{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J7GTEDLDVMOM7PC725VBIQRAYK","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":"91ca18ab71634e5791444df5ae96f6161b9fe0db0ddce9babb3a7508b0bdc9fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T03:52:16Z","title_canon_sha256":"bad658e65c913eaa649cbe12e9fde362ebd3b61b19e584ef00ccac1b1078fd42"},"schema_version":"1.0","source":{"id":"1808.02202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02202","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02202v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02202","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"J7GTEDLDVMOM","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J7GTEDLDVMOM7PC7","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J7GTEDLD","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:63f610939664e884d7fe4dad122c931672b6308f99f1d1893a3c8a76886b4400","target":"graph","created_at":"2026-05-18T00:08:47Z","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 this paper, we present some second-order sufficient conditions in terms of the Demyanov-Pevnyi's second-order directional derivatives for efficiency of $C^1$ vector optimization problems with constraints. Our results improve and generalize conditions obtained by various authors in recent papers.","authors_text":"Ching-Feng Wen, Jen-Chih Yao, Nguyen Van Tuyen, Yi-Bin Xiao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T03:52:16Z","title":"On second-order sufficient optimality conditions for $C^1$ vector optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02202","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":"sha256:9f37ba9d07ba86badaf1b5bd05302e7534bd5f6a43123e13d28b6d3d472ab6b9","target":"record","created_at":"2026-05-18T00:08:47Z","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":"91ca18ab71634e5791444df5ae96f6161b9fe0db0ddce9babb3a7508b0bdc9fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T03:52:16Z","title_canon_sha256":"bad658e65c913eaa649cbe12e9fde362ebd3b61b19e584ef00ccac1b1078fd42"},"schema_version":"1.0","source":{"id":"1808.02202","kind":"arxiv","version":1}},"canonical_sha256":"4fcd320d63ab1ccfbc5fd76a144220c2af7c14bb73af0dc899407eb4b2737d72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fcd320d63ab1ccfbc5fd76a144220c2af7c14bb73af0dc899407eb4b2737d72","first_computed_at":"2026-05-18T00:08:47.239534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:47.239534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kXAzEr+dN/mXNtpBniVwx3U9a+L/jrEjOC+sXG8l404Zzon7pnWysT2dIFL/56AIVVy1vfh4bErFBO6JPKOhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:47.240136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f37ba9d07ba86badaf1b5bd05302e7534bd5f6a43123e13d28b6d3d472ab6b9","sha256:63f610939664e884d7fe4dad122c931672b6308f99f1d1893a3c8a76886b4400"],"state_sha256":"65d6fb3c41e4e9f85797fcbe2e67a0cd8f1e17c6dfe2adba9caf04d122fcfbf1"}