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We actually prove a general result: define \\[\n  f(d):=\\frac{1-\\sqrt{(4d-1)/3}}2. \\] We prove that "},"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":"2607.23748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-26T16:49:30Z","cross_cats_sorted":[],"title_canon_sha256":"d805b529da5d085337c8123b34c98e83af82678b3999dc6a0ebd64cd14b51592","abstract_canon_sha256":"260bb960157981f8afa42f9cbf4884a70b147815a91318a339d22011450ccbb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:09.217725Z","signature_b64":"CMeIIghtOV/vpUqEzMaYPYqF0pHu4IcBDxfKR+QadvKe2Tb/r8iHspkPS09oqeN0uwLVHClsZs3JYZXfskF+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faba9366c9d1b59ef74a692ef54e1b580c311d650aaa5917d7fd96b1f90c423e","last_reissued_at":"2026-07-28T01:23:09.216833Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:09.216833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Diagonal Thresholds for Tight Hamilton Cycles in Uniformly Dense $3$-Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Hao Lin, Wenling Zhou","submitted_at":"2026-07-26T16:49:30Z","abstract_excerpt":"A $3$-uniform hypergraph (or $3$-graph) $H$ on $n$ vertices is \\emph{$(n,d,\\mu)$-dense} if $e_H(X,Y,Z)\\ge d|X||Y||Z|-\\mu n^3$ for all $X,Y,Z\\subseteq V(H)$. 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