{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:E6PZ2766XIYVC45MIFDFUV2EUV","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":"9024149f78a2c0fbf2e849836ecb8950d87829d21a15fd0d26c770d0ff176523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-24T07:43:24Z","title_canon_sha256":"94e0cc641a050fc5b89146545a8b645cdaac07058fe949bffeb8cdfae425f9b8"},"schema_version":"1.0","source":{"id":"1402.5739","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5739","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5739v1","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5739","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"E6PZ2766XIYV","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"E6PZ2766XIYVC45M","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"E6PZ2766","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9e24aede8545bce379478f66fad2f05afd011b3e4bc9baa0f4ff69fee2a73e0a","target":"graph","created_at":"2026-05-18T02:58:13Z","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":"Beginning with the concepts of orientation for a 3-hypergraph and transitivity for an oriented 3-hypergraph, it is natural to study the class of comparability 3-hypergraphs (those that can be transitively oriented). In this work we show three different behaviors in respect to the relationship between the chromatic number and the clique number of a comparability 3-hypergraph, this is in contrast with the fact that a comparability simple graph is a perfect graph.","authors_text":"Amanda Montejano, Deborah Oliveros, Natalia Garcia-Colin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-24T07:43:24Z","title":"The chromatic number of comparability 3-hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5739","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:dbdaa056cb34d8b0c93758b21d9c228a694b41090e0e3958677e5731a1feb79d","target":"record","created_at":"2026-05-18T02:58:13Z","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":"9024149f78a2c0fbf2e849836ecb8950d87829d21a15fd0d26c770d0ff176523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-24T07:43:24Z","title_canon_sha256":"94e0cc641a050fc5b89146545a8b645cdaac07058fe949bffeb8cdfae425f9b8"},"schema_version":"1.0","source":{"id":"1402.5739","kind":"arxiv","version":1}},"canonical_sha256":"279f9d7fdeba315173ac41465a5744a567642b646e0fbfe05c9bd0fe21d1e8b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"279f9d7fdeba315173ac41465a5744a567642b646e0fbfe05c9bd0fe21d1e8b7","first_computed_at":"2026-05-18T02:58:13.848448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:13.848448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tHV9pOY505WVVp2o7zD0oW2pv+y5yooCU/VAT8xXQFwFW9smtw0PF2+1j4VJvaSKik1smvJ+fm/hOWLZnyvYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:13.849228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbdaa056cb34d8b0c93758b21d9c228a694b41090e0e3958677e5731a1feb79d","sha256:9e24aede8545bce379478f66fad2f05afd011b3e4bc9baa0f4ff69fee2a73e0a"],"state_sha256":"2c1c87ae015191906d06c1d8e66721c3ebdd30d7dea6b5669a758e73026c3506"}