{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XTBDFTPPZUT62RLDOABFCTFGOW","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":"ea90d046d4897e536976af946a1f6c095c8f1387a45b50e7716a1374ec87002b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-13T16:55:47Z","title_canon_sha256":"9801b0f11ae7f17426fa7b73f08f0d211044c50c2f3c2044375ad0b4ccfb885a"},"schema_version":"1.0","source":{"id":"1609.03934","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03934","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03934v2","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03934","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"XTBDFTPPZUT6","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XTBDFTPPZUT62RLD","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XTBDFTPP","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:a5a02515446e6cdd45efe5001923a463ff05900232d08b8d83354701e0853606","target":"graph","created_at":"2026-05-18T00:35:51Z","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":"Gy\\'arf\\'as, Gy\\H{o}ri and Simonovits proved that if a $3$-uniform hypergraph with $n$ vertices has no linear cycles, then its independence number $\\alpha \\ge \\frac{2n} {5}$. The hypergraph consisting of vertex disjoint copies of a complete hypergraph $K_5^3$ on five vertices, shows that equality can hold. They asked whether this bound can be improved if we exclude $K_5^3$ as a subhypergraph and whether such a hypergraph is $2$-colorable.\n  In this paper we answer these questions affirmatively. Namely, we prove that if a $3$-uniform linear-cycle-free hypergraph doesn't contain $K_5^3$ as a sub","authors_text":"Abhishek Methuku, Beka Ergemlidze, Ervin Gy\\H{o}ri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-13T16:55:47Z","title":"$3$-uniform hypergraphs and linear cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03934","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":"sha256:7e8d9bda862eaf46089d44b9dc692f751ae4d69592a3ba48841850840943f980","target":"record","created_at":"2026-05-18T00:35:51Z","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":"ea90d046d4897e536976af946a1f6c095c8f1387a45b50e7716a1374ec87002b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-13T16:55:47Z","title_canon_sha256":"9801b0f11ae7f17426fa7b73f08f0d211044c50c2f3c2044375ad0b4ccfb885a"},"schema_version":"1.0","source":{"id":"1609.03934","kind":"arxiv","version":2}},"canonical_sha256":"bcc232cdefcd27ed45637002514ca675bdbd415374aae96da2c97a82194f18f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcc232cdefcd27ed45637002514ca675bdbd415374aae96da2c97a82194f18f2","first_computed_at":"2026-05-18T00:35:51.746307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:51.746307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzdTgC+VTUIdPEkOsJXKtNRWXLST56qRDMNkbDUC6MTpbjeBFHWM0egOZ6Pjht/1uk98Od0T5N9btf84sH4KDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:51.746930Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03934","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e8d9bda862eaf46089d44b9dc692f751ae4d69592a3ba48841850840943f980","sha256:a5a02515446e6cdd45efe5001923a463ff05900232d08b8d83354701e0853606"],"state_sha256":"85ce4a3797d69fa4a282078be4195a6a44187e132f57aa00b459b3caf932e0e5"}