{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VRQQSXXFKY33AI3SBDX5PCSNGN","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":"b879b2501111633ed5ae5736a96408848a1e77ce27ddfbf5508c5b3389fee336","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-18T09:18:49Z","title_canon_sha256":"5f764bb7be343abe1b71b372ff4559c9080ab81fb0c20636e182738ea4a52d67"},"schema_version":"1.0","source":{"id":"2309.09603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.09603","created_at":"2026-07-05T06:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"2309.09603v1","created_at":"2026-07-05T06:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.09603","created_at":"2026-07-05T06:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"VRQQSXXFKY33","created_at":"2026-07-05T06:51:41Z"},{"alias_kind":"pith_short_16","alias_value":"VRQQSXXFKY33AI3S","created_at":"2026-07-05T06:51:41Z"},{"alias_kind":"pith_short_8","alias_value":"VRQQSXXF","created_at":"2026-07-05T06:51:41Z"}],"graph_snapshots":[{"event_id":"sha256:a25a9d81b856935172957942568f45b35264b7fedb7f1d61dd9540b806a276ae","target":"graph","created_at":"2026-07-05T06:51:41Z","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/2309.09603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The generalized Tur\\'an number $\\ex(n,K_s,F)$ denotes the maximum number of copies of $K_s$ in an $n$-vertex $F$-free graph. Let $kF$ denote $k$ disjoint copies of $F$. Gerbner, Methuku and Vizer [DM, 2019, 3130-3141] gave a lower bound for $\\ex(n,K_3,2C_5)$ and obtained the magnitude of $\\ex(n, K_s, kK_r)$. In this paper, we determine the exact value of $\\ex(n,K_3,2C_5)$ and described the unique extremal graph for large $n$. Moreover, we also determine the exact value of $\\ex(n,K_r,(k+1)K_r)$ which generalizes some known results.","authors_text":"Ervin Gyori, Fangfang Zhang, Xiutao Zhu, Yaojun Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-18T09:18:49Z","title":"Maximum cliques in a graph without disjoint given subgraph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.09603","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:a2713dce0b4081d425f890619f695d7ee51535d90d8958c28dd242b6f3fe8116","target":"record","created_at":"2026-07-05T06:51:41Z","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":"b879b2501111633ed5ae5736a96408848a1e77ce27ddfbf5508c5b3389fee336","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-18T09:18:49Z","title_canon_sha256":"5f764bb7be343abe1b71b372ff4559c9080ab81fb0c20636e182738ea4a52d67"},"schema_version":"1.0","source":{"id":"2309.09603","kind":"arxiv","version":1}},"canonical_sha256":"ac61095ee55637b0237208efd78a4d33417d33229c7c646cb611992bac93db59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac61095ee55637b0237208efd78a4d33417d33229c7c646cb611992bac93db59","first_computed_at":"2026-07-05T06:51:41.757866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:51:41.757866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+YWyjFICBS4C9pJwfCCuE7qnXhAcOfdDnHWGWeJf9vcKEUeHoST+Jxok3X7N0i+eIsIcWLpxUeJqnNqeo4EHCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:51:41.758294Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.09603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2713dce0b4081d425f890619f695d7ee51535d90d8958c28dd242b6f3fe8116","sha256:a25a9d81b856935172957942568f45b35264b7fedb7f1d61dd9540b806a276ae"],"state_sha256":"6a305294146cb3823275e613360a068239b605cb22c6dd5343d1be9a261c4659"}