{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:26L7TEVMIPWX7FR2SJYPM4PAP3","short_pith_number":"pith:26L7TEVM","canonical_record":{"source":{"id":"1704.06368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-21T00:06:08Z","cross_cats_sorted":[],"title_canon_sha256":"8db7dcdf2cbb5b6514af51b71f0d8c96e5df03f6c452474beb87f06402a6bd99","abstract_canon_sha256":"92e2cd181da0ea9e768855cc84877d88e2be997dcaa6595f57c75c80286d3d90"},"schema_version":"1.0"},"canonical_sha256":"d797f992ac43ed7f963a9270f671e07ef56cf566c080133c7647adce9d5c95dd","source":{"kind":"arxiv","id":"1704.06368","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06368","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06368v2","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06368","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"26L7TEVMIPWX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"26L7TEVMIPWX7FR2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"26L7TEVM","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:26L7TEVMIPWX7FR2SJYPM4PAP3","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-21T00:06:08Z","cross_cats_sorted":[],"title_canon_sha256":"8db7dcdf2cbb5b6514af51b71f0d8c96e5df03f6c452474beb87f06402a6bd99","abstract_canon_sha256":"92e2cd181da0ea9e768855cc84877d88e2be997dcaa6595f57c75c80286d3d90"},"schema_version":"1.0"},"canonical_sha256":"d797f992ac43ed7f963a9270f671e07ef56cf566c080133c7647adce9d5c95dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:29.507092Z","signature_b64":"4fFk7RWTCmRBb2Na1baTJuZ09CsuUjYO3v9XI42aVZVpAvcITg8UezdXPF9YrdrTZhnF/NM4V52KSgT88CQtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d797f992ac43ed7f963a9270f671e07ef56cf566c080133c7647adce9d5c95dd","last_reissued_at":"2026-05-17T23:52:29.506486Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:29.506486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06368","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DXybI5gC3X5mLvCJ45W4DUCZ37+CkUEimoDenVFM61bKH8e+/I0IasUxrPWHstVuDP6uF1rnw3IkoFhNB9EYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:09:55.828087Z"},"content_sha256":"5e27c916cf87bc411e251bcd74523723d0e6730c507cf999729312935fc37c05","schema_version":"1.0","event_id":"sha256:5e27c916cf87bc411e251bcd74523723d0e6730c507cf999729312935fc37c05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:26L7TEVMIPWX7FR2SJYPM4PAP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Facially Dual Complete (Nice) cones and lexicographic tangents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Levent Tun\\c{c}el, Vera Roshchina","submitted_at":"2017-04-21T00:06:08Z","abstract_excerpt":"We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the well-known and commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of faces of convex sets. Based on these new notions, we obtain a necessary condition and a sufficient condition for a cone to be facially dual complete. In our sufficient condition, we utilize a new notion calle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06368","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j19TwrHRom+2k5aC7z50Lw3HpTn2K3QiAbeSM8fIt/b3MoqGn7P13N4J5wuAm3idOiUjMP8ACe1+sVM8bF/kBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:09:55.828448Z"},"content_sha256":"8ff122f78179ba9c0c6161de6d94443cb7ead3f35bba1609ae306dfe68dbc2b4","schema_version":"1.0","event_id":"sha256:8ff122f78179ba9c0c6161de6d94443cb7ead3f35bba1609ae306dfe68dbc2b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/bundle.json","state_url":"https://pith.science/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T15:09:55Z","links":{"resolver":"https://pith.science/pith/26L7TEVMIPWX7FR2SJYPM4PAP3","bundle":"https://pith.science/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/bundle.json","state":"https://pith.science/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26L7TEVMIPWX7FR2SJYPM4PAP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:26L7TEVMIPWX7FR2SJYPM4PAP3","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":"92e2cd181da0ea9e768855cc84877d88e2be997dcaa6595f57c75c80286d3d90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-21T00:06:08Z","title_canon_sha256":"8db7dcdf2cbb5b6514af51b71f0d8c96e5df03f6c452474beb87f06402a6bd99"},"schema_version":"1.0","source":{"id":"1704.06368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06368","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06368v2","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06368","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"26L7TEVMIPWX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"26L7TEVMIPWX7FR2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"26L7TEVM","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:8ff122f78179ba9c0c6161de6d94443cb7ead3f35bba1609ae306dfe68dbc2b4","target":"graph","created_at":"2026-05-17T23:52:29Z","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 study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the well-known and commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of faces of convex sets. Based on these new notions, we obtain a necessary condition and a sufficient condition for a cone to be facially dual complete. In our sufficient condition, we utilize a new notion calle","authors_text":"Levent Tun\\c{c}el, Vera Roshchina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-21T00:06:08Z","title":"Facially Dual Complete (Nice) cones and lexicographic tangents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06368","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":"sha256:5e27c916cf87bc411e251bcd74523723d0e6730c507cf999729312935fc37c05","target":"record","created_at":"2026-05-17T23:52:29Z","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":"92e2cd181da0ea9e768855cc84877d88e2be997dcaa6595f57c75c80286d3d90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-21T00:06:08Z","title_canon_sha256":"8db7dcdf2cbb5b6514af51b71f0d8c96e5df03f6c452474beb87f06402a6bd99"},"schema_version":"1.0","source":{"id":"1704.06368","kind":"arxiv","version":2}},"canonical_sha256":"d797f992ac43ed7f963a9270f671e07ef56cf566c080133c7647adce9d5c95dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d797f992ac43ed7f963a9270f671e07ef56cf566c080133c7647adce9d5c95dd","first_computed_at":"2026-05-17T23:52:29.506486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:29.506486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4fFk7RWTCmRBb2Na1baTJuZ09CsuUjYO3v9XI42aVZVpAvcITg8UezdXPF9YrdrTZhnF/NM4V52KSgT88CQtAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:29.507092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e27c916cf87bc411e251bcd74523723d0e6730c507cf999729312935fc37c05","sha256:8ff122f78179ba9c0c6161de6d94443cb7ead3f35bba1609ae306dfe68dbc2b4"],"state_sha256":"112d2ba554028d3455bda01b5d0e8d4d0c6a8875192d9a1e0542f7362ffc8eb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZaBDpBSe/dBchTPB53CnLdT3x5z9Fy0GphINvr9REJ41ujGBgh7Ny/7bvThBm3UWqXw5XCtWRo1fqgN8QA6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:09:55.830432Z","bundle_sha256":"978484386a2f437eb45242e11addb08f8ce9f4cb5600259e7a1e1dd171e78011"}}