{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DRELA3MWQSN3HVMTZ3F3SFKBO6","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":"632510c3c44320eb680f55657ef06be5e58883836d40229cfdc5f3c5c75e495b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-29T19:04:55Z","title_canon_sha256":"c813753ffd4ef55fbac3a225543884346ff181846fb65d8e02e2e8cf4eefcb0b"},"schema_version":"1.0","source":{"id":"1701.08417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08417","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08417v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08417","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"DRELA3MWQSN3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DRELA3MWQSN3HVMT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DRELA3MW","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f2e833bb44924bf47e10928ab6169f00aca40c5aab58f5b81ee5ed8f3dc4222a","target":"graph","created_at":"2026-05-18T00:04:24Z","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 graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms of the Hadwiger number and we also characterize the families of graphs such that for each induced subgraph $H$, (1) the Hadwiger number of $H$ is equal to the maximum clique order of $H$, (2) the Hadwiger number of $H$ is equal to the achromatic number of $H$, (3) the $b$-chromatic number is equal to the pseudoachromatic number, (4) the pseudo-$b$-chromatic number is equal to the pseudoachromatic number, (5) the Had","authors_text":"Christian Rubio-Montiel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-29T19:04:55Z","title":"The Hadwiger number, chordal graphs and $ab$-perfection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08417","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":"sha256:3d9cc74ad32818675ca2d843865305be338ddd5f1f05a3858beaccab5c57d405","target":"record","created_at":"2026-05-18T00:04:24Z","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":"632510c3c44320eb680f55657ef06be5e58883836d40229cfdc5f3c5c75e495b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-29T19:04:55Z","title_canon_sha256":"c813753ffd4ef55fbac3a225543884346ff181846fb65d8e02e2e8cf4eefcb0b"},"schema_version":"1.0","source":{"id":"1701.08417","kind":"arxiv","version":1}},"canonical_sha256":"1c48b06d96849bb3d593cecbb9154177a2f45d5ee2965a8bd73c3d6b86d096a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c48b06d96849bb3d593cecbb9154177a2f45d5ee2965a8bd73c3d6b86d096a3","first_computed_at":"2026-05-18T00:04:24.204098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.204098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JnL2kTxjfLUh2KBalQoWyJ8BibI8BvvCRe6U2dCAdXs9VocgCOeuskRNz50XpmRoPxRYA1pTP7AMmBTtiY6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.204687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d9cc74ad32818675ca2d843865305be338ddd5f1f05a3858beaccab5c57d405","sha256:f2e833bb44924bf47e10928ab6169f00aca40c5aab58f5b81ee5ed8f3dc4222a"],"state_sha256":"c1b8f016462da6790c7c99acd4cac4bff733c6f3af4a4deebdf5c52318587cd1"}