{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3J72IVWF3XCFDP7KAPP32NOVJZ","short_pith_number":"pith:3J72IVWF","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"},"canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","source":{"kind":"arxiv","id":"1309.0438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0438","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0438v1","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0438","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"3J72IVWF3XCF","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3J72IVWF3XCFDP7K","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3J72IVWF","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3J72IVWF3XCFDP7KAPP32NOVJZ","target":"record","payload":{"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"},"canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","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"},"source_kind":"arxiv","source_id":"1309.0438","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmsJE0M/riqbFrerROBewe6zJA3hv1ofRHeh2d7cDc7U0kl3377hgMz2jV69prYwYbGDD+J36AIRuyG9jmgzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:07:39.239831Z"},"content_sha256":"0d08a5ebaf9f0fdd74caf8e98388af1e011510d11ce76b57d53e3f7c6fe7eb36","schema_version":"1.0","event_id":"sha256:0d08a5ebaf9f0fdd74caf8e98388af1e011510d11ce76b57d53e3f7c6fe7eb36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3J72IVWF3XCFDP7KAPP32NOVJZ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92QEzPfS13FSq28SP3PHx//r5MAtV4vYvcvqq6l/tSZwVDZi+58zji01aBtBuMZMiKm13geqSv9vuM3pC6PBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:07:39.240698Z"},"content_sha256":"66f4f505fae58f0f133db1fd403f312c0ec5368754c55a4b30c36d5976655db9","schema_version":"1.0","event_id":"sha256:66f4f505fae58f0f133db1fd403f312c0ec5368754c55a4b30c36d5976655db9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/bundle.json","state_url":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/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":"2026-05-30T23:07:39Z","links":{"resolver":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ","bundle":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/bundle.json","state":"https://pith.science/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3J72IVWF3XCFDP7KAPP32NOVJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3J72IVWF3XCFDP7KAPP32NOVJZ","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":"43d80ad3ac812750b5e78d180831de127b808c1e55d0ab151cd079c934c3db15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T15:25:00Z","title_canon_sha256":"b42fecb8af375fd81d7b3730eee20b89e6a39aacb7261eedec6b71a67ecabeb6"},"schema_version":"1.0","source":{"id":"1309.0438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0438","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0438v1","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0438","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"3J72IVWF3XCF","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3J72IVWF3XCFDP7K","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3J72IVWF","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:66f4f505fae58f0f133db1fd403f312c0ec5368754c55a4b30c36d5976655db9","target":"graph","created_at":"2026-05-18T03:14:27Z","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 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","authors_text":"Fr\\'ed\\'eric Maffray, Nicolas Trotignon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T15:25:00Z","title":"A class of perfectly contractile graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0438","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":"sha256:0d08a5ebaf9f0fdd74caf8e98388af1e011510d11ce76b57d53e3f7c6fe7eb36","target":"record","created_at":"2026-05-18T03:14:27Z","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":"43d80ad3ac812750b5e78d180831de127b808c1e55d0ab151cd079c934c3db15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-02T15:25:00Z","title_canon_sha256":"b42fecb8af375fd81d7b3730eee20b89e6a39aacb7261eedec6b71a67ecabeb6"},"schema_version":"1.0","source":{"id":"1309.0438","kind":"arxiv","version":1}},"canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7fa456c5ddc451bfea03dfbd35d54e45c5c8e4a8f92266b71323f455e760b7","first_computed_at":"2026-05-18T03:14:27.297988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:27.297988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sStlbpBGSyJ8mwkulvipbhfS6YmLikN6IKA+LSh3NgPYXCKSOeRPiZeBqocOvE9lLLaQpvooKAFyhfhU+q/YAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:27.298429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d08a5ebaf9f0fdd74caf8e98388af1e011510d11ce76b57d53e3f7c6fe7eb36","sha256:66f4f505fae58f0f133db1fd403f312c0ec5368754c55a4b30c36d5976655db9"],"state_sha256":"688f892f88dd4283b212f080d8640e796d726d95af094c6baa622d58af6ed38b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3osZeZ3G2JKpmAwvjkbLqNnW0tzxihCeFKvo9kTxan9TBsuw2dgFXwPbody+Ki2G5l92P2pMt3LcbQUYihx/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:07:39.245212Z","bundle_sha256":"8060925034cd1f3c352a149487893364f80a754d58f907eb2e27ae1395c74369"}}