{
  "abstract": "We establish that the R12 rendering algebra of Array Cosmology carries a natural adelic structure dictated by the prime factorisation 12 = 2 2 × 3. Eleven A-layer results are proved (using only standard number theory): ten theorems and one corollary.\n\n(1) The structure constant ω = e 2πi/12 = ζ12 defines the cyclotomic field Q(ζ12) whose Galois group Gal(Q(ζ12)/Q) ∼= (Z/12Z)\n\n∗ ∼= Z2 × Z2 has four elements corresponding to the four Volma types of R12.\n\n(2) The four Dirichlet characters mod 12 define four L-functions; the special value L(1, χ1) = π/(2√3) (where χ1 is the lift of the primitive character χ−3 to mod 12) provides a number-theoretic invariant of the electroweak sector, while the\n\nWeinberg angle sin2 θW = ln 2/3 is independently derived from the Landauer principle (Paper V).\n\n(3) The tensor factorisation M3(C) ⊗ M4(C) = M12(C) is the algebraic realisation of Rankin-Selberg functoriality GL(3) × GL(4) → GL(12).\n\n(4) The ramification structure of Q(ζ12) determines the gauge hierarchy: p = 3 ramified → SU(3)C, p = 2 ramified → SU(2)L × U(1)Y, p ≥ 5 unramified → energy desert.\n\n(5) The Z3 centre obstruction (ω3 residual phase) is the Artin conductor at p = 3, providing the number-theoretic origin of colour confinement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ywcj7ds49g8b.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603559",
  "fulltext_url": null,
  "id": "9ywcj7ds49g8b",
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  "landing_url": "https://zenodo.org/records/23603559",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "pdf_url": "https://zenodo.org/api/records/23603559/files/Lim_ArrayCosmology_AdelicLanglands_2026_v5.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ywcj7ds49g8b.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:58Z",
      "native_id": "23603559",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603559"
    }
  ],
  "subjects": [],
  "title": "The Adelic Structure of the R12 Rendering Algebra: Ramification, L-Functions, and the Standard Model Gauge Hierarchy",
  "title_text": "The Adelic Structure of the R12 Rendering Algebra: Ramification, L-Functions, and the Standard Model Gauge Hierarchy",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:58Z",
  "url": "https://research.draconitic.com/paper/9ywcj7ds49g8b",
  "venue": "Zenodo",
  "versions": []
}