{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XBSFHIMFSOG5PFNF27ERBQHLLP","short_pith_number":"pith:XBSFHIMF","schema_version":"1.0","canonical_sha256":"b86453a185938dd795a5d7c910c0eb5bdda0368e3935dad66609ae4029c5cfe8","source":{"kind":"arxiv","id":"2402.09831","version":2},"attestation_state":"computed","paper":{"title":"A note on stationarity in constrained optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Edouard Pauwels (TSE-R)","submitted_at":"2024-02-15T09:48:59Z","abstract_excerpt":"Minimizing a smooth function f on a closed subset C leads to different notions of stationarity: Fr{\\'e}chet stationarity, which carries a strong variational meaning, and criticality, which is defined through a closure process and involves the notion of limiting, or Mordukovitch, subdifferential. The latter is an optimality condition which may loose the variational meaning of Fr{\\'e}chet stationarity in some settings. The purpose of this note is to illustrate that, while criticality is the appropriate notion in full generality, Fr{\\'e}chet stationarity is typical in practical scenarios.We gathe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2402.09831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:48:59Z","cross_cats_sorted":[],"title_canon_sha256":"cad1bc133e89a27ec8f64c6303c8311ad0be10441cc75131af99819f2f189545","abstract_canon_sha256":"e01da34252bd806bd37d2b8ca8895481646c854656a00b04b23f7cdec724809a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:08.045938Z","signature_b64":"in/ESkYqqIi8QlHWiZTTHayAfNB3kzNA14ocWzyRA/yRJJkQAPsEJW3ALK3ti4L8dxYq5y93Oae2MFG+Ytw6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b86453a185938dd795a5d7c910c0eb5bdda0368e3935dad66609ae4029c5cfe8","last_reissued_at":"2026-07-05T09:30:08.045429Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:08.045429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on stationarity in constrained optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Edouard Pauwels (TSE-R)","submitted_at":"2024-02-15T09:48:59Z","abstract_excerpt":"Minimizing a smooth function f on a closed subset C leads to different notions of stationarity: Fr{\\'e}chet stationarity, which carries a strong variational meaning, and criticality, which is defined through a closure process and involves the notion of limiting, or Mordukovitch, subdifferential. The latter is an optimality condition which may loose the variational meaning of Fr{\\'e}chet stationarity in some settings. The purpose of this note is to illustrate that, while criticality is the appropriate notion in full generality, Fr{\\'e}chet stationarity is typical in practical scenarios.We gathe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09831","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.09831/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.09831","created_at":"2026-07-05T09:30:08.045486+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.09831v2","created_at":"2026-07-05T09:30:08.045486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.09831","created_at":"2026-07-05T09:30:08.045486+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBSFHIMFSOG5","created_at":"2026-07-05T09:30:08.045486+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBSFHIMFSOG5PFNF","created_at":"2026-07-05T09:30:08.045486+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBSFHIMF","created_at":"2026-07-05T09:30:08.045486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP","json":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP.json","graph_json":"https://pith.science/api/pith-number/XBSFHIMFSOG5PFNF27ERBQHLLP/graph.json","events_json":"https://pith.science/api/pith-number/XBSFHIMFSOG5PFNF27ERBQHLLP/events.json","paper":"https://pith.science/paper/XBSFHIMF"},"agent_actions":{"view_html":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP","download_json":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP.json","view_paper":"https://pith.science/paper/XBSFHIMF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.09831&json=true","fetch_graph":"https://pith.science/api/pith-number/XBSFHIMFSOG5PFNF27ERBQHLLP/graph.json","fetch_events":"https://pith.science/api/pith-number/XBSFHIMFSOG5PFNF27ERBQHLLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP/action/storage_attestation","attest_author":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP/action/author_attestation","sign_citation":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP/action/citation_signature","submit_replication":"https://pith.science/pith/XBSFHIMFSOG5PFNF27ERBQHLLP/action/replication_record"}},"created_at":"2026-07-05T09:30:08.045486+00:00","updated_at":"2026-07-05T09:30:08.045486+00:00"}