{
  "abstract": "FINDING: The Monster Lie algebra is a generalized Kac-Moody algebra whose denominator identity encodes the elliptic modular function \\(j(q)\\), and its construction via vertex algebras links the Monster group to a rank-2 hyperbolic lattice with Weyl vector \\((0,1)\\). MATH: - Denominator identity: \\(j(p) - j(q) = p^{-1} \\prod_{m>0, n\\in\\mathbb{Z}} (1 - p^m q^n)^{c(mn)}\\), where \\(c(k)\\) are coefficients of \\(j(q) - 744 = q^{-1} + 196884q + \\dots\\) (Frenkel–Lepowsky–Meurman; Borcherds). - Monster Lie algebra is graded by \\(\\mathbb{Z}^2\\) with bilinear form \\(\\langle (m,n), (m',n') \\rangle = mn' + nm'\\) — a hyperbolic lattice of signature \\((1,1)\\). - Weyl vector \\(\\rho = (0,1)\\); simple roots are \\((1,-n)\\) for \\(n \\in \\mathbb{Z}\\) and \\((1,1)\\). - Borcherds' proof uses the no-ghost theorem from bosonic string theory in 26 dimensions, with the Leech lattice (24-dimensional even unimodular) providing the necessary positive-definite subspace. CONNECTION: - The hyperbolic latti\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
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  "bibtex": "https://research.draconitic.com/paper/2p7naw31tnx92.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635419",
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  "id": "2p7naw31tnx92",
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  "landing_url": "https://zenodo.org/records/23635419",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2p7naw31tnx92.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635419",
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      "url": "https://zenodo.org/records/23635419"
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  "subjects": [],
  "title": "Monster Lie Algebra's Denominator Identity Encodes the Elliptic Modular Function j(q) — E8 Intelligence Research",
  "title_text": "Monster Lie Algebra's Denominator Identity Encodes the Elliptic Modular Function j(q) — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/2p7naw31tnx92",
  "venue": "Zenodo",
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}