{
  "abstract": "We study the minimal dimension of a nonsingular anisotropic universal quadratic form over a field $F$ of $\\operatorname{char}(F)=2$, which we call the ``$m$-invariant\" of $F$. We show that every even number is the $m$-invariant of some field of characteristic 2, and consider cases when $u(F)$ and $m(F)$ are equal and when they are not.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30502",
  "author_total": 2,
  "authors": [
    {
      "name": "Adam Chapman"
    },
    {
      "name": "Kelly McKinnie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exh9z19m2srht.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30502",
  "fulltext_url": null,
  "id": "exh9z19m2srht",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30502",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214616433",
  "pdf_url": "https://arxiv.org/pdf/2609.30502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exh9z19m2srht.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The $m$-Invariant of Fields of Characteristic 2",
  "title_text": "The m-Invariant of Fields of Characteristic 2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/exh9z19m2srht",
  "venue": "arXiv",
  "versions": []
}