{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VE7P254BASJF5O6NOGNDU5GTNO","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":"ed0cdf4475e2c1789aaf6e928c85346622d87388cf88101699e925d65af65ee7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-26T20:53:36Z","title_canon_sha256":"4b1f6c688c0dfa31df3e03eef8dfdb676afccf8980429cfe6e22ad8ea3e9fc42"},"schema_version":"1.0","source":{"id":"2404.17696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.17696","created_at":"2026-07-05T10:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"2404.17696v2","created_at":"2026-07-05T10:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.17696","created_at":"2026-07-05T10:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"VE7P254BASJF","created_at":"2026-07-05T10:22:45Z"},{"alias_kind":"pith_short_16","alias_value":"VE7P254BASJF5O6N","created_at":"2026-07-05T10:22:45Z"},{"alias_kind":"pith_short_8","alias_value":"VE7P254B","created_at":"2026-07-05T10:22:45Z"}],"graph_snapshots":[{"event_id":"sha256:09650426a0c4ab6cd4877af9579ceb6b45eb31df1d2816eb9f78767fd11372e3","target":"graph","created_at":"2026-07-05T10:22:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.17696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a directional neighborhood) in pursuit of developing these new optimality conditions. First-order necessary conditions for local optimality in given directions are provided by virtue of the corresponding directional normal cones. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions for l","authors_text":"Binbin Zhang, Jane Ye, Wei Ouyang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-26T20:53:36Z","title":"New second-order optimality conditions for directional optimality of a general set-constrained optimization problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.17696","kind":"arxiv","version":2},"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:d2d4c36f79aa5810d6eaddf754bdb3b44ce9a5be8fb59536fd88077701a7590b","target":"record","created_at":"2026-07-05T10:22:45Z","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":"ed0cdf4475e2c1789aaf6e928c85346622d87388cf88101699e925d65af65ee7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-26T20:53:36Z","title_canon_sha256":"4b1f6c688c0dfa31df3e03eef8dfdb676afccf8980429cfe6e22ad8ea3e9fc42"},"schema_version":"1.0","source":{"id":"2404.17696","kind":"arxiv","version":2}},"canonical_sha256":"a93efd778104925ebbcd719a3a74d36b8a215e2d50fe3b937ad55f799b220439","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a93efd778104925ebbcd719a3a74d36b8a215e2d50fe3b937ad55f799b220439","first_computed_at":"2026-07-05T10:22:45.740842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:22:45.740842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"horm8dYzLEC/VoIUtrzvzU7q3Pqv5QI1YF/kg2eMpqKAPfcvsEEm+vwdAA8bhsKK2EeiDSxJkU+/ap0qxY6RBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:22:45.741842Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.17696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2d4c36f79aa5810d6eaddf754bdb3b44ce9a5be8fb59536fd88077701a7590b","sha256:09650426a0c4ab6cd4877af9579ceb6b45eb31df1d2816eb9f78767fd11372e3"],"state_sha256":"f97c9599810f3fe89bb4b7f168fe9f46d5a233a828de8445db1570284fc4f2f6"}