{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WKLIMBD7UQAM3FQYNYBJA2M6AI","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":"0dd9c4ab8642ada6e0fd0c3f8e0d368ebef1e9d569527c8fc324dbcc08c13b0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-23T22:42:15Z","title_canon_sha256":"3de0ffe61b379363f815d9cc8032edb53d92ebdb1b4810e4e609f463edb16922"},"schema_version":"1.0","source":{"id":"1107.4715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4715","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4715v1","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4715","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"WKLIMBD7UQAM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WKLIMBD7UQAM3FQY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WKLIMBD7","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:f637d9f5059373839f614dd3672534afe4fdede6ac6bdb39fb81500b3e982c30","target":"graph","created_at":"2026-05-18T03:02:44Z","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":"Let $\\mc{F}$ be a family of graphs. A graph is {\\em $\\mc{F}$-free} if it contains no copy of a graph in $\\mc{F}$ as a subgraph. A cornerstone of extremal graph theory is the study of the {\\em Tur\\'an number} $ex(n,\\mc{F})$, the maximum number of edges in an $\\mc{F}$-free graph on $n$ vertices. Define the {\\em Zarankiewicz number} $z(n,\\mc{F})$ to be the maximum number of edges in an $\\mc{F}$-free {\\em bipartite} graph on $n$ vertices. Let $C_k$ denote a cycle of length $k$, and let $\\mc{C}_k$ denote the set of cycles $C_{\\ell}$, where $3 \\le \\ell \\leq k$ and $\\ell$ and $k$ have the same parity","authors_text":"Benny Sudakov, Jacques Verstraete, Peter Keevash","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-23T22:42:15Z","title":"On a conjecture of Erdos and Simonovits: Even Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4715","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":"sha256:59f09b714a11fe084234c12a9bfb05671f992ba49ad977776dc1215c92ae09b2","target":"record","created_at":"2026-05-18T03:02:44Z","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":"0dd9c4ab8642ada6e0fd0c3f8e0d368ebef1e9d569527c8fc324dbcc08c13b0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-23T22:42:15Z","title_canon_sha256":"3de0ffe61b379363f815d9cc8032edb53d92ebdb1b4810e4e609f463edb16922"},"schema_version":"1.0","source":{"id":"1107.4715","kind":"arxiv","version":1}},"canonical_sha256":"b29686047fa400cd96186e0290699e021b32f9849e56e875d8ff6cb984d6daed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b29686047fa400cd96186e0290699e021b32f9849e56e875d8ff6cb984d6daed","first_computed_at":"2026-05-18T03:02:44.157138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:44.157138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxhqVcHix+ddzBlu+Mqe+OdWTyNDnvmFQxaZmyI5plFRbLl8KJdIKgjVEUbCyF7c/ghFoLPv++tmoBWk7CcSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:44.157825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59f09b714a11fe084234c12a9bfb05671f992ba49ad977776dc1215c92ae09b2","sha256:f637d9f5059373839f614dd3672534afe4fdede6ac6bdb39fb81500b3e982c30"],"state_sha256":"7b6016cd979de10e14ecd0a743cc9e901f67077911dae620bf13fdad0f34d399"}