{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3J72IVWF3XCFDP7KAPP32NOVJZ","short_pith_number":"pith:3J72IVWF","schema_version":"1.0","canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","source":{"kind":"arxiv","id":"1309.0438","version":1},"attestation_state":"computed","paper":{"title":"A class of perfectly contractile graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, Nicolas Trotignon","submitted_at":"2013-09-02T15:25:00Z","abstract_excerpt":"We consider the class ${\\cal A}$ of graphs that contain no odd hole, no antihole, and no \"prism\" (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph $G\\in{\\cal A}$ different from a clique has an \"even pair\" (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter \"Even pairs\" in the book {\\it Perfect Graphs}, J.L. Ram\\'{\\i}rez-Alfons\\'{\\i}n and B.A. Reed, eds., Wiley Interscience, 2001]. Our proof is a polynomial-time algorithm that produces an even pair with the additi"},"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":"1309.0438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T15:25:00Z","cross_cats_sorted":[],"title_canon_sha256":"b42fecb8af375fd81d7b3730eee20b89e6a39aacb7261eedec6b71a67ecabeb6","abstract_canon_sha256":"43d80ad3ac812750b5e78d180831de127b808c1e55d0ab151cd079c934c3db15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:27.298429Z","signature_b64":"sStlbpBGSyJ8mwkulvipbhfS6YmLikN6IKA+LSh3NgPYXCKSOeRPiZeBqocOvE9lLLaQpvooKAFyhfhU+q/YAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","last_reissued_at":"2026-05-18T03:14:27.297988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:27.297988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A class of perfectly contractile graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, Nicolas Trotignon","submitted_at":"2013-09-02T15:25:00Z","abstract_excerpt":"We consider the class ${\\cal A}$ of graphs that contain no odd hole, no antihole, and no \"prism\" (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph $G\\in{\\cal A}$ different from a clique has an \"even pair\" (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter \"Even pairs\" in the book {\\it Perfect Graphs}, J.L. Ram\\'{\\i}rez-Alfons\\'{\\i}n and B.A. Reed, eds., Wiley Interscience, 2001]. Our proof is a polynomial-time algorithm that produces an even pair with the additi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0438","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":"1309.0438","created_at":"2026-05-18T03:14:27.298057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0438v1","created_at":"2026-05-18T03:14:27.298057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0438","created_at":"2026-05-18T03:14:27.298057+00:00"},{"alias_kind":"pith_short_12","alias_value":"3J72IVWF3XCF","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3J72IVWF3XCFDP7K","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3J72IVWF","created_at":"2026-05-18T12:27:32.513160+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/3J72IVWF3XCFDP7KAPP32NOVJZ","json":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ.json","graph_json":"https://pith.science/api/pith-number/3J72IVWF3XCFDP7KAPP32NOVJZ/graph.json","events_json":"https://pith.science/api/pith-number/3J72IVWF3XCFDP7KAPP32NOVJZ/events.json","paper":"https://pith.science/paper/3J72IVWF"},"agent_actions":{"view_html":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ","download_json":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ.json","view_paper":"https://pith.science/paper/3J72IVWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0438&json=true","fetch_graph":"https://pith.science/api/pith-number/3J72IVWF3XCFDP7KAPP32NOVJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3J72IVWF3XCFDP7KAPP32NOVJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/action/storage_attestation","attest_author":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/action/author_attestation","sign_citation":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/action/citation_signature","submit_replication":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/action/replication_record"}},"created_at":"2026-05-18T03:14:27.298057+00:00","updated_at":"2026-05-18T03:14:27.298057+00:00"}