{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7BN2BJ3DMEEYGJ5Z6H42VOTAYY","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":"1f5edda2a4ef6fbe9a009590f9ad6a6230226397ef7b2bc2b734ed3f0ec01386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-05T19:09:03Z","title_canon_sha256":"011511be454b1d4cd7dfb1c4e3a107be33ad7ce9ccb4b9acc3ab363c207012aa"},"schema_version":"1.0","source":{"id":"1309.1446","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1446","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1446v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1446","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"7BN2BJ3DMEEY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7BN2BJ3DMEEYGJ5Z","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7BN2BJ3D","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:c9c053b7b7add7884b7a0989cab5b8f53e1b73f15a51f607d5f13d1877a654a7","target":"graph","created_at":"2026-05-18T02:30:47Z","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 show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.","authors_text":"A.D. Ioffe, D. Drusvyatskiy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-05T19:09:03Z","title":"Quadratic growth and critical point stability of semi-algebraic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1446","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":"sha256:7d73fd695c002770d63a74e8866721cab3cc59d5b5f1dd98479d231ba2876efa","target":"record","created_at":"2026-05-18T02:30:47Z","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":"1f5edda2a4ef6fbe9a009590f9ad6a6230226397ef7b2bc2b734ed3f0ec01386","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-05T19:09:03Z","title_canon_sha256":"011511be454b1d4cd7dfb1c4e3a107be33ad7ce9ccb4b9acc3ab363c207012aa"},"schema_version":"1.0","source":{"id":"1309.1446","kind":"arxiv","version":2}},"canonical_sha256":"f85ba0a76361098327b9f1f9aaba60c609abdbd89ebccc05ddc9094295febf99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f85ba0a76361098327b9f1f9aaba60c609abdbd89ebccc05ddc9094295febf99","first_computed_at":"2026-05-18T02:30:47.661922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:47.661922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3FLhsVteqhgWBiFySa4oco0uazyzSz4OJDa5/oExWSa8fIvFrTwICCXJw0K/3e0WPTqZzIDv5gVPk8aGZMnmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:47.662380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1446","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d73fd695c002770d63a74e8866721cab3cc59d5b5f1dd98479d231ba2876efa","sha256:c9c053b7b7add7884b7a0989cab5b8f53e1b73f15a51f607d5f13d1877a654a7"],"state_sha256":"1600269b8e562ea4c49e7f45da225b1eef8e84f1462c73f65e9a3f0f1f489d8e"}