{
  "abstract": "We prove that Cavallar and Lemmermeyer's list of $58$ norm-Euclidean complex cubic fields is complete. The proof combines a classical discriminant bound with exact certificates of non-Euclideanity. The unit action reduces their verification to finite lattice enumeration with rigorous interval arithmetic. An independent covering computation confirms norm-Euclideanity for the $58$ fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38073",
  "author_total": 3,
  "authors": [
    {
      "name": "Gustav Kjærbye Bagger"
    },
    {
      "name": "Andrew R. Booker"
    },
    {
      "name": "Tim Trudgian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efdpvdq93ggen.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38073",
  "fulltext_url": null,
  "id": "efdpvdq93ggen",
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  "landing_url": "https://arxiv.org/abs/2610.38073",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efdpvdq93ggen.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38073"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Determining norm-Euclidean complex cubic fields",
  "title_text": "Determining norm-Euclidean complex cubic fields",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/efdpvdq93ggen",
  "venue": "arXiv",
  "versions": []
}