{
  "abstract": "FINDING: Monstrous moonshine is the proven correspondence between the Monster group's irreducible representations and the Fourier coefficients of the modular j-function, with the genus-zero property as the central structural constraint. | MATH: j(τ) = q⁻¹ + 744 + 196884q + 21493760q² + …; Monster order |M| = 808017424794512875886459904961710757005754368000000000 ≈ 8.08×10⁵³; McKay–Thompson series T_g(τ) = Σ Tr(g|V_n) qⁿ⁻¹, each T_g a Hauptmodul for a genus-zero quotient of the upper half-plane; Conway–Norton conjectures (1979) → Borcherds' proof (1992) via vertex operator algebras and the no-ghost theorem. | CONNECTION: The j-function's pole at q=0 and its value j(i)=1728, j(e^{2πi/3})=0 are tied to the elliptic curve's complex multiplication — but the deeper geometric link is the Leech lattice: the Monster is the automorphism group of the Leech lattice modulo ±1, and the Leech lattice is the unique even unimodular lattice in 24 dimensions with no roots. The genus-zero property means e\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "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/8k4p56ngmy9sf.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23446713",
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  "id": "8k4p56ngmy9sf",
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  "language": "eng",
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  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8k4p56ngmy9sf.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:54Z",
      "native_id": "23446713",
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  "title": "Monstrous Moonshine: The Genus-Zero Link Between the Monster Group and Modular j-Function — E8 Intelligence Research",
  "title_text": "Monstrous Moonshine: The Genus-Zero Link Between the Monster Group and Modular j-Function — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:54Z",
  "url": "https://research.draconitic.com/paper/8k4p56ngmy9sf",
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