194b5b90a1f3c6515310204abb7fc67","abstract_canon_sha256":"1fe925d7151acb3e8a6f2baadc4bcc2a2a290ede7759ac582598b06b76e9cc9e"},"schema_version":"1.0"},"canonical_sha256":"6c27c0f2902ccfe0b7bda5771fc1cb410e0892bd0c7d96bc93401f242c759159","source":{"kind":"arxiv","id":"1203.1774","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1774","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1774v5","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1774","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"NQT4B4UQFTH6","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NQT4B4UQFTH6BN55","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NQT4B4UQ","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NQT4B4UQFTH6BN55UV3R7QOLIE","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1774","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T12:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"31edbc61e3e8e3914dafd11c180b98e23194b5b90a1f3c6515310204abb7fc67","abstract_canon_sha256":"1fe925d7151acb3e8a6f2baadc4bcc2a2a290ede7759ac582598b06b76e9cc9e"},"schema_version":"1.0"},"canonical_sha256":"6c27c0f2902ccfe0b7bda5771fc1cb410e0892bd0c7d96bc93401f242c759159","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.481308Z","signature_b64":"50NoZh6fZsIrx95wGw7n1/btR6ajvDnQSZaF7Ax9BrJ8yib5BTlYRaXEwumeJZxmZ66nq7kvMcDMQUSC+E+iAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c27c0f2902ccfe0b7bda5771fc1cb410e0892bd0c7d96bc93401f242c759159","last_reissued_at":"2026-05-18T02:28:55.480784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.480784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1774","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkdEnoZjJjz5m5fwmpnWwjpDoua4SPZgj4g3YODQBexyN0ataptNjW7m69O7DatV/+JY41+dRSKDLy9fquWACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:56:24.368376Z"},"content_sha256":"047c651c82409a17901123641bf3a3af724dc6675c14cf41166fd820623a51b0","schema_version":"1.0","event_id":"sha256:047c651c82409a17901123641bf3a3af724dc6675c14cf41166fd820623a51b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NQT4B4UQFTH6BN55UV3R7QOLIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jianhui Huang, Liangquan Zhang, Xun Li","submitted_at":"2012-03-08T12:34:57Z","abstract_excerpt":"This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex. In the previous work (Theorem 3.1) of the second and third authors [\\textit{% Automatica} \\textbf{46} (2010) 397-404], some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it. The necessary condition of the near"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1774","kind":"arxiv","version":5},"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":"2026-05-18T02:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSUkb+Z/N7ycteOONJb37lAVtEL2Y1jwqzanWMZq4wcCGmXtAE3tWQzMArIZQdKZvcx2VygXkRKgx6IvMUzgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:56:24.369016Z"},"content_sha256":"27fb363ee4b142556b62754d9ff1d3a063d22c628ad7f2730806a530e8db5ceb","schema_version":"1.0","event_id":"sha256:27fb363ee4b142556b62754d9ff1d3a063d22c628ad7f2730806a530e8db5ceb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/bundle.json","state_url":"https://pith.science/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/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":"2026-05-27T00:56:24Z","links":{"resolver":"https://pith.science/pith/NQT4B4UQFTH6BN55UV3R7QOLIE","bundle":"https://pith.science/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/bundle.json","state":"https://pith.science/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQT4B4UQFTH6BN55UV3R7QOLIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NQT4B4UQFTH6BN55UV3R7QOLIE","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":"1fe925d7151acb3e8a6f2baadc4bcc2a2a290ede7759ac582598b06b76e9cc9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T12:34:57Z","title_canon_sha256":"31edbc61e3e8e3914dafd11c180b98e23194b5b90a1f3c6515310204abb7fc67"},"schema_version":"1.0","source":{"id":"1203.1774","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1774","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1774v5","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1774","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"NQT4B4UQFTH6","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NQT4B4UQFTH6BN55","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NQT4B4UQ","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:27fb363ee4b142556b62754d9ff1d3a063d22c628ad7f2730806a530e8db5ceb","target":"graph","created_at":"2026-05-18T02:28:55Z","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 investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex. In the previous work (Theorem 3.1) of the second and third authors [\\textit{% Automatica} \\textbf{46} (2010) 397-404], some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it. The necessary condition of the near","authors_text":"Jianhui Huang, Liangquan Zhang, Xun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T12:34:57Z","title":"Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1774","kind":"arxiv","version":5},"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":"sha256:047c651c82409a17901123641bf3a3af724dc6675c14cf41166fd820623a51b0","target":"record","created_at":"2026-05-18T02:28:55Z","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":"1fe925d7151acb3e8a6f2baadc4bcc2a2a290ede7759ac582598b06b76e9cc9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T12:34:57Z","title_canon_sha256":"31edbc61e3e8e3914dafd11c180b98e23194b5b90a1f3c6515310204abb7fc67"},"schema_version":"1.0","source":{"id":"1203.1774","kind":"arxiv","version":5}},"canonical_sha256":"6c27c0f2902ccfe0b7bda5771fc1cb410e0892bd0c7d96bc93401f242c759159","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c27c0f2902ccfe0b7bda5771fc1cb410e0892bd0c7d96bc93401f242c759159","first_computed_at":"2026-05-18T02:28:55.480784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:55.480784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"50NoZh6fZsIrx95wGw7n1/btR6ajvDnQSZaF7Ax9BrJ8yib5BTlYRaXEwumeJZxmZ66nq7kvMcDMQUSC+E+iAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:55.481308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1774","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:047c651c82409a17901123641bf3a3af724dc6675c14cf41166fd820623a51b0","sha256:27fb363ee4b142556b62754d9ff1d3a063d22c628ad7f2730806a530e8db5ceb"],"state_sha256":"e081814fabc158e763c693d88bed1f8e9f04553db657be9b2841a599fdbb59ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4G1lUww7POG9yK8zx5cqiBeB0eJEHHLUpUIzxq/FbuDPAm1XL5NvdFpIQBeMQghH7j3pfB0y/EsIWhKjARi/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:56:24.372225Z","bundle_sha256":"2e121be8ba9207c8e786c7ade534f30b3ddc5852ca8ba65f0f0e1d03cb19302d"}}