{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BB7JPTWFOZ6D7655UZMEBEM5GA","short_pith_number":"pith:BB7JPTWF","canonical_record":{"source":{"id":"1502.03695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-12T15:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd9b5267cba622f1c9bcb18ca152dfaba575c71841b4865b6968e93e15612d6d","abstract_canon_sha256":"bcdf4c958ba912d7dd91813b68f61d4edf24696f148a2863ffa713b9a4a1abb9"},"schema_version":"1.0"},"canonical_sha256":"087e97cec5767c3ffbbda65840919d300da1b1b8a195ecfa3353c1cd2910bc19","source":{"kind":"arxiv","id":"1502.03695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03695","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03695v1","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03695","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"BB7JPTWFOZ6D","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BB7JPTWFOZ6D7655","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BB7JPTWF","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BB7JPTWFOZ6D7655UZMEBEM5GA","target":"record","payload":{"canonical_record":{"source":{"id":"1502.03695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-12T15:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd9b5267cba622f1c9bcb18ca152dfaba575c71841b4865b6968e93e15612d6d","abstract_canon_sha256":"bcdf4c958ba912d7dd91813b68f61d4edf24696f148a2863ffa713b9a4a1abb9"},"schema_version":"1.0"},"canonical_sha256":"087e97cec5767c3ffbbda65840919d300da1b1b8a195ecfa3353c1cd2910bc19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:17.023835Z","signature_b64":"l/FUhL3SSrWPpLCvXrFYyxTXskzwPzlCQvhY775WLVOMFDO3C+zNx0DrBeEsXF66XYI4WSFD+SzCHbBBbmWgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"087e97cec5767c3ffbbda65840919d300da1b1b8a195ecfa3353c1cd2910bc19","last_reissued_at":"2026-05-18T02:27:17.023113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:17.023113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.03695","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":"2026-05-18T02:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttuUwZmndU5qYyboWgJvpxOB+YTsU6CAlHILARo6oXxZ+WM2vaUxqomWs0H5iUNdCyva+bUXeGnCzMJGEhqKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:30:04.838061Z"},"content_sha256":"2c568c17afa85806279badd2a6564deafe47a0516ac0928974966ba3cf485837","schema_version":"1.0","event_id":"sha256:2c568c17afa85806279badd2a6564deafe47a0516ac0928974966ba3cf485837"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BB7JPTWFOZ6D7655UZMEBEM5GA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Even pairs in square-free Berge graphs with no odd prism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray","submitted_at":"2015-02-12T15:09:57Z","abstract_excerpt":"We consider the class of Berge graphs that contain no odd prism and no square (cycle on four vertices). We prove that every graph G in this class either is a clique or has an even pair, as conjectured by Everett and Reed. This result is used to devise a polynomial-time algorithm to color optimally every graph in this class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03695","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":"2026-05-18T02:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"noDq2ZXFFHBaO9J8rqDND9h0LQR1WeC396zGenhOEMiPR5xzlO/++Byisg/PWHZQpJxDW5Tuv2xhCGCwaBBmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:30:04.838434Z"},"content_sha256":"22032a9eca2c913d7ceaad47ca00b55274c4e40eeeecd6a562485a3c6afb6fda","schema_version":"1.0","event_id":"sha256:22032a9eca2c913d7ceaad47ca00b55274c4e40eeeecd6a562485a3c6afb6fda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/bundle.json","state_url":"https://pith.science/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/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":"2026-05-31T00:30:04Z","links":{"resolver":"https://pith.science/pith/BB7JPTWFOZ6D7655UZMEBEM5GA","bundle":"https://pith.science/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/bundle.json","state":"https://pith.science/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BB7JPTWFOZ6D7655UZMEBEM5GA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BB7JPTWFOZ6D7655UZMEBEM5GA","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":"bcdf4c958ba912d7dd91813b68f61d4edf24696f148a2863ffa713b9a4a1abb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-12T15:09:57Z","title_canon_sha256":"cd9b5267cba622f1c9bcb18ca152dfaba575c71841b4865b6968e93e15612d6d"},"schema_version":"1.0","source":{"id":"1502.03695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03695","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03695v1","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03695","created_at":"2026-05-18T02:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"BB7JPTWFOZ6D","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BB7JPTWFOZ6D7655","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BB7JPTWF","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:22032a9eca2c913d7ceaad47ca00b55274c4e40eeeecd6a562485a3c6afb6fda","target":"graph","created_at":"2026-05-18T02:27:17Z","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 of Berge graphs that contain no odd prism and no square (cycle on four vertices). We prove that every graph G in this class either is a clique or has an even pair, as conjectured by Everett and Reed. This result is used to devise a polynomial-time algorithm to color optimally every graph in this class.","authors_text":"Fr\\'ed\\'eric Maffray","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-12T15:09:57Z","title":"Even pairs in square-free Berge graphs with no odd prism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03695","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":"sha256:2c568c17afa85806279badd2a6564deafe47a0516ac0928974966ba3cf485837","target":"record","created_at":"2026-05-18T02:27:17Z","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":"bcdf4c958ba912d7dd91813b68f61d4edf24696f148a2863ffa713b9a4a1abb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-12T15:09:57Z","title_canon_sha256":"cd9b5267cba622f1c9bcb18ca152dfaba575c71841b4865b6968e93e15612d6d"},"schema_version":"1.0","source":{"id":"1502.03695","kind":"arxiv","version":1}},"canonical_sha256":"087e97cec5767c3ffbbda65840919d300da1b1b8a195ecfa3353c1cd2910bc19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087e97cec5767c3ffbbda65840919d300da1b1b8a195ecfa3353c1cd2910bc19","first_computed_at":"2026-05-18T02:27:17.023113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:17.023113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/FUhL3SSrWPpLCvXrFYyxTXskzwPzlCQvhY775WLVOMFDO3C+zNx0DrBeEsXF66XYI4WSFD+SzCHbBBbmWgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:17.023835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c568c17afa85806279badd2a6564deafe47a0516ac0928974966ba3cf485837","sha256:22032a9eca2c913d7ceaad47ca00b55274c4e40eeeecd6a562485a3c6afb6fda"],"state_sha256":"846ef01f933ba57d938d441b26ea0f0481e3dd56bf7c4ee24aa0ead0ecd3d57b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+UjCSODyI/lSlxduC5KdRnjQkKEdWTOAmTRkJq1tLD3FPAbB1VBUiNfbnPFmfPTmEZOEP6Je08dICYZx+Ry0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:30:04.840542Z","bundle_sha256":"2dbc7a5d1e19461b35499bc316279651fb4532a9182d6f6b49ebc92413f3f6fe"}}