{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JWUAUD4SV6OC4WPY5DQKMMOMRG","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":"b6a988b702d44efe5c2955c28fd85020a55de51deecd57d8a2efd5fdd958bbdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-10T07:28:56Z","title_canon_sha256":"7fb38815758cbd4fe49ec2199f66b022e4890ff67fc922c88b52289b9f886df2"},"schema_version":"1.0","source":{"id":"1304.2862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2862","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2862v1","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2862","created_at":"2026-05-18T03:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"JWUAUD4SV6OC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JWUAUD4SV6OC4WPY","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JWUAUD4S","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:01c19453e14b765735ed6c0ff6f0f08ee2cd0311642c3fd91390a91189ab6cfc","target":"graph","created_at":"2026-05-18T03:13:58Z","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 class of graphs closed under taking induced subgraphs is $\\chi$-bounded if there exists a function $f$ such that for all graphs $G$ in the class, $\\chi(G) \\leq f(\\omega(G))$. We consider the following question initially studied in [A. Gy{\\'a}rf{\\'a}s, Problems from the world surrounding perfect graphs, {\\em Zastowania Matematyki Applicationes Mathematicae}, 19:413--441, 1987]. For a $\\chi$-bounded class $\\cal C$, is the class $\\bar{C}$ $\\chi$-bounded (where $\\bar{\\cal C}$ is the class of graphs formed by the complements of graphs from $\\cal C$)? We show that if $\\cal C$ is $\\chi$-bounded by ","authors_text":"Andr\\'as Gy\\'arf\\'as, Andr\\'as Sebo, Nicolas Trotignon, Raphael Machado, St\\'ephan Thomass\\'e, Zhentao Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-10T07:28:56Z","title":"Complements of nearly perfect graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2862","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:dd23dc61ed952d9f16f7aaa8bc625da0a195ad7f506db60ef53d9668028dfdcc","target":"record","created_at":"2026-05-18T03:13:58Z","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":"b6a988b702d44efe5c2955c28fd85020a55de51deecd57d8a2efd5fdd958bbdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-10T07:28:56Z","title_canon_sha256":"7fb38815758cbd4fe49ec2199f66b022e4890ff67fc922c88b52289b9f886df2"},"schema_version":"1.0","source":{"id":"1304.2862","kind":"arxiv","version":1}},"canonical_sha256":"4da80a0f92af9c2e59f8e8e0a631cc899609e961627d54247ec8cb118772ad44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4da80a0f92af9c2e59f8e8e0a631cc899609e961627d54247ec8cb118772ad44","first_computed_at":"2026-05-18T03:13:58.010774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:58.010774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HoxpLVm5kCpDG8gEQ/oliYAK7XAjm+dU1P2rGFPF102rXiVqzYxCRrCGo4lN+OgoNPOA1g4k5hZ836DZ4XD1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:58.011427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd23dc61ed952d9f16f7aaa8bc625da0a195ad7f506db60ef53d9668028dfdcc","sha256:01c19453e14b765735ed6c0ff6f0f08ee2cd0311642c3fd91390a91189ab6cfc"],"state_sha256":"9ec0ad95d75d5b789084f77df3d35bc0de0a8a0b35ccd7797918c41bfeed2a60"}