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Ciolan, Garc\\'ia-S\\'anchez, and Moree conjectured that for every embedding dimension at least $4$, there exists some numerical semigroup which is symmetric but not cyclotomic. We affirm this conjecture by giving an infinite class of numerical semigroup families $S_{n, t}$, which for every fixed $t$ is symmetric but not cyclotomic when $n\\ge \\max(8(t+1)^3,40(t+2))$ and then verify through a finite case check that 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":"1707.00782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-03T23:42:25Z","cross_cats_sorted":[],"title_canon_sha256":"3407e2fd7731e6c4dfe3f76c318a1d655f0ea4a74bff9cf88c97515a53b2fe34","abstract_canon_sha256":"a2235041ef505bdbbef49d1b755e789db0c714d84897043c0652e81bed562c47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:48.381094Z","signature_b64":"luzHCvoqNGvMdqPL/RNry88duGXvkVPynzpHIMd804tirT9jRwW7IpEVeDKfJL6sGXrOeovau+MFDka9R+5PBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"870410ca4f4b28c29c99d43848b4d96ff43a807da8511f970027f2a8ea05a5c8","last_reissued_at":"2026-05-18T00:40:48.380402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:48.380402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Symmetric But Not Cyclotomic Numerical Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Stoner, Mehtaab Sawhney","submitted_at":"2017-07-03T23:42:25Z","abstract_excerpt":"A numerical semigroup is called cyclotomic if its corresponding numerical semigroup polynomial $P_S(x)=(1-x)\\sum_{s\\in S}x^s$ is expressable as the product of cyclotomic polynomials. Ciolan, Garc\\'ia-S\\'anchez, and Moree conjectured that for every embedding dimension at least $4$, there exists some numerical semigroup which is symmetric but not cyclotomic. 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