{
  "abstract": "FINDING: Jones polynomial at 5th roots of unity connects to Fibonacci anyons and golden-ratio braiding, linking knot invariants to topological quantum computing. | MATH: Jones polynomial \\(V_L(t)\\) satisfies skein relation \\(t^{-1}V_{L_+} - tV_{L_-} = (t^{1/2} - t^{-1/2})V_{L_0}\\). At \\(t = e^{2\\pi i/5}\\), the quantum dimension \\(d = \\phi = (1+\\sqrt{5})/2 \\approx 1.618\\) (Fibonacci anyon fusion rule \\(\\phi \\otimes \\phi = 1 \\oplus \\phi\\)). R-matrix eigenvalues at 5th root: \\(\\lambda_1 = e^{4\\pi i/5}, \\lambda_2 = -e^{-2\\pi i/5}\\), satisfying \\(\\lambda_1/\\lambda_2 = -\\phi^2\\). Fibonacci numbers appear via \\(F_{n+1} = \\phi F_n + (-\\phi)^{-n}\\) (Binet form). | CONNECTION: Golden ratio \\(\\phi = 1.618\\) and its inverse \\(\\phi^{-1} = 0.618\\) are the quantum dimensions of the Fibonacci anyon — the simplest non-Abelian anyon model. The 5th root of unity \\(e^{2\\pi i/5}\\) generates the dihedral symmetry \\(D_5\\) (pentagonal, crystallographic point group 5/m in 2D), and the Jones polynomial at this\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/9vyc7kstv06r3.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23616600",
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  "id": "9vyc7kstv06r3",
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  "landing_url": "https://zenodo.org/records/23616600",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vyc7kstv06r3.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:50Z",
      "native_id": "23616600",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23616600"
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  "title": "Jones Polynomial at 5th Roots Links Knots to Fibonacci Anyons — E8 Intelligence Research",
  "title_text": "Jones Polynomial at 5th Roots Links Knots to Fibonacci Anyons — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9vyc7kstv06r3",
  "venue": "Zenodo",
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