{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:53JVP26Z4BSYEIWNMBD2VUWLJX","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":"a023c5df96330028a99501f5ecba5f1877252e1b261501917942a34579e79f4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-26T08:40:31Z","title_canon_sha256":"980e9ead127d2076ab79ff7cf7c8a8b0a5ff42293968019a2753022b1b74d734"},"schema_version":"1.0","source":{"id":"1110.5736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5736","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5736v1","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5736","created_at":"2026-05-18T04:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"53JVP26Z4BSY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"53JVP26Z4BSYEIWN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"53JVP26Z","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:02102b0d51e8aa1c153ecbe2e0e614102b1213acc8a8a374b7bab1e4224c6a2a","target":"graph","created_at":"2026-05-18T04:10:11Z","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":"The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most the ceiling of n/2. The bound is optimal.","authors_text":"Ingo Schiermeyer, Jan Ekstein, Maria Koch, P\\v{r}emysl Holub, Stephan Matos Camacho, Tom\\'a\\v{s} Kaiser, Zden\\v{e}k Ryj\\'a\\v{c}ek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-26T08:40:31Z","title":"The rainbow connection number of 2-connected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5736","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":"sha256:2ba0bc0f6151ed0a99f04dd2212611c56059463b33adc6d5418d438ee40af24f","target":"record","created_at":"2026-05-18T04:10:11Z","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":"a023c5df96330028a99501f5ecba5f1877252e1b261501917942a34579e79f4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-26T08:40:31Z","title_canon_sha256":"980e9ead127d2076ab79ff7cf7c8a8b0a5ff42293968019a2753022b1b74d734"},"schema_version":"1.0","source":{"id":"1110.5736","kind":"arxiv","version":1}},"canonical_sha256":"eed357ebd9e0658222cd6047aad2cb4dd1b80b44524b19c677cf8d5f7c8d2749","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eed357ebd9e0658222cd6047aad2cb4dd1b80b44524b19c677cf8d5f7c8d2749","first_computed_at":"2026-05-18T04:10:11.442726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:11.442726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IXP5FKQrZlvCRB3ugSrwQaUJqW1gBAya+NDVLtyQ/pPL5NAWjnxLW1jLGdDbCF6eS9cRZCI18SEug5zMxVY+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:11.443560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba0bc0f6151ed0a99f04dd2212611c56059463b33adc6d5418d438ee40af24f","sha256:02102b0d51e8aa1c153ecbe2e0e614102b1213acc8a8a374b7bab1e4224c6a2a"],"state_sha256":"04e497f0caf4e615e4a49384e6d0579a090d66407b316f1bd0cbe62ba3059e2a"}