{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FGAHAJ22OESXCJYSWZT7IJ452T","short_pith_number":"pith:FGAHAJ22","schema_version":"1.0","canonical_sha256":"298070275a7125712712b667f4279dd4d642c86cad1b0ad30c5bf2ffb1a2b4a5","source":{"kind":"arxiv","id":"1309.0449","version":1},"attestation_state":"computed","paper":{"title":"Odd pairs of cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, Michel Burlet, Nicolas Trotignon","submitted_at":"2013-09-02T16:12:35Z","abstract_excerpt":"A graph is Berge if it has no induced odd cycle on at least 5 vertices and no complement of induced odd cycle on at least 5 vertices. A graph is perfect if the chromatic number equals the maximum clique number for every induced subgraph. Chudnovsky, Robertson, Seymour and Thomas proved that every Berge graph either falls into some classical family of perfect graphs, or has a structural fault that cannot occur in a minimal imperfect graph. A corollary of this is the strong perfect graph theorem conjectured by Berge: every Berge graph is perfect. An even pair of vertices in a graph is a pair of "},"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":"1309.0449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T16:12:35Z","cross_cats_sorted":[],"title_canon_sha256":"3b856e5342229778667e9dc74b0987f790fecfca8e09dd31d372ddca0d340faf","abstract_canon_sha256":"44048d42f254e79f491dd064cac845273eab5eef08053001e2da405f5506df6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:57.605698Z","signature_b64":"VRUBiAz9zA3ms1V4+N1bmuI3e1MHo8GOBcSVr1w1ylzf1sZbghR8yevoY7RmJ2H3meRkLz7cYFLc6hOjRnv+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"298070275a7125712712b667f4279dd4d642c86cad1b0ad30c5bf2ffb1a2b4a5","last_reissued_at":"2026-05-18T03:13:57.604828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:57.604828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Odd pairs of cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, Michel Burlet, Nicolas Trotignon","submitted_at":"2013-09-02T16:12:35Z","abstract_excerpt":"A graph is Berge if it has no induced odd cycle on at least 5 vertices and no complement of induced odd cycle on at least 5 vertices. A graph is perfect if the chromatic number equals the maximum clique number for every induced subgraph. Chudnovsky, Robertson, Seymour and Thomas proved that every Berge graph either falls into some classical family of perfect graphs, or has a structural fault that cannot occur in a minimal imperfect graph. A corollary of this is the strong perfect graph theorem conjectured by Berge: every Berge graph is perfect. An even pair of vertices in a graph is a pair of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0449","kind":"arxiv","version":1},"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":"1309.0449","created_at":"2026-05-18T03:13:57.604981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0449v1","created_at":"2026-05-18T03:13:57.604981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0449","created_at":"2026-05-18T03:13:57.604981+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGAHAJ22OESX","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGAHAJ22OESXCJYS","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGAHAJ22","created_at":"2026-05-18T12:27:45.050594+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/FGAHAJ22OESXCJYSWZT7IJ452T","json":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T.json","graph_json":"https://pith.science/api/pith-number/FGAHAJ22OESXCJYSWZT7IJ452T/graph.json","events_json":"https://pith.science/api/pith-number/FGAHAJ22OESXCJYSWZT7IJ452T/events.json","paper":"https://pith.science/paper/FGAHAJ22"},"agent_actions":{"view_html":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T","download_json":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T.json","view_paper":"https://pith.science/paper/FGAHAJ22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0449&json=true","fetch_graph":"https://pith.science/api/pith-number/FGAHAJ22OESXCJYSWZT7IJ452T/graph.json","fetch_events":"https://pith.science/api/pith-number/FGAHAJ22OESXCJYSWZT7IJ452T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T/action/storage_attestation","attest_author":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T/action/author_attestation","sign_citation":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T/action/citation_signature","submit_replication":"https://pith.science/pith/FGAHAJ22OESXCJYSWZT7IJ452T/action/replication_record"}},"created_at":"2026-05-18T03:13:57.604981+00:00","updated_at":"2026-05-18T03:13:57.604981+00:00"}