{
  "abstract": "FINDING: The golden angle's continued-fraction structure is not directly addressed in these papers, but the convergence rate of Fibonacci ratios to φ (1.618…) is implicitly tied to the optimality of continued fraction approximants, and the Rogers-Ramanujan continued fraction provides an algebraic bridge to quintic solvability. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.6180339887; its conjugate ψ = (1−√5)/2 ≈ −0.6180339887. Fibonacci convergence rate: |F_{n+1}/F_n − φ| ~ 1/(φ^{2n}) (since F_n ~ φ^n/√5). Continued fraction of φ = [1;1,1,1,…] — the slowest-converging simple continued fraction, giving optimal rational approximants with error ~ 1/(q_n^2) where q_n = F_n. Rogers-Ramanujan continued fraction: R(q) = q^{1/5}/(1 + q/(1 + q²/(1 + q³/(…)))) — for q = e^{−2π}, R(e^{−2π}) = √(5−√5)/2 − (√5−1)/2, an algebraic number involving √5. | CONNECTION: The golden angle = 2π(1−1/φ) ≈ 2.399963… rad ≈ 137.507764° — its continued fraction [2;1,1,1,…] yields convergents 2, 3, 5/2, 8/3, 13/5, 21/8,… (\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/c3thq8hgekqp1.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490667",
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  "id": "c3thq8hgekqp1",
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  "landing_url": "https://zenodo.org/records/23490667",
  "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/c3thq8hgekqp1.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:27Z",
      "native_id": "23490667",
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      "url": "https://zenodo.org/records/23490667"
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  "subjects": [],
  "title": "Golden Ratio's Continued Fractions Bridge Fibonacci Convergence and Quintic Solvability — E8 Intelligence Research",
  "title_text": "Golden Ratio's Continued Fractions Bridge Fibonacci Convergence and Quintic Solvability — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:27Z",
  "url": "https://research.draconitic.com/paper/c3thq8hgekqp1",
  "venue": "Zenodo",
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}