{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WS3IHKVEPBUZLN22AEQYJN7ZSM","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":"a0bc6a5763610aaaa423fdca5c3f354cab9aff4d4a307e01fe5471346c23134c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-13T18:40:14Z","title_canon_sha256":"d9c30cc844c8270e6e4041f57169daee744a8331c88339908e69a5d2d87279b3"},"schema_version":"1.0","source":{"id":"1806.05215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05215","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05215v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05215","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"WS3IHKVEPBUZ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WS3IHKVEPBUZLN22","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WS3IHKVE","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:9c3a6bcc2acd9ff4481b8e692deb3fe44aff0e73d5786f2177a4d9ad90198908","target":"graph","created_at":"2026-05-18T00:13:16Z","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":"Recently it has been found that for a stochastic linear-quadratic optimal control problem (LQ problem, for short) in a finite horizon, open-loop solvability is strictly weaker than closed-loop solvability which is equivalent to the regular solvability of the corresponding Riccati equation. Therefore, when an LQ problem is merely open-loop solvable not closed-loop solvable, which is possible, the usual Riccati equation approach will fail to produce a state feedback representation of open-loop optimal controls. The objective of this paper is to introduce and investigate the notion of weak closed","authors_text":"Hanxiao Wang, Jingrui Sun, Jiongmin Yong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-13T18:40:14Z","title":"Weak Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05215","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:a3d59988296fcc3d95adcbcd6d67d3d442129619f216ff1aeb9ad06ff6eb65c1","target":"record","created_at":"2026-05-18T00:13:16Z","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":"a0bc6a5763610aaaa423fdca5c3f354cab9aff4d4a307e01fe5471346c23134c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-13T18:40:14Z","title_canon_sha256":"d9c30cc844c8270e6e4041f57169daee744a8331c88339908e69a5d2d87279b3"},"schema_version":"1.0","source":{"id":"1806.05215","kind":"arxiv","version":1}},"canonical_sha256":"b4b683aaa4786995b75a012184b7f99328425a7fbd83c2b9aa7a277b505dbad6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4b683aaa4786995b75a012184b7f99328425a7fbd83c2b9aa7a277b505dbad6","first_computed_at":"2026-05-18T00:13:16.804091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:16.804091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKyxWKM496CS/ljusiJOK31AyR98zmS3/mOvYvfRadm/eqZC6dnybasboJIEzyYxIc339mIpcrRIWM4sXQRcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:16.804798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3d59988296fcc3d95adcbcd6d67d3d442129619f216ff1aeb9ad06ff6eb65c1","sha256:9c3a6bcc2acd9ff4481b8e692deb3fe44aff0e73d5786f2177a4d9ad90198908"],"state_sha256":"3986d63f191748cdda4330162256cd753ec637fd789a2d75abfe5f9ea8c7b618"}