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Given a hypergraph $\\mathcal H$, for a $d$-subset $A\\subseteq V(\\mathcal H)$, we denote by $d_{\\mathcal H}(A)$ the number of distinct \\emph{edges} $f\\in E(\\mathcal H)$ for which $A\\subseteq f$, and set $\\delta_d(\\mathcal H)$ to be the minimum $d_{\\mathcal H}(A)$ over all $A\\subseteq V(\\mathcal H)$ of size $d$. We show that if a $k$-uniform hypergraph on $n$ vertices $\\mathcal H$ satisfies $\\delta_{k-1}(\\mathcal H)\\geq \\alpha n$ for some $\\alpha>1/2$, then for every $\\ell<k/2$ $\\mathca"},"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":"1406.3091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-12T00:49:54Z","cross_cats_sorted":[],"title_canon_sha256":"f8d36d17e2f25a1ba3013fa541e98f25c56b5dc99644d8b5788c6064ff452460","abstract_canon_sha256":"a65bbbb327d9437bf7ee2fe1dc282dac294eec993e9d8cc716a33b9be4a681ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:12.588155Z","signature_b64":"V9P1XEPGItLK1+ihoStKDJCFllBri6ZJp9DC7+Hl7IYiOnQpazHuosLh5Bao+r6si7LGYZocb6eXv0js+dHPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"769a88b13cc49deaaa389211c63f06b46c5bed3cb6be6af0efada48781071c48","last_reissued_at":"2026-05-18T02:20:12.587732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:12.587732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting and packing Hamilton $\\ell$-cycles in dense hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Ferber, Benny Sudakov, Michael Krivelevich","submitted_at":"2014-06-12T00:49:54Z","abstract_excerpt":"We consider problems about packing and counting Hamilton $\\ell$-cycles in hypergraphs of large minimum degree. 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