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Such cycles are said to be linear when $\\ell = 1$, and nonlinear when $\\ell > 1$. We determine the sharp threshold for nonlinear Hamiltonian cycles and show that for all $r > \\ell > 1$, the threshold $p^*_{r, \\ell} (n)$ for the appearance of a Hamiltonian $\\ell$-cycle in t"},"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":"1906.05142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T13:58:57Z","cross_cats_sorted":[],"title_canon_sha256":"1a4ec94d8948e3635beacb9acac7447cb91988eed94d5bebeb0fac9a0369fd84","abstract_canon_sha256":"e82e208858886ae2beeef7a79f7f59fddb3732ebf45790907b3504ceb9eac127"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:29.353691Z","signature_b64":"lWkfkgHN6RjzLtBMvzyqm6XJ/GJ1AuGirJwiIF5eJldENzccS8fFftH5WQBJASkBVMP4oXW8XyZaFGcdGxiuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"022d72e1c07d729e066b254284521af4a9dc663d8beacb941c3d4ccb6b8f453c","last_reissued_at":"2026-05-17T23:43:29.353035Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:29.353035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp thresholds for nonlinear Hamiltonian cycles in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhargav Narayanan, Mathias Schacht","submitted_at":"2019-06-12T13:58:57Z","abstract_excerpt":"For positive integers $r > \\ell$, an $r$-uniform hypergraph is called an $\\ell$-cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of $r$ consecutive vertices, and such that every pair of consecutive edges (in the natural ordering of the edges) intersect in precisely $\\ell$ vertices. 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