{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IZS7JCIKOVECAKICRLKBLGAQMG","short_pith_number":"pith:IZS7JCIK","schema_version":"1.0","canonical_sha256":"4665f4890a75482029028ad415981061915818237ea1f4d99dba0bc695b68cc5","source":{"kind":"arxiv","id":"1501.01913","version":2},"attestation_state":"computed","paper":{"title":"Tur\\'an Number of Generalized Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liana Yepremyan, Sergey Norin","submitted_at":"2015-01-08T17:47:46Z","abstract_excerpt":"The family $\\Sigma_r$ consists of all $r$-graphs with three edges $D_1,D_2,D_3$ such that $|D_1\\cap D_2|=r-1$ and $D_1 \\triangle D_2 \\subseteq D_3$. A generalized triangle, $\\mathcal{T}_r \\in \\Sigma_r$ is an $r$-graph on $\\{1,2,\\ldots,2r-1\\}$ with three edges $D_1, D_2, D_3$, such that $D_1=\\{1,2,\\dots,r-1, r\\}, D_2= \\{1, 2, \\dots, r-1, r+1 \\}$ and $D_3 = \\{r, r+1, \\dots, 2r-1\\}.$ Frankl and F\\\"{u}redi conjectured that for all $r\\geq 4$, $ex(n,\\Sigma_r) = ex(n,\\mathcal{T}_r )$ for all sufficiently large $n$ and they also proved it for $r=3$. Later, Pikhurko showed that the conjecture holds for"},"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":"1501.01913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-08T17:47:46Z","cross_cats_sorted":[],"title_canon_sha256":"b0bbcb61d79a08e50d3240afef97d2bb7ad6e74c0a60b141ae77b4475e30b166","abstract_canon_sha256":"cff2d28794430689ed15d09e20095323efbd81ca7e8448d6f546b7e03f300627"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:57.289656Z","signature_b64":"HSt/EataiX825QLn+vZ8hkmIBWEfo5pGPEO+XznmpSKJXcBSAwDzQxd+VyYGafMKyNbqjcfIJXipegDQVxHUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4665f4890a75482029028ad415981061915818237ea1f4d99dba0bc695b68cc5","last_reissued_at":"2026-05-18T01:34:57.289018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:57.289018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tur\\'an Number of Generalized Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liana Yepremyan, Sergey Norin","submitted_at":"2015-01-08T17:47:46Z","abstract_excerpt":"The family $\\Sigma_r$ consists of all $r$-graphs with three edges $D_1,D_2,D_3$ such that $|D_1\\cap D_2|=r-1$ and $D_1 \\triangle D_2 \\subseteq D_3$. A generalized triangle, $\\mathcal{T}_r \\in \\Sigma_r$ is an $r$-graph on $\\{1,2,\\ldots,2r-1\\}$ with three edges $D_1, D_2, D_3$, such that $D_1=\\{1,2,\\dots,r-1, r\\}, D_2= \\{1, 2, \\dots, r-1, r+1 \\}$ and $D_3 = \\{r, r+1, \\dots, 2r-1\\}.$ Frankl and F\\\"{u}redi conjectured that for all $r\\geq 4$, $ex(n,\\Sigma_r) = ex(n,\\mathcal{T}_r )$ for all sufficiently large $n$ and they also proved it for $r=3$. 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