{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DNKA7EKNOI6ADAIHZ67QQ2RSUM","short_pith_number":"pith:DNKA7EKN","schema_version":"1.0","canonical_sha256":"1b540f914d723c018107cfbf086a32a31d5c016185e7a8531c35d01cbcb4688c","source":{"kind":"arxiv","id":"1202.4043","version":4},"attestation_state":"computed","paper":{"title":"On the connection of facially exposed and nice cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabor Pataki","submitted_at":"2012-02-18T00:21:09Z","abstract_excerpt":"A closed convex cone K is called nice, if the set K^* + F^\\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\\perp is the orthogonal complement of the linear span of F. The niceness property is important for two reasons: it plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer.\n  We prove several characterizations of nice cones and show a strong connection with facial exposedness. We prove that a nice cone must be facially exposed; in reverse, facial exposedn"},"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":"1202.4043","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-18T00:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"6f7c1c50a59c2e07262b4ced1171e937e5065220775afead6ff91df9a971364e","abstract_canon_sha256":"bd2ccaa1abfea10ffe0f29fdb8ab1be55739b256bca8680f063e01e2ec4c913a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:01.252227Z","signature_b64":"8c76dDTvY7li/MMHbuvU2clegwLe7f9SXPkp+mNVxmPoynlnM1/MdciDZs3HbSRwkFwS6cIucniYwG6q5Lm8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b540f914d723c018107cfbf086a32a31d5c016185e7a8531c35d01cbcb4688c","last_reissued_at":"2026-05-18T03:41:01.251505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:01.251505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the connection of facially exposed and nice cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabor Pataki","submitted_at":"2012-02-18T00:21:09Z","abstract_excerpt":"A closed convex cone K is called nice, if the set K^* + F^\\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\\perp is the orthogonal complement of the linear span of F. The niceness property is important for two reasons: it plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer.\n  We prove several characterizations of nice cones and show a strong connection with facial exposedness. We prove that a nice cone must be facially exposed; in reverse, facial exposedn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4043","kind":"arxiv","version":4},"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":"1202.4043","created_at":"2026-05-18T03:41:01.251599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4043v4","created_at":"2026-05-18T03:41:01.251599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4043","created_at":"2026-05-18T03:41:01.251599+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNKA7EKNOI6A","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNKA7EKNOI6ADAIH","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNKA7EKN","created_at":"2026-05-18T12:27:04.183437+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/DNKA7EKNOI6ADAIHZ67QQ2RSUM","json":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM.json","graph_json":"https://pith.science/api/pith-number/DNKA7EKNOI6ADAIHZ67QQ2RSUM/graph.json","events_json":"https://pith.science/api/pith-number/DNKA7EKNOI6ADAIHZ67QQ2RSUM/events.json","paper":"https://pith.science/paper/DNKA7EKN"},"agent_actions":{"view_html":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM","download_json":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM.json","view_paper":"https://pith.science/paper/DNKA7EKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4043&json=true","fetch_graph":"https://pith.science/api/pith-number/DNKA7EKNOI6ADAIHZ67QQ2RSUM/graph.json","fetch_events":"https://pith.science/api/pith-number/DNKA7EKNOI6ADAIHZ67QQ2RSUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM/action/storage_attestation","attest_author":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM/action/author_attestation","sign_citation":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM/action/citation_signature","submit_replication":"https://pith.science/pith/DNKA7EKNOI6ADAIHZ67QQ2RSUM/action/replication_record"}},"created_at":"2026-05-18T03:41:01.251599+00:00","updated_at":"2026-05-18T03:41:01.251599+00:00"}