{
  "abstract": "FINDING: The icosahedron and dodecahedron are geometrically defined by the golden ratio φ, and their rotational symmetry group is isomorphic to A₅ (the alternating group on 5 elements), which also appears in particle physics as a family symmetry for neutrino mixing. | MATH: Icosahedron vertices: (0, ±1, ±φ), (±1, ±φ, 0), (±φ, 0, ±1) where φ = (1+√5)/2 ≈ 1.6180339887. Dodecahedron vertices are the dual: (±1, ±1, ±1) and (0, ±1/φ, ±φ) permutations. The golden ratio satisfies φ² = φ + 1, and its reciprocal φ⁻¹ = φ − 1 ≈ 0.6180339887. The group order |A₅| = 60, isomorphic to the rotational icosahedral group I (proper rotations of the icosahedron). The neutrino mixing prediction uses the golden ratio: sin²θ₁₂ = 1/(√5 φ) ≈ 0.276 (tribimaximal-like with golden ratio correction), and the solar mixing angle satisfies tan²θ₁₂ = 1/φ² ≈ 0.382. | CONNECTION: Direct geometric harmony: φ appears as the ratio of diagonal to side in a regular pentagon (diagonal = φ × side). The pentagon's internal angl\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"
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  ],
  "bibtex": "https://research.draconitic.com/paper/40373yzvs95ke.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490873",
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  "id": "40373yzvs95ke",
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  "landing_url": "https://zenodo.org/records/23490873",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40373yzvs95ke.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:24Z",
      "native_id": "23490873",
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      "url": "https://zenodo.org/records/23490873"
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  "subjects": [],
  "title": "Golden Ratio Links Platonic Solids to Neutrino Symmetry — E8 Intelligence Research",
  "title_text": "Golden Ratio Links Platonic Solids to Neutrino Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:24Z",
  "url": "https://research.draconitic.com/paper/40373yzvs95ke",
  "venue": "Zenodo",
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}