{
  "abstract": "FINDING: Cyclotomic field ℚ(ζ₁₀) has real subfield ℚ(√5), whose Galois group and units generate the golden-ratio arithmetic underlying E₈'s icosahedral quasicrystal projections. | MATH: ℚ(ζ₁₀) = ℚ(ζ₅) (since ζ₁₀ = -ζ₅²), degree φ(10)=4; real subfield ℚ(ζ₁₀+ζ₁₀⁻¹) = ℚ(√5). Ring of integers ℤ[(1+√5)/2] = ℤ[ζ₅+ζ₅⁻¹]. Units: (1+√5)/2 = 1.618..., (1-√5)/2 = -0.618... . E₈ root system: 240 roots, norm²=2; projection to 3D icosahedral shell uses the 6D subspace fixed by the Coxeter element of order 30 (since |W(E₈)|/|W(H₃)| = 696729600/120 = 5806080, and the icosian group is a subquotient). The diffraction pattern's Bragg peaks lie in ℤ[ζ₁₀] ⊕ ℤ[ζ₁₀] ⊕ ℤ[ζ₁₀] (real subfield coordinates), giving the golden-ratio scaling hierarchy. | CONNECTION: √5 = 2.236...; (1+√5)/2 = 1.618 (φ); φ⁻¹ = 0.618; φ⁻² = 0.382; φ⁻³ = 0.236; φ⁻⁴ = 0.146. The E₈ → H₃ projection uses the golden ratio as the irrational cut parameter (τ = 1.618) in the strip-projection method. The 12 vertices of the icosahedron are (±1,\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/ezm5s8vbk5sp6.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635057",
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  "id": "ezm5s8vbk5sp6",
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  "landing_url": "https://zenodo.org/records/23635057",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezm5s8vbk5sp6.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:22:00Z",
      "native_id": "23635057",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635057"
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  "subjects": [],
  "title": "Golden Ratio Fields Link E₈'s Icosahedral Quasicrystal Projections — E8 Intelligence Research",
  "title_text": "Golden Ratio Fields Link E₈'s Icosahedral Quasicrystal Projections — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:22:00Z",
  "url": "https://research.draconitic.com/paper/ezm5s8vbk5sp6",
  "venue": "Zenodo",
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}