{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QF3FJJOW2GMTMCYIMB73NWWULY","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":"d5645773c8cdb141ca390c516b6f0796f50b6e794a3c024547a5830e07f2067b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-19T13:58:53Z","title_canon_sha256":"b608cf56c5d81bee34bff62a4d993622290685ed759f72807e8df6c4912805e4"},"schema_version":"1.0","source":{"id":"1110.4287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4287","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4287v3","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4287","created_at":"2026-05-18T02:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"QF3FJJOW2GMT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QF3FJJOW2GMTMCYI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QF3FJJOW","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:429174dc5afc18f3faa7d42a7985a40b290e1b84c824a7ab3928d44f92b11558","target":"graph","created_at":"2026-05-18T02:25:11Z","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":"If $\\mathcal{F}$ is a family of graphs then the Tur\\'an density of $\\mathcal{F}$ is determined by the minimum chromatic number of the members of $\\mathcal{F}$.\n  The situation for Tur\\'an densities of 3-graphs is far more complex and still very unclear. Our aim in this paper is to present new exact Tur\\'an densities for individual and finite families of 3-graphs, in many cases we are also able to give corresponding stability results. As well as providing new examples of individual 3-graphs with Tur\\'an densities equal to 2/9,4/9,5/9 and 3/4 we also give examples of irrational Tur\\'an densities","authors_text":"John Talbot, Rahil Baber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-19T13:58:53Z","title":"New Tur\\'an densities for 3-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4287","kind":"arxiv","version":3},"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:d054e4fa5d5cf4aba6ef940aa6384097c0c9e737e4fc3e5c5d589544bf699054","target":"record","created_at":"2026-05-18T02:25:11Z","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":"d5645773c8cdb141ca390c516b6f0796f50b6e794a3c024547a5830e07f2067b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-19T13:58:53Z","title_canon_sha256":"b608cf56c5d81bee34bff62a4d993622290685ed759f72807e8df6c4912805e4"},"schema_version":"1.0","source":{"id":"1110.4287","kind":"arxiv","version":3}},"canonical_sha256":"817654a5d6d199360b08607fb6dad45e1317f4fb754162d79588c10babd9d4ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"817654a5d6d199360b08607fb6dad45e1317f4fb754162d79588c10babd9d4ab","first_computed_at":"2026-05-18T02:25:11.625239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:11.625239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N2UjwCPXilOOFbVVsv8N0+lDmjjm2H7qiPQW0850MehJNlxNBU7XTAJ9KCeNRvmgV5rJJqKvJeRmc6IuQEn0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:11.625688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d054e4fa5d5cf4aba6ef940aa6384097c0c9e737e4fc3e5c5d589544bf699054","sha256:429174dc5afc18f3faa7d42a7985a40b290e1b84c824a7ab3928d44f92b11558"],"state_sha256":"2d934de029c830afe89d791631980282841d817ebf485a9071016cccf472cfe1"}