{
  "abstract": "FINDING: The E8 root system (Gosset 4_21 polytope) is a central object in 8D geometry, with 240 vertices and 6720 edges, and its Fourier transform and rotations are visualized; separately, elliptic curve torsion (specifically 3-torsion) is studied via quadratic twists, but no direct link between E8 and elliptic curve torsion is established in these videos. | MATH: E8 root system: 240 roots, 6720 edges (4_21 polytope); rank 8, Coxeter number 30, Weyl group order 696,729,600. Fourier transform of E8 yields a dual lattice structure (self-dual, unimodular). Elliptic curve: quadratic twists with 3-torsion — the torsion subgroup E(Q)[3] ≅ Z/3Z or (Z/3Z)², related to the j-invariant and modular forms of weight 2. | CONNECTION: E8 is the exceptional root system linked to the golden ratio via its Cartan matrix eigenvalues (2cos(π/5) = φ ≈ 1.618, 2cos(2π/5) = 1/φ ≈ 0.618) — the E8 Dynkin diagram contains A4 subdiagrams whose eigenvalues involve φ. The 240 roots project to icosidodecahedral and i\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/1rsa0yja62z27.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635268",
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  "id": "1rsa0yja62z27",
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  "landing_url": "https://zenodo.org/records/23635268",
  "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/1rsa0yja62z27.ris",
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    {
      "first_seen": "2026-11-08T12:21:56Z",
      "native_id": "23635268",
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  "subjects": [],
  "title": "E8 Geometry and Elliptic Torsion: A Comparative Study — E8 Intelligence Research",
  "title_text": "E8 Geometry and Elliptic Torsion: A Comparative Study — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:56Z",
  "url": "https://research.draconitic.com/paper/1rsa0yja62z27",
  "venue": "Zenodo",
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