{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MJD4OZRYWBKH3WNHJYVQNHHU7M","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":"6de2dd02c8933f1389d4581db546f510230b3556cf4956bc0de4136a99bd13c4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-16T23:33:47Z","title_canon_sha256":"6f4b3d80cf0c24e4bb4936f868af92fc37946299da7a47035058728430310efb"},"schema_version":"1.0","source":{"id":"2507.12682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12682","created_at":"2026-07-05T11:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12682v1","created_at":"2026-07-05T11:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12682","created_at":"2026-07-05T11:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"MJD4OZRYWBKH","created_at":"2026-07-05T11:38:37Z"},{"alias_kind":"pith_short_16","alias_value":"MJD4OZRYWBKH3WNH","created_at":"2026-07-05T11:38:37Z"},{"alias_kind":"pith_short_8","alias_value":"MJD4OZRY","created_at":"2026-07-05T11:38:37Z"}],"graph_snapshots":[{"event_id":"sha256:886858c05f04d1e53d2b892922e1159d8f12c0416a5df3529f4f3ed46c575e23","target":"graph","created_at":"2026-07-05T11:38:37Z","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/2507.12682/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficien","authors_text":"Binbin Zhang, Jane Ye, Wei Ouyang, Xiaoxiao Ma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-16T23:33:47Z","title":"On second-order weak sharp minima of general nonconvex set-constrained optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12682","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:c7bb24b2d2184d21c63d7293d0cea9e1b8b0550be17c2fc6d15215ed6c1075df","target":"record","created_at":"2026-07-05T11:38:37Z","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":"6de2dd02c8933f1389d4581db546f510230b3556cf4956bc0de4136a99bd13c4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-16T23:33:47Z","title_canon_sha256":"6f4b3d80cf0c24e4bb4936f868af92fc37946299da7a47035058728430310efb"},"schema_version":"1.0","source":{"id":"2507.12682","kind":"arxiv","version":1}},"canonical_sha256":"6247c76638b0547dd9a74e2b069cf4fb3e15366dd1ac6df297f0a611070c55db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6247c76638b0547dd9a74e2b069cf4fb3e15366dd1ac6df297f0a611070c55db","first_computed_at":"2026-07-05T11:38:37.236495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:37.236495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ASb6dpvcQ6fH7pPl1RYZsMpil5+5AGWvcCmzl4B6iIBxkEv2/xUD+q55DCL6J0xWk5eS3EryNFLZ78+pIs68CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:37.236917Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7bb24b2d2184d21c63d7293d0cea9e1b8b0550be17c2fc6d15215ed6c1075df","sha256:886858c05f04d1e53d2b892922e1159d8f12c0416a5df3529f4f3ed46c575e23"],"state_sha256":"27b34558dd9e290193e66ef6e896e628af3be5dda1f01e66f502fdf7af9c5b87"}