{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SX5AANXV6LQ7QYHSB5EYHVNFPS","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":"545d34b5951638bb41a95d79acebe9a41d552c2b54fe5798daefb3d4a56273df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-22T20:31:58Z","title_canon_sha256":"1a83585f2548a0d422d6dfed864ba6eef1b9352438965ef047cf3c5d7fc08143"},"schema_version":"1.0","source":{"id":"1507.06335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06335","created_at":"2026-05-18T01:36:25Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06335v1","created_at":"2026-05-18T01:36:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06335","created_at":"2026-05-18T01:36:25Z"},{"alias_kind":"pith_short_12","alias_value":"SX5AANXV6LQ7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SX5AANXV6LQ7QYHS","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SX5AANXV","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:403bfd887536f869d1576336b299e0dd8a4b8be91a9aeef41320f406f565aaef","target":"graph","created_at":"2026-05-18T01:36:25Z","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":"We generalize Wonham's theorem on solvability of algebraic operator Riccati equations to Banach spaces, namely there is a unique stabilizing solution to A*P+PA-PBB*P+C*C=0 when (A,B) is exponentially stabilizable and (C,A) is exponentially detectable. The proof is based on a new approach that treats the linear part of the equation as the generator of a positive semigroup on the space of symmetric operators from a Banach space to its dual, and the quadratic part as an order concave map. A direct analog of global Newton's iteration for concave functions is then used to approximate the solution, ","authors_text":"Sergiy Koshkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-22T20:31:58Z","title":"Positive semigroups and algebraic Riccati equations in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06335","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":"sha256:0167d6139952593a1b69bf2cc6a46730aa488f02878507dc0841834f5527c889","target":"record","created_at":"2026-05-18T01:36:25Z","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":"545d34b5951638bb41a95d79acebe9a41d552c2b54fe5798daefb3d4a56273df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-22T20:31:58Z","title_canon_sha256":"1a83585f2548a0d422d6dfed864ba6eef1b9352438965ef047cf3c5d7fc08143"},"schema_version":"1.0","source":{"id":"1507.06335","kind":"arxiv","version":1}},"canonical_sha256":"95fa0036f5f2e1f860f20f4983d5a57cbc980368394d5ed8923c7108715ee124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95fa0036f5f2e1f860f20f4983d5a57cbc980368394d5ed8923c7108715ee124","first_computed_at":"2026-05-18T01:36:25.220448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:25.220448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/EwsF/Tj5eVJrZcRvvg7stKvpoqg3N3Nfhf++G24mIspGaIBxtUl7tuPe0eICVZcD4GoJWPwakwvarhDUzcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:25.221013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0167d6139952593a1b69bf2cc6a46730aa488f02878507dc0841834f5527c889","sha256:403bfd887536f869d1576336b299e0dd8a4b8be91a9aeef41320f406f565aaef"],"state_sha256":"8c3401cb94ed20f5285af8c6fb33bf3321055e6b7883c6b97a9d61b6016d91ff"}