{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HZQE22UW4GCXI5ZKE75NDDPHST","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":"94a2eb14f39642464064195fb417b913dd233b12c84ed91004211aab5359f2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T10:37:49Z","title_canon_sha256":"c705602caf77f79527f816077cb94cac703da94bc1b1fd5a3c80dbd6db2d0de2"},"schema_version":"1.0","source":{"id":"1309.1304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1304","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1304v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1304","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"HZQE22UW4GCX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HZQE22UW4GCXI5ZK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HZQE22UW","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:9bfea3616346c6c24117d21893e9b30fa7664feef2c55b2154455366c39c6745","target":"graph","created_at":"2026-05-18T03:14:07Z","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":"In the present article we provide a sufficient condition for a closed set F in R^d to have the following property which we call c-removability: Whenever a function f:R^d->R is locally convex on the complement of F, it is convex on the whole R^d. We also prove that no generalized rectangle of positive Lebesgue measure in R^2 is c-removable. Our results also answer the following question asked in an article by Jacek Tabor and Jozef Tabor [J. Math. Anal. Appl. 365 (2010)]: Assume the closed set F in R^d is such that any locally convex function defined on R^d\\F has a unique convex extension on R^d","authors_text":"Dusan Pokorny, Martin Rmoutil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T10:37:49Z","title":"On Removable Sets For Convex Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1304","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":"sha256:2a9658f9d8179d4ba0b4c3f3ddc2569c263441e06d2eddd901fe7e13b266ecc6","target":"record","created_at":"2026-05-18T03:14:07Z","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":"94a2eb14f39642464064195fb417b913dd233b12c84ed91004211aab5359f2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T10:37:49Z","title_canon_sha256":"c705602caf77f79527f816077cb94cac703da94bc1b1fd5a3c80dbd6db2d0de2"},"schema_version":"1.0","source":{"id":"1309.1304","kind":"arxiv","version":1}},"canonical_sha256":"3e604d6a96e18574772a27fad18de794d967d89e58609d231180478adb96975e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e604d6a96e18574772a27fad18de794d967d89e58609d231180478adb96975e","first_computed_at":"2026-05-18T03:14:07.669582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.669582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZyxZeMspNwVRF+fPjKvs9/29bHK3VXhMyCPzCcZ+yHTEq46Wisr9QgPE9Owl+BrqWeVzraukPyIzytme0NrmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.669974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a9658f9d8179d4ba0b4c3f3ddc2569c263441e06d2eddd901fe7e13b266ecc6","sha256:9bfea3616346c6c24117d21893e9b30fa7664feef2c55b2154455366c39c6745"],"state_sha256":"0a6bc7f7aec8a8a419c7ba3bf23219ffb98087b19519a02da0f0944a41452742"}