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We extend Cerri's works by applying recent dynamical results of Lindenstrauss and Wang. In particular, the following facts are proved:\n  (1) For any number field $K$ of unit rank 3 or higher, $M(K)$ is isolated and attained and Cerri's algorithm computes $M(K)$ in finite time.\n "},"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":"1207.5101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-21T05:11:53Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"32bdd12757ebd3db510eecbb362b60a06c0116737c4f9466f12077640b8635bb","abstract_canon_sha256":"7db12e6377ed7999f04e1d40ff23fae09592554778fe0a14bfcef80eab98f6ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:24.594558Z","signature_b64":"BMXiV4F/ThiehzdEGP0cifkVbeuP1bqqAuHY9hGrgOMGm1RwOGYpSmjBqKIEIV04T9tdJPc13/3mL5xoypiFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f856ccc0b15af3edefa82a5e57ac96d37e026f4c7663f86c2216e3cb4bde6cd","last_reissued_at":"2026-05-18T03:50:24.593843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:24.593843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Euclidean Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Uri Shapira, Zhiren Wang","submitted_at":"2012-07-21T05:11:53Z","abstract_excerpt":"The Euclidean minimum $M(K)$ of a number field $K$ is an important numerical invariant that indicates whether $K$ is norm-Euclidean. 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