{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HPYPUUNVJUFZ5GGL3YSTQZAEBA","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":"748375b01fd4995cbdc614fb2dd9ad62f5d304847f866d8668ef255d5f857d76","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T19:47:28Z","title_canon_sha256":"05dad56e2b9b1dd286a383df83dbff6874efacda45238a0a6b17ea21854e9e11"},"schema_version":"1.0","source":{"id":"1411.1719","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1719","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1719v3","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1719","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"HPYPUUNVJUFZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HPYPUUNVJUFZ5GGL","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HPYPUUNV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:f6510a9cf50cd283baa0b4708abcd3e35fd577545f7333a9748b91ef683403ba","target":"graph","created_at":"2026-05-17T23:56:30Z","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":"In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.","authors_text":"Bean San Goh, Fr\\'ed\\'eric Bonnans, M. Soledad Aronna","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T19:47:28Z","title":"Second order analysis of control-affine problems with scalar state constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1719","kind":"arxiv","version":3},"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":"sha256:63cbb8782318d90a55f088ebaffab27ba29b7b34196390fd3eefd3b2107e45ee","target":"record","created_at":"2026-05-17T23:56:30Z","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":"748375b01fd4995cbdc614fb2dd9ad62f5d304847f866d8668ef255d5f857d76","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T19:47:28Z","title_canon_sha256":"05dad56e2b9b1dd286a383df83dbff6874efacda45238a0a6b17ea21854e9e11"},"schema_version":"1.0","source":{"id":"1411.1719","kind":"arxiv","version":3}},"canonical_sha256":"3bf0fa51b54d0b9e98cbde25386404080cb62852cb1232d81ee080d8f23a99ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf0fa51b54d0b9e98cbde25386404080cb62852cb1232d81ee080d8f23a99ac","first_computed_at":"2026-05-17T23:56:30.546003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.546003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v7Ha213FA6qmOltMsMIMvd9g2Z6nWhzbpQWBSZTJD2s99dMdzawOQG16gGDrrU3FZSMq6wTU6cVRaVgr0njTDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.546395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1719","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63cbb8782318d90a55f088ebaffab27ba29b7b34196390fd3eefd3b2107e45ee","sha256:f6510a9cf50cd283baa0b4708abcd3e35fd577545f7333a9748b91ef683403ba"],"state_sha256":"556568bfb6782c3529a06b9b0a232dc15b0de6b3409dc8da0143964c313f264b"}