{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G3POQNL2DS42WT42L647GRCLVB","short_pith_number":"pith:G3POQNL2","schema_version":"1.0","canonical_sha256":"36dee8357a1cb9ab4f9a5fb9f3444ba8713280cc03762836989b018c7eff4662","source":{"kind":"arxiv","id":"1807.11211","version":1},"attestation_state":"computed","paper":{"title":"The Tur\\'an number of Berge-K_4 in triple systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andras Gyarfas","submitted_at":"2018-07-30T07:45:26Z","abstract_excerpt":"A Berge-$K_4$ in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\\{e_{ij}: 1\\le i< j \\le 4\\}$ such that $\\{v_i,v_j\\}\\subset e_{ij}$ for every $1\\le i<j\\le 4$. We denote by $\\cal{B}$ the set of Berge-$K_4$ configurations. A triple system is $\\cal{B}$-free if it does not contain any member of $\\cal{B}$. We prove that the maximum number of triples in a $\\cal{B}$-free triple system on $n\\ge 6$ points is obtained by the balanced complete $3$-partite triple system: all triples $\\{abc: a\\in A, b\\in B, c\\in C\\}$ where $A,B,C$ is a partition of $n$ poin"},"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":"1807.11211","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T07:45:26Z","cross_cats_sorted":[],"title_canon_sha256":"9b1424e86e32ae87c4c4f2b2db57ed14e6dad9b06349cba46e568e26e3a1a6fe","abstract_canon_sha256":"ce47e4c181cab1528ec7b10305aa675a18a9a9d9f00ef4037c76ea8a419af2d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.622163Z","signature_b64":"m9CzKN3UpoJ0nWCWOM3yS0umsLVArhbtURFoqwf9mHH9XuKNaf2Wc1NqEbCcWt/Yyr3ndbfu/zjEuxCq5WukCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36dee8357a1cb9ab4f9a5fb9f3444ba8713280cc03762836989b018c7eff4662","last_reissued_at":"2026-05-18T00:09:32.621292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.621292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tur\\'an number of Berge-K_4 in triple systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andras Gyarfas","submitted_at":"2018-07-30T07:45:26Z","abstract_excerpt":"A Berge-$K_4$ in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\\{e_{ij}: 1\\le i< j \\le 4\\}$ such that $\\{v_i,v_j\\}\\subset e_{ij}$ for every $1\\le i<j\\le 4$. We denote by $\\cal{B}$ the set of Berge-$K_4$ configurations. A triple system is $\\cal{B}$-free if it does not contain any member of $\\cal{B}$. We prove that the maximum number of triples in a $\\cal{B}$-free triple system on $n\\ge 6$ points is obtained by the balanced complete $3$-partite triple system: all triples $\\{abc: a\\in A, b\\in B, c\\in C\\}$ where $A,B,C$ is a partition of $n$ poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11211","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":"1807.11211","created_at":"2026-05-18T00:09:32.621451+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11211v1","created_at":"2026-05-18T00:09:32.621451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11211","created_at":"2026-05-18T00:09:32.621451+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3POQNL2DS42","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3POQNL2DS42WT42","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3POQNL2","created_at":"2026-05-18T12:32:25.280505+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/G3POQNL2DS42WT42L647GRCLVB","json":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB.json","graph_json":"https://pith.science/api/pith-number/G3POQNL2DS42WT42L647GRCLVB/graph.json","events_json":"https://pith.science/api/pith-number/G3POQNL2DS42WT42L647GRCLVB/events.json","paper":"https://pith.science/paper/G3POQNL2"},"agent_actions":{"view_html":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB","download_json":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB.json","view_paper":"https://pith.science/paper/G3POQNL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11211&json=true","fetch_graph":"https://pith.science/api/pith-number/G3POQNL2DS42WT42L647GRCLVB/graph.json","fetch_events":"https://pith.science/api/pith-number/G3POQNL2DS42WT42L647GRCLVB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB/action/storage_attestation","attest_author":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB/action/author_attestation","sign_citation":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB/action/citation_signature","submit_replication":"https://pith.science/pith/G3POQNL2DS42WT42L647GRCLVB/action/replication_record"}},"created_at":"2026-05-18T00:09:32.621451+00:00","updated_at":"2026-05-18T00:09:32.621451+00:00"}