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A second result gives a bound in terms of the toric degree of the subvariety.\n  As a consequence, we prove the conjectures of Ruppert and of Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respective"},"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":"1509.05898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-19T14:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"f9e9a04c13a162a168e297439d8e744ccc61210f850c7b39b0e1e7798b90cca2","abstract_canon_sha256":"dffcaf377505b59473401360bdfbfc5606cfe1d1523d866d3685d9b0475e9f65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:36.430628Z","signature_b64":"unF2YRDhld/qNVQXwKgShK3HnrHrMu5uHzZxPF1SD8W3nnvo8mHEImAFJH4Ln/EWcR6EJODuch2atF9iHPwrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a942dfd4fb76466fa88e23ea8fb1b65a773005c3db6677c46e48d99d5d8ade2","last_reissued_at":"2026-05-18T01:32:36.430010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:36.430010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of maximal torsion cosets in subvarieties of tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C\\'esar Mart\\'inez","submitted_at":"2015-09-19T14:28:35Z","abstract_excerpt":"We present sharp bounds on the number of maximal torsion cosets in a subvariety of the complex algebraic torus $\\mathbb{G}_{\\textrm{m}}^n$. 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