{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G4JZXG6727VDHEF7WCHUKHPIRG","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":"cecc6da2e397280dd28afcd2213aa8e78376b0073b57eb626c3e424c639e1b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-19T17:36:20Z","title_canon_sha256":"3876c81eda9fd336038f7ff698b96c77a866ebb3db55c3bd2950189940d43df2"},"schema_version":"1.0","source":{"id":"1712.07072","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07072","created_at":"2026-05-18T00:14:22Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07072v2","created_at":"2026-05-18T00:14:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07072","created_at":"2026-05-18T00:14:22Z"},{"alias_kind":"pith_short_12","alias_value":"G4JZXG6727VD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G4JZXG6727VDHEF7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G4JZXG67","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:40e1c61ad3f0b9084ec1ccd0e45d48733440c7feac656afd63d8dbe3909272fd","target":"graph","created_at":"2026-05-18T00:14:22Z","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":"Given two graphs $H$ and $F$, the maximum possible number of copies of $H$ in an $F$-free graph on $n$ vertices is denoted by $ex(n,H,F)$. We investigate the function $ex(n,H,kF)$, where $kF$ denotes $k$ vertex disjoint copies of a fixed graph $F$. Our results include cases when $F$ is a complete graph, cycle or a complete bipartite graph.","authors_text":"Abhishek Methuku, D\\'aniel Gerbner, M\\'at\\'e Vizer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-19T17:36:20Z","title":"Generalized Tur\\'an problems for disjoint copies of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07072","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":"sha256:49cad1c5e90635acda64596eddcfbefdf996c5d8e040b9075407f42d0fffccca","target":"record","created_at":"2026-05-18T00:14:22Z","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":"cecc6da2e397280dd28afcd2213aa8e78376b0073b57eb626c3e424c639e1b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-19T17:36:20Z","title_canon_sha256":"3876c81eda9fd336038f7ff698b96c77a866ebb3db55c3bd2950189940d43df2"},"schema_version":"1.0","source":{"id":"1712.07072","kind":"arxiv","version":2}},"canonical_sha256":"37139b9bdfd7ea3390bfb08f451de8899d791e90336ceae53d1508ead64517da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37139b9bdfd7ea3390bfb08f451de8899d791e90336ceae53d1508ead64517da","first_computed_at":"2026-05-18T00:14:22.012027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:22.012027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5fhVq7S5uZW3rbVgD2v7hcrx9s9/oC/cnL9ir1C1Fl90wISksOwLHwekLR0mzJZK4G/h4wmWWv183b2G5i9xBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:22.012635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49cad1c5e90635acda64596eddcfbefdf996c5d8e040b9075407f42d0fffccca","sha256:40e1c61ad3f0b9084ec1ccd0e45d48733440c7feac656afd63d8dbe3909272fd"],"state_sha256":"fe19f7cab18413035a565178bf9fb3831aacb67f0cc30b5e75927e721f8872fc"}