{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RU5OCWDRE46GIOXPZFPKZ4LB2R","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":"306e68183788d56cb52d9cdedcbef8ea943cfee213827f30113ccdc14c016064","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-07T04:03:24Z","title_canon_sha256":"132f94d15012def544aa3075fbed2fa4ae91880544e87d73aab8eee29db4b84a"},"schema_version":"1.0","source":{"id":"2211.03291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.03291","created_at":"2026-07-05T05:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"2211.03291v1","created_at":"2026-07-05T05:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.03291","created_at":"2026-07-05T05:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"RU5OCWDRE46G","created_at":"2026-07-05T05:13:47Z"},{"alias_kind":"pith_short_16","alias_value":"RU5OCWDRE46GIOXP","created_at":"2026-07-05T05:13:47Z"},{"alias_kind":"pith_short_8","alias_value":"RU5OCWDR","created_at":"2026-07-05T05:13:47Z"}],"graph_snapshots":[{"event_id":"sha256:8cc8d955c4065bdb6c527c895b72ce3c6a8d24051737b0681f8b22f651087cd2","target":"graph","created_at":"2026-07-05T05:13:47Z","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/2211.03291/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every properly edge-colored $n$-vertex graph with average degree at least $100(\\log n)^2$ contains a rainbow cycle, improving upon $(\\log n)^{2+o(1)}$ bound due to Tomon. We also prove that every properly colored $n$-vertex graph with at least $10^5 k^2 n^{1+1/k}$ edges contains a rainbow $2k$-cycle, which improves the previous bound $2^{ck^2}n^{1+1/k}$ obtained by Janzer.\n  Our method using homomorphism inequalities and a lopsided regularization lemma also provides a simple way to prove the Erd\\H{o}s--Simonovits supersaturation theorem for even cycles, which may be of independen","authors_text":"Hong Liu, Jaehoon Kim, Joonkyung Lee, Tuan Tran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-07T04:03:24Z","title":"Rainbow cycles in properly edge-colored graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.03291","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:e829503532b4f56f2ceb437bbea90ca68e45d64e63c61e5e9f19f5ab8ed0c078","target":"record","created_at":"2026-07-05T05:13:47Z","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":"306e68183788d56cb52d9cdedcbef8ea943cfee213827f30113ccdc14c016064","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-07T04:03:24Z","title_canon_sha256":"132f94d15012def544aa3075fbed2fa4ae91880544e87d73aab8eee29db4b84a"},"schema_version":"1.0","source":{"id":"2211.03291","kind":"arxiv","version":1}},"canonical_sha256":"8d3ae15871273c643aefc95eacf161d446488c873d8cc8dee01c49ddd5298cd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d3ae15871273c643aefc95eacf161d446488c873d8cc8dee01c49ddd5298cd6","first_computed_at":"2026-07-05T05:13:47.145728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:47.145728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bx2OxewEoxpsKSldRNjzeCzfLjXM3PI9xTqVPeCViWZvCXUi051ds7TXEBrF0G2ORwPxgPmxSiP+F8PFbD8HBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:47.146152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.03291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e829503532b4f56f2ceb437bbea90ca68e45d64e63c61e5e9f19f5ab8ed0c078","sha256:8cc8d955c4065bdb6c527c895b72ce3c6a8d24051737b0681f8b22f651087cd2"],"state_sha256":"54143dfca5dfd50d2675505de8199f7b9c29266624dcb9f307948a34dcd89f70"}