{
  "abstract": "Let $δ=xz-yt$. We give an explicit tame factorization of the Anick automorphism $(x+δt,y+δz,z,t)$ of $F[x,y,z,t]$. After a linear change of coordinates, the factorization consists of sixteen elementary automorphisms, all fixing $z$. The proof uses a commutator construction with variables already present in the algebra. A complete list of the elementary factors is included in Section 5. The explicit polynomial factorization identities are defined over $\\ZZ[1/2]$; no conclusion in characteristic $2$ is asserted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11013",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexei Miasnikov"
    },
    {
      "name": "Ivan Shestakov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aptspapz4txx6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11013",
  "fulltext_url": null,
  "id": "aptspapz4txx6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11013",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221189031",
  "pdf_url": "https://arxiv.org/pdf/2610.11013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aptspapz4txx6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.11013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An explicit tame factorization of the four-variable Anick automorphism",
  "title_text": "An explicit tame factorization of the four-variable Anick automorphism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/aptspapz4txx6",
  "venue": "arXiv",
  "versions": []
}