{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XE5SQVWVOFEQNAU2OXEUKSHTFE","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":"360799bfc09525b7eae299a01294a76978e29bc7727778db39b2c286404cb37e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-21T22:46:43Z","title_canon_sha256":"4726a4440611a07c03a75428143f09f0320c8947ac8e509af65dc4571f4d6830"},"schema_version":"1.0","source":{"id":"2409.14257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.14257","created_at":"2026-07-05T09:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"2409.14257v2","created_at":"2026-07-05T09:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14257","created_at":"2026-07-05T09:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"XE5SQVWVOFEQ","created_at":"2026-07-05T09:40:42Z"},{"alias_kind":"pith_short_16","alias_value":"XE5SQVWVOFEQNAU2","created_at":"2026-07-05T09:40:42Z"},{"alias_kind":"pith_short_8","alias_value":"XE5SQVWV","created_at":"2026-07-05T09:40:42Z"}],"graph_snapshots":[{"event_id":"sha256:2b5da437e71cd904d4003dc72113b52240e39a6e5ff3acfab797134d0b3f3b59","target":"graph","created_at":"2026-07-05T09:40:42Z","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/2409.14257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A tight $\\ell$-cycle minus an edge $C_\\ell^-$ is the $3$-graph on the vertex set $[\\ell]$, where any three consecutive vertices in the string $123\\ldots\\ell 1$ form an edge. We show that for every $\\ell\\ge 5$, $\\ell$ not divisible by $3$, the extremal number is\n  $\n  ex\\left(C_\\ell^-,n\\right)=\\tfrac1{24}n^3+O(n\\ln n)=\\left(\\tfrac14+o(1)\\right){n\\choose 3}.\n  $\n  We determine the extremal graph up to $O(n)$ edge edits.","authors_text":"Bernard Lidicky, Connor Mattes, Florian Pfender","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-21T22:46:43Z","title":"The Hypergraph Tur\\'{a}n Densities of Tight Cycles Minus an Edge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14257","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":"sha256:81f4a5d1565745c6dc49588317800be423c712114b4127505128040779673e93","target":"record","created_at":"2026-07-05T09:40:42Z","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":"360799bfc09525b7eae299a01294a76978e29bc7727778db39b2c286404cb37e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-21T22:46:43Z","title_canon_sha256":"4726a4440611a07c03a75428143f09f0320c8947ac8e509af65dc4571f4d6830"},"schema_version":"1.0","source":{"id":"2409.14257","kind":"arxiv","version":2}},"canonical_sha256":"b93b2856d5714906829a75c94548f329096da676298e3302d1c3744e3baffffe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b93b2856d5714906829a75c94548f329096da676298e3302d1c3744e3baffffe","first_computed_at":"2026-07-05T09:40:42.550652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:42.550652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"viD0lmcGhIxr1AE3spuKopaY7UCK8I9F0Julj2nqiCN5MgdixbYUhdB0GO7IH5vxM3p8GjPOy+eGUOht4rQhCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:42.551160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.14257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81f4a5d1565745c6dc49588317800be423c712114b4127505128040779673e93","sha256:2b5da437e71cd904d4003dc72113b52240e39a6e5ff3acfab797134d0b3f3b59"],"state_sha256":"64e0e970da02e393fe0c4305d93b65e5cce6001fa234372d036ed189589175d4"}