{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6VS6ZCWA776ITRJCRJFIJAXSCY","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":"acf4fe1a53ac5dd347bc140d9ba48f67a96793c232e5fcbf3b0e1b20c3c1c960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-22T12:14:04Z","title_canon_sha256":"8eafb7cab87d4f7ea34240aa1decf3eb1ddae685528e9f9f578924d909e987f3"},"schema_version":"1.0","source":{"id":"1509.06563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06563","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06563v2","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06563","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"6VS6ZCWA776I","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6VS6ZCWA776ITRJC","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6VS6ZCWA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:972bebe7c91c4f0137e7fbc31eec44b924608c08fcef9c4a64c2e842aebed775","target":"graph","created_at":"2026-05-18T00:23:57Z","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":"A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for every positive integer k, every triangle-free graph with sufficiently large chromatic number contains holes of k consecutive lengths.","authors_text":"Alex Scott, Paul Seymour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-22T12:14:04Z","title":"Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06563","kind":"arxiv","version":2},"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:b6e2a709b6e00f2408fd1b689f4b1264f99297598c41be20c2908624322b9e3e","target":"record","created_at":"2026-05-18T00:23:57Z","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":"acf4fe1a53ac5dd347bc140d9ba48f67a96793c232e5fcbf3b0e1b20c3c1c960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-22T12:14:04Z","title_canon_sha256":"8eafb7cab87d4f7ea34240aa1decf3eb1ddae685528e9f9f578924d909e987f3"},"schema_version":"1.0","source":{"id":"1509.06563","kind":"arxiv","version":2}},"canonical_sha256":"f565ec8ac0fffc89c5228a4a8482f216079dd8267a20bd47266796797f572708","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f565ec8ac0fffc89c5228a4a8482f216079dd8267a20bd47266796797f572708","first_computed_at":"2026-05-18T00:23:57.390619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.390619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0A9WsPIHuVSba3qIy4ntmJaV7vDslHHJxdRPAj6OLjYSTXOiY7mR6KbK0qIP2Ep/L2UQSNf6jYMqDAtjLTWrAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.391272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e2a709b6e00f2408fd1b689f4b1264f99297598c41be20c2908624322b9e3e","sha256:972bebe7c91c4f0137e7fbc31eec44b924608c08fcef9c4a64c2e842aebed775"],"state_sha256":"bd41b50dccedf3fd8bc546e5c9e8ad13cd03ca94b7f3f5882f455cb70a787aa1"}