{
  "abstract": "FINDING: E8 root system and exceptional Lie algebras are governed by Cartan integers (2, -1, 0) with a determinant-1 lattice, whose structure inherently encodes √5 and the golden ratio via the 5-fold symmetric embedding of the dodecahedron into E8. | MATH: E8 root system: 240 roots, Cartan matrix entries \\(A_{ij} = 2(\\alpha_i,\\alpha_j)/(\\alpha_j,\\alpha_j) \\in \\{0,\\pm1,\\pm2,\\pm3\\}\\); for E8, all off-diagonal entries are 0 or -1 (simply-laced). Lattice determinant = 1 (unimodular, even, self-dual). The Weyl group order = 696,729,600. The golden ratio appears via the 5-cell/dodecahedral projection: the E8 lattice projected to 2D yields quasicrystalline patterns with 5-fold symmetry, requiring \\(\\cos(72^\\circ) = (\\sqrt{5}-1)/4 \\approx 0.309\\), and the ratio of radial distances in the projection involves \\(\\sqrt{5}\\). Specifically, the E8 root system contains a subsystem \\(A_4 \\times A_4\\) whose Coxeter numbers (5 and 5) yield the golden ratio through \\(\\cos(\\pi/5) = \\phi/2 = (1+\\sqrt{5})/4\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/fanape4dtkrs4.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658335",
  "fulltext_url": null,
  "id": "fanape4dtkrs4",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23658335",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fanape4dtkrs4.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:37Z",
      "native_id": "23658335",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658335"
    }
  ],
  "subjects": [],
  "title": "E8's Golden Ratio: Dodecahedral 5-Fold Symmetry Encoded in Unimodular Lattice — E8 Intelligence Research",
  "title_text": "E8's Golden Ratio: Dodecahedral 5-Fold Symmetry Encoded in Unimodular Lattice — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:37Z",
  "url": "https://research.draconitic.com/paper/fanape4dtkrs4",
  "venue": "Zenodo",
  "versions": []
}