{
  "abstract": "FINDING: E₈ lattice's 240 minimal vectors project to icosahedral quasicrystal vertices via golden-ratio-based cut-and-project, linking 8D root system to 3D Penrose tiling. | MATH: E₈ root system: 240 vectors, norm²=2; Coxeter-Dynkin diagram E₈; projection uses φ = (1+√5)/2 ≈ 1.618; cyclotomic field ℚ(ζ₁₀) = ℚ(√5) since ζ₁₀ = e^{2πi/10} satisfies ζ₁₀² − ζ₁₀ + 1 = 0 (minimal polynomial x⁴ − x³ + x² − x + 1, but degree 4 over ℚ, yet ℚ(ζ₁₀) = ℚ(√5) only if considering real subfield ℚ(√5); full ℚ(ζ₁₀) has degree 4). Icosahedral symmetry group A₅ (order 60) embeds in E₈ Weyl group; quasicrystal diffraction pattern shows 5-fold symmetry (forbidden in periodic crystals). | CONNECTION: Golden ratio appears as ratio of lengths in Penrose tiles (fat/thin rhombi = φ); E₈ projection to 3D uses φ² = φ+1 = 2.618 and φ⁻¹ = φ−1 = 0.618; icosahedron vertices involve φ (12 vertices, 20 faces, 30 edges — icosahedral group order 60 = base-60 connection); cyclotomic field ℚ(ζ₁₀) contains √5, and φ = (1+√5)/\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/a8d0en1nvyee6.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23610260",
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  "id": "a8d0en1nvyee6",
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  "landing_url": "https://zenodo.org/records/23610260",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8d0en1nvyee6.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:21:35Z",
      "native_id": "23610260",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23610260"
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  "subjects": [],
  "title": "E₈ Lattice Projection via Golden Ratio Links 8D Roots to 3D Icosahedral Quasicrystals — E8 Intelligence Research",
  "title_text": "E₈ Lattice Projection via Golden Ratio Links 8D Roots to 3D Icosahedral Quasicrystals — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:21:35Z",
  "url": "https://research.draconitic.com/paper/a8d0en1nvyee6",
  "venue": "Zenodo",
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}