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Let $X$ be the minimal proper regular model of $C$ over $S$. Let $\\mathrm{Art}\\ (C/K)$ denote the Artin conductor of the $S$-scheme $X$ and let $\\nu (\\Delta_C)$ denote the minimal discriminant of $C$. We prove that $-\\mathrm{Art}\\ (C/K) \\leq \\nu (\\Delta_C)$. The key ingredients are a combinatorial refinement of the discriminant introduced in this paper (called the metric tr"},"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":"1910.08228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-10-18T02:11:14Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7e8de0504f9e1b09fab8866aca6c857e58935ea72db0df413ac80cb438666036","abstract_canon_sha256":"2a5d2fd4ad361ee770e54906ab22dcded6369cacd573880c6d75c9d298b84099"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:26.058806Z","signature_b64":"ilWzruROPFdiyroaL628hxLw7SBI7Qb5l179TIf22XAn5Em5sb7Mlj6Grm0b+mDuPly4s4U2PK8La5jU+4a6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c309e63740925f7e09727e4946505ef330c9cfc4134465fbf362bbd8fdbaeb","last_reissued_at":"2026-07-05T03:09:26.058462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:26.058462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conductors and minimal discriminants of hyperelliptic curves: A comparison in the tame case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Padmavathi Srinivasan","submitted_at":"2019-10-18T02:11:14Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $\\mathrm{char}\\ k > 2g+1$. Let $S = \\mathrm{Spec}\\ R$. Let $X$ be the minimal proper regular model of $C$ over $S$. Let $\\mathrm{Art}\\ (C/K)$ denote the Artin conductor of the $S$-scheme $X$ and let $\\nu (\\Delta_C)$ denote the minimal discriminant of $C$. We prove that $-\\mathrm{Art}\\ (C/K) \\leq \\nu (\\Delta_C)$. 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