{
  "abstract": "We construct the Conway-Wales lattice from a self-dual even code $C$ over $\\mathbb{Z}_4$ whose binary layers interweave the Hamming codes $\\mathcal{H}_7$ and $\\mathcal{H}_8$. Explicit signed symmetries lift every automorphism of the binary residue, and the full signed code group is the coordinate-frame stabilizer of the Gaussian lattice. An integral reflection in an embedded scaled self-dual sublattice supplies an additional symmetry, from which the classical frame exchange is recovered. Counting intrinsically defined frames determines the full Gaussian isometry group, of order $583\\,704\\,576\\,000$. Its quotient by the four Gaussian scalars is the Rudvalis simple group, and the derived subgroup of a cross stabilizer is the Tits simple group of order $17\\,971\\,200$. The construction, automorphism-group determination, and both simplicity proofs are carried out within the lattice, without assuming the known group orders or using a recognition or classification theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10553",
  "author_total": 1,
  "authors": [
    {
      "name": "Gerald Höhn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x8enthfp7x6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10553",
  "fulltext_url": null,
  "id": "9x8enthfp7x6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10553",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221080756",
  "pdf_url": "https://arxiv.org/pdf/2610.10553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x8enthfp7x6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Conway-Wales lattice and the Rudvalis and Tits groups",
  "title_text": "The Conway-Wales lattice and the Rudvalis and Tits groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/9x8enthfp7x6y",
  "venue": "arXiv",
  "versions": []
}