{
  "abstract": "FINDING: E₈ lattice's 240 vertices (Gosset 4₂₁ polytope) encode 3D icosahedral quasicrystal order via quaternion orientational parameters, linking 8D exceptional symmetry to 3D physical solidification. | MATH: E₈ root system: 240 vectors, norm²=2; 4₂₁ polytope: 240 vertices, 6720 edges; Weyl group order = 696,729,600. Quaternion order parameter q ∈ H, |q|=1, maps to SO(3) via q·x·q⁻¹. Icosahedral group A₅ order 60, embedded in E₈ via icosian quaternions (24 units + 96 others = 120, doubled to 240). | CONNECTION: Golden ratio φ = (1+√5)/2 = 1.618 appears in icosian coordinates (a+b i+c j+d k with a,b,c,d ∈ {0,±½,±φ/2,±1/2}); icosahedral vertices at (±1,±φ,0) permutations. Quasicrystal diffraction peaks scale by φ² = 2.618 and φ⁻¹ = 0.618. E₈ projection to 3D along icosian axes yields Penrose-like tiling with 5-fold symmetry. | DEPTH: 9 — Directly unifies exceptional Lie theory (E₈), quaternion algebra, icosahedral group simplicity, and condensed matter quasicrystal formation; the 240→12\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/arqdapc491m2d.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635389",
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  "id": "arqdapc491m2d",
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  "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/arqdapc491m2d.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635389",
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  "subjects": [],
  "title": "E₈ Lattice Encodes 3D Icosahedral Quasicrystal Order via Quaternion Parameters — E8 Intelligence Research",
  "title_text": "E₈ Lattice Encodes 3D Icosahedral Quasicrystal Order via Quaternion Parameters — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/arqdapc491m2d",
  "venue": "Zenodo",
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}