{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YWSJIEDHIN7BHFVZCKNY5PF353","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":"61bba632a9de6049f3a23f2b950885c37573fd12ce51668951bb250461b107b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-26T22:54:26Z","title_canon_sha256":"627507d9a3a9e438fba04afedf6eb39553ed96e646ac6ab4662a5b5dce5cfbac"},"schema_version":"1.0","source":{"id":"1902.10258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10258","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10258v1","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10258","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"YWSJIEDHIN7B","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YWSJIEDHIN7BHFVZ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YWSJIEDH","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:589222fb75bbf52933c5379fb57c6ea5ebe0bf204920398b028865e0bc8f8b50","target":"graph","created_at":"2026-05-17T23:52:31Z","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":"Let $t$ be an integer such that $t\\geq 2$. Let $K_{2,t}^{(3)}$ denote the triple system consisting of the $2t$ triples $\\{a,x_i,y_i\\}$, $\\{b,x_i,y_i\\}$ for $1 \\le i \\le t$, where the elements $a, b, x_1, x_2, \\ldots, x_t,$ $y_1, y_2, \\ldots, y_t$ are all distinct. Let $ex(n,K_{2,t}^{(3)})$ denote the maximum size of a triple system on $n$ elements that does not contain $K_{2,t}^{(3)}$. This function was studied by Mubayi and Verstra\\\"ete, where the special case $t=2$ was a problem of Erd\\H{o}s that was studied by various authors.\n  Mubayi and Verstra\\\"ete proved that $ex(n,K_{2,t}^{(3)})<t^4\\b","authors_text":"Abhishek Methuku, Beka Ergemlidze, Tao Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-26T22:54:26Z","title":"New bounds for a hypergraph Bipartite Tur\\'an problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10258","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:bd6073e10b35981403cb473c91f2fa82b7e39830b6b34c95712dcb274f070037","target":"record","created_at":"2026-05-17T23:52:31Z","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":"61bba632a9de6049f3a23f2b950885c37573fd12ce51668951bb250461b107b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-26T22:54:26Z","title_canon_sha256":"627507d9a3a9e438fba04afedf6eb39553ed96e646ac6ab4662a5b5dce5cfbac"},"schema_version":"1.0","source":{"id":"1902.10258","kind":"arxiv","version":1}},"canonical_sha256":"c5a4941067437e1396b9129b8ebcbbeec6054b92cd161b8507bd0250fd5873da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a4941067437e1396b9129b8ebcbbeec6054b92cd161b8507bd0250fd5873da","first_computed_at":"2026-05-17T23:52:31.363845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:31.363845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3BuhqXUsT6DGGOw0BdlvTAZyj7ClQBDt4ffYjLaaXcoip9BdAAq11qBQ089E3QE63ro4EOiIKWJf7c95vec/CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:31.364228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd6073e10b35981403cb473c91f2fa82b7e39830b6b34c95712dcb274f070037","sha256:589222fb75bbf52933c5379fb57c6ea5ebe0bf204920398b028865e0bc8f8b50"],"state_sha256":"0bd0d6e5844d5f4a68a3a962d302a4ef93daf223f08d400fd0bea6ed8c193c71"}