{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LP6USHRFVEOQOATLUIS2KGHJGX","short_pith_number":"pith:LP6USHRF","schema_version":"1.0","canonical_sha256":"5bfd491e25a91d07026ba225a518e935ef2093e88d2ceaa5c432e6dca767a5cb","source":{"kind":"arxiv","id":"1608.03360","version":1},"attestation_state":"computed","paper":{"title":"On Error Bound Moduli for Locally Lipschitz and Regular Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaiwen Meng, Minghua Li, Xiaoqi Yang","submitted_at":"2016-08-11T03:49:43Z","abstract_excerpt":"In this paper we study local error bound moduli for a locally Lipschitz and regular function via its outer limiting subdifferential set. We show that the distance of 0 from the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance of 0 from the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance of 0 from the outer limiting subdifferential set of a lower $\\mathcal{C}^1$ function "},"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":"1608.03360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-11T03:49:43Z","cross_cats_sorted":[],"title_canon_sha256":"24b78066cd5c50e844eb2dc6752d06da499c59a3907f79f727c4f7a58852361a","abstract_canon_sha256":"d97249f98b9923c5b3d866fa1113e28179244b897f874048c3b812e5bd447b36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:29.073344Z","signature_b64":"ZWPFHcPN/kUvquEljXu13A8r+n78Lq9yFl2hlnpV7spAvgzunb2p/WL4YJD6wL3VFQFu/F/gK27kSYf4vUN+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bfd491e25a91d07026ba225a518e935ef2093e88d2ceaa5c432e6dca767a5cb","last_reissued_at":"2026-05-18T01:09:29.072907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:29.072907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Error Bound Moduli for Locally Lipschitz and Regular Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaiwen Meng, Minghua Li, Xiaoqi Yang","submitted_at":"2016-08-11T03:49:43Z","abstract_excerpt":"In this paper we study local error bound moduli for a locally Lipschitz and regular function via its outer limiting subdifferential set. We show that the distance of 0 from the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance of 0 from the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance of 0 from the outer limiting subdifferential set of a lower $\\mathcal{C}^1$ function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03360","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1608.03360","created_at":"2026-05-18T01:09:29.072982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03360v1","created_at":"2026-05-18T01:09:29.072982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03360","created_at":"2026-05-18T01:09:29.072982+00:00"},{"alias_kind":"pith_short_12","alias_value":"LP6USHRFVEOQ","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LP6USHRFVEOQOATL","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LP6USHRF","created_at":"2026-05-18T12:30:29.479603+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/LP6USHRFVEOQOATLUIS2KGHJGX","json":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX.json","graph_json":"https://pith.science/api/pith-number/LP6USHRFVEOQOATLUIS2KGHJGX/graph.json","events_json":"https://pith.science/api/pith-number/LP6USHRFVEOQOATLUIS2KGHJGX/events.json","paper":"https://pith.science/paper/LP6USHRF"},"agent_actions":{"view_html":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX","download_json":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX.json","view_paper":"https://pith.science/paper/LP6USHRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03360&json=true","fetch_graph":"https://pith.science/api/pith-number/LP6USHRFVEOQOATLUIS2KGHJGX/graph.json","fetch_events":"https://pith.science/api/pith-number/LP6USHRFVEOQOATLUIS2KGHJGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX/action/storage_attestation","attest_author":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX/action/author_attestation","sign_citation":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX/action/citation_signature","submit_replication":"https://pith.science/pith/LP6USHRFVEOQOATLUIS2KGHJGX/action/replication_record"}},"created_at":"2026-05-18T01:09:29.072982+00:00","updated_at":"2026-05-18T01:09:29.072982+00:00"}