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Let $e(X)$ be the so-called ``stabilization index'' of $X$, defined by Halle and Nicaise as the lcm of the multiplicities of the ``principal'' irreducible components of a minimal regular snc-model of $X$.\n  It is known that if $L/K$ is tame, then $e(X) = e(L/K)$. If one drops the tameness assumption, but instead assumes that $X$ has index one and potentially multiplicative 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":"2112.14728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-29T18:35:45Z","cross_cats_sorted":[],"title_canon_sha256":"15da6490e5368e4b624f6908c029632d338fcbb6e653a7bb86ebf6f5181bb940","abstract_canon_sha256":"10254535ade8206017123f9a0fe7c5851faa21062d39afc13c79f6beef7d45a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:05:02.978511Z","signature_b64":"y16BMWCE19h45j5z2dU6/Tv9qzsbv4vCjcUh7tdLolSmhuhaAPNKMHhYJateiwuW5axJD5as6qX2KweWnFABBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"012626be0c58124e003ec5b26aac63460806a6535957529c1875e70986d51fc7","last_reissued_at":"2026-06-02T03:05:02.978017Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:05:02.978017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilization indices of potentially Mumford curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrew Obus, Daniele Turchetti","submitted_at":"2021-12-29T18:35:45Z","abstract_excerpt":"Let $X$ be a smooth projective curve over a complete discretely valued field $K$. Let $L/K$ be the minimal extension such that $X \\times_K L$ has a semi-stable model, and write $e(L/K)$ for the ramification index of $L/K$. Let $e(X)$ be the so-called ``stabilization index'' of $X$, defined by Halle and Nicaise as the lcm of the multiplicities of the ``principal'' irreducible components of a minimal regular snc-model of $X$.\n  It is known that if $L/K$ is tame, then $e(X) = e(L/K)$. 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