{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YWSJIEDHIN7BHFVZCKNY5PF353","short_pith_number":"pith:YWSJIEDH","schema_version":"1.0","canonical_sha256":"c5a4941067437e1396b9129b8ebcbbeec6054b92cd161b8507bd0250fd5873da","source":{"kind":"arxiv","id":"1902.10258","version":1},"attestation_state":"computed","paper":{"title":"New bounds for a hypergraph Bipartite Tur\\'an problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Beka Ergemlidze, Tao Jiang","submitted_at":"2019-02-26T22:54:26Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.10258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-26T22:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"627507d9a3a9e438fba04afedf6eb39553ed96e646ac6ab4662a5b5dce5cfbac","abstract_canon_sha256":"61bba632a9de6049f3a23f2b950885c37573fd12ce51668951bb250461b107b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:31.364228Z","signature_b64":"3BuhqXUsT6DGGOw0BdlvTAZyj7ClQBDt4ffYjLaaXcoip9BdAAq11qBQ089E3QE63ro4EOiIKWJf7c95vec/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a4941067437e1396b9129b8ebcbbeec6054b92cd161b8507bd0250fd5873da","last_reissued_at":"2026-05-17T23:52:31.363845Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:31.363845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New bounds for a hypergraph Bipartite Tur\\'an problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Beka Ergemlidze, Tao Jiang","submitted_at":"2019-02-26T22:54:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10258","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.10258","created_at":"2026-05-17T23:52:31.363901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.10258v1","created_at":"2026-05-17T23:52:31.363901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10258","created_at":"2026-05-17T23:52:31.363901+00:00"},{"alias_kind":"pith_short_12","alias_value":"YWSJIEDHIN7B","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"YWSJIEDHIN7BHFVZ","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"YWSJIEDH","created_at":"2026-05-18T12:33:33.725879+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353","json":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353.json","graph_json":"https://pith.science/api/pith-number/YWSJIEDHIN7BHFVZCKNY5PF353/graph.json","events_json":"https://pith.science/api/pith-number/YWSJIEDHIN7BHFVZCKNY5PF353/events.json","paper":"https://pith.science/paper/YWSJIEDH"},"agent_actions":{"view_html":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353","download_json":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353.json","view_paper":"https://pith.science/paper/YWSJIEDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.10258&json=true","fetch_graph":"https://pith.science/api/pith-number/YWSJIEDHIN7BHFVZCKNY5PF353/graph.json","fetch_events":"https://pith.science/api/pith-number/YWSJIEDHIN7BHFVZCKNY5PF353/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353/action/storage_attestation","attest_author":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353/action/author_attestation","sign_citation":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353/action/citation_signature","submit_replication":"https://pith.science/pith/YWSJIEDHIN7BHFVZCKNY5PF353/action/replication_record"}},"created_at":"2026-05-17T23:52:31.363901+00:00","updated_at":"2026-05-17T23:52:31.363901+00:00"}