{
  "abstract": "FINDING: The Rogers-Ramanujan continued fraction (RRCF) provides an explicit algebraic bridge to solving the general quintic, linking modular equations to degree-5 solvability beyond Abel–Galois impossibility via special functions. | MATH: RRCF \\( R(q) = \\frac{q^{1/5}}{1+\\frac{q}{1+\\frac{q^2}{1+\\cdots}}} \\) satisfies the modular equation \\( R(q)^5 - 11 R(q)^4 + 11 R(q)^3 + 11 R(q)^2 - 11 R(q) + 1 = 0 \\) (for \\( q = e^{2\\pi i \\tau} \\), with \\( \\tau \\) related to the quintic's resolvent). The general quintic \\( x^5 + a x^4 + b x^3 + c x^2 + d x + e = 0 \\) is reduced to Bring–Jerrard form \\( y^5 + 5y = u \\), then solved via \\( y = R(q) - 1/R(q) - 1 \\) or similar rational expression, where \\( q \\) is determined by \\( u \\) through a modular equation of level 5. Key constants: the coefficients 1, 11, and the golden ratio \\( \\phi = (1+\\sqrt{5})/2 \\) appear in the RRCF's special values (e.g., \\( R(e^{-2\\pi}) = \\sqrt{\\phi} - \\phi^{1/2} \\cdot \\text{(algebraic)} \\)). | CONNECTION: The RRCF is dee\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/ew52wmw3xeqg8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23446830",
  "fulltext_url": null,
  "id": "ew52wmw3xeqg8",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23446830",
  "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": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ew52wmw3xeqg8.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:53Z",
      "native_id": "23446830",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23446830"
    }
  ],
  "subjects": [],
  "title": "Rogers–Ramanujan Continued Fraction as Algebraic Key to Quintic Solvability — E8 Intelligence Research",
  "title_text": "Rogers–Ramanujan Continued Fraction as Algebraic Key to Quintic Solvability — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:53Z",
  "url": "https://research.draconitic.com/paper/ew52wmw3xeqg8",
  "venue": "Zenodo",
  "versions": []
}