{
  "abstract": "We express every admissible word as a $\\mathbb{Z}_{(2)}$-linear combination of Hoffman words and explicit confluence relations. This implies that every multiple zeta value is a linear combination of elements of the Hoffman basis with coefficients having odd denominators, as conjectured by Hirose and Sato. Combined with Brown's theorem and Furusho's characterization of the Grothendieck--Teichmüller group $\\mathrm{GRT}$ by confluence relations, our result identifies the de Rham motivic Galois group of mixed Tate motives over $\\mathbb{Z}$ with $\\mathrm{GRT}$ and gives an alternative proof of the Deligne--Drinfeld conjecture, for which a proof was previously presented in the OpenAI Math Release.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23719",
  "author_total": 1,
  "authors": [
    {
      "name": "Minoru Hirose"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/025wdjd7yfwpb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23719",
  "fulltext_url": null,
  "id": "025wdjd7yfwpb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23719",
  "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.NT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7222936838",
  "pdf_url": "https://arxiv.org/pdf/2610.23719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/025wdjd7yfwpb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Confluence relations, Hoffman basis over \\mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture",
  "title_text": "Confluence relations, Hoffman basis over \\mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/025wdjd7yfwpb",
  "venue": "arXiv",
  "versions": []
}