{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:P7ZC5YEZGJFS5M732XTV7FWNVK","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":"5329773c2846f783613689c5d01196da894811f9018cb2b91bddf24b00a4883c","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-08T17:42:11Z","title_canon_sha256":"f389885c35913ee7edeea2fc9ef46b6d40c41971b3e8706806dea0d87433b4ad"},"schema_version":"1.0","source":{"id":"2309.04460","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.04460","created_at":"2026-07-05T10:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2309.04460v2","created_at":"2026-07-05T10:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.04460","created_at":"2026-07-05T10:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"P7ZC5YEZGJFS","created_at":"2026-07-05T10:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"P7ZC5YEZGJFS5M73","created_at":"2026-07-05T10:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"P7ZC5YEZ","created_at":"2026-07-05T10:20:09Z"}],"graph_snapshots":[{"event_id":"sha256:e7cface8214d35cc572d6d929a3d4f5361c906d9034b1b4564251e9af6dd480e","target":"graph","created_at":"2026-07-05T10:20:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.04460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a variety of areas. A particularly intensively studied question due to Keevash, Mubayi, Sudakov and Verstra\\\"ete from 2007 asks for the maximum possible average degree of a properly edge-coloured graph on $n$ vertices without a rainbow cycle. Improving upon a series of earlier bounds, Tomon proved an upper bound of $(\\log n)^{2+o(1)}$ for this quest","authors_text":"Dmitrii Zakharov, Lisa Sauermann, Matija Buci\\'c, Noga Alon, Or Zamir","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-08T17:42:11Z","title":"Essentially tight bounds for rainbow cycles in proper edge-colourings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04460","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":"sha256:87afc6b977f5c37b2e09769d06c2090d41ca255ebe65a771cc29144c628ffa20","target":"record","created_at":"2026-07-05T10:20:09Z","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":"5329773c2846f783613689c5d01196da894811f9018cb2b91bddf24b00a4883c","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-08T17:42:11Z","title_canon_sha256":"f389885c35913ee7edeea2fc9ef46b6d40c41971b3e8706806dea0d87433b4ad"},"schema_version":"1.0","source":{"id":"2309.04460","kind":"arxiv","version":2}},"canonical_sha256":"7ff22ee099324b2eb3fbd5e75f96cdaa80054cc9e4ab2f9f9898b4b63c000a70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff22ee099324b2eb3fbd5e75f96cdaa80054cc9e4ab2f9f9898b4b63c000a70","first_computed_at":"2026-07-05T10:20:09.793684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:09.793684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cvm9z2IcaiKGfFqYHRKPoT1bOFa70qmDAPoa624tDryRiOxLFVqD2iLMKzylF+S0Vied5MfCrOvGKF9gI6UkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:09.794163Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.04460","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87afc6b977f5c37b2e09769d06c2090d41ca255ebe65a771cc29144c628ffa20","sha256:e7cface8214d35cc572d6d929a3d4f5361c906d9034b1b4564251e9af6dd480e"],"state_sha256":"4ab098fb3f3c34a5ebbe5c870a5f5f315a8c8476eff7d60cb059efb8e8e0d547"}