{
  "abstract": "FINDING: Weyl groups of root systems (including icosahedral H₃/H₄) are the discrete symmetry engines of Lie theory, with super-Weyl generalizations extending to Lie superalgebras; the icosahedral group A₅ ≅ H₃ Weyl group is the exceptional finite reflection group linked to E₈ via folding and to geometric Langlands through root data. | MATH: Weyl group W = ⟨s_α : α ∈ Δ⟩, s_α(β) = β − 2⟨β,α⟩/⟨α,α⟩·α; Cartan matrix A_ij = 2⟨α_i,α_j⟩/⟨α_j,α_j⟩; H₃ has Coxeter matrix m_ij = 5 (icosahedral), order |W(H₃)| = 120; H₄ order = 14400; E₈ root system has 240 roots, Weyl group order = 696,729,600; super Weyl groups (arXiv:2401.11068) are quotients of classical Weyl groups by parity/odd root actions. | CONNECTION: Icosahedral symmetry is the rank-3 Weyl group H₃ — its golden ratio φ = (1+√5)/2 = 1.618 appears in the Cartan integers: for adjacent simple roots, 4cos²(π/5) = φ+2 ≈ 3.618, and the squared length ratio of long/short roots in non-crystallographic H₃ is φ² = 2.618. The H₃ root system coordi\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"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s05qhxr69nrp.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635567",
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  "id": "5s05qhxr69nrp",
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  "landing_url": "https://zenodo.org/records/23635567",
  "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/5s05qhxr69nrp.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:52Z",
      "native_id": "23635567",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635567"
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  "subjects": [],
  "title": "Weyl Groups as Discrete Symmetry Engines Linking Icosahedral H₃ to E₈ and Langlands — E8 Intelligence Research",
  "title_text": "Weyl Groups as Discrete Symmetry Engines Linking Icosahedral H₃ to E₈ and Langlands — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:52Z",
  "url": "https://research.draconitic.com/paper/5s05qhxr69nrp",
  "venue": "Zenodo",
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}