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In our construction we can have $p_i>h(p_1p_2\\ldots p_{i-1})$ for all $i=1,2,\\ldots,\\omega$ and any function $h:\\mathbb{R}_+\\to\\mathbb{R}_+$."},"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":"1407.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"d0bc2f1b6a65843d85631ef845bff98686a349b319bfc6457250c7db9681acb8","abstract_canon_sha256":"bba71cac0adeb31f28f8b40e0c683db2c3b73fa27011956cd4970d6d9aff48a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.962452Z","signature_b64":"NCaYbugZVlER3AGATCGN1KpBoDLvji4/hhzpwcpxVmxgdrP+JyNaTlwtngPkrg82X3z4RlZBDubJpUurOAeZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","last_reissued_at":"2026-05-18T01:11:57.961953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.961953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a generalization of Beiter Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bartlomiej Bzdega","submitted_at":"2014-07-12T07:54:44Z","abstract_excerpt":"We prove that for every $\\varepsilon>0$ and a nonnegative integer $\\omega$ there exist primes $p_1,p_2,\\ldots,p_\\omega$ such that for $n=p_1p_2\\ldots p_\\omega$ the height of the cyclotomic polynomial $\\Phi_n$ is at least $(1-\\varepsilon)c_\\omega M_n$, where $M_n=\\prod_{i=1}^{\\omega-2}p_i^{2^{\\omega-1-i}-1}$ and $c_\\omega$ is a constant depending only on $\\omega$; furthermore $\\lim_{\\omega\\to\\infty}c_\\omega^{2^{-\\omega}}\\approx0.71$. 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