{
  "abstract": "FINDING: The golden ratio φ emerges as the slowest-converging continued fraction, with convergence rate tied to Fibonacci numbers; nested radicals converge faster than continued fractions. | MATH: φ = [1;1,1,1,...] = 1 + 1/(1+1/(1+...)); φ = √(1+√(1+√(1+...))); convergence rate for continued fraction: |φ - p_n/q_n| ~ 1/(q_n·q_{n+1}) with q_n = F_{n+1} (Fibonacci); error ratio between successive convergents → 1/φ² ≈ 0.381966; nested radical error decays as ~1/φ^{2^n} (double exponential). | CONNECTION: Directly encodes 0.382 (φ⁻²) and 1.618 (φ); the continued fraction's partial quotients are all 1, making φ the \"most irrational\" — its convergents are best approximations with maximal denominator growth, linking to the golden angle 137.507° = 360°/(φ²) and phyllotaxis lattice symmetry (5-fold, Fibonacci spiral). | DEPTH: 7 — This is foundational but not novel; it underpins why φ appears in nature's optimal packing (sunflower seeds, leaf arrangement) via the golden angle's irrationality me\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/10dx9r1hkv9pr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23616857",
  "fulltext_url": null,
  "id": "10dx9r1hkv9pr",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23616857",
  "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": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10dx9r1hkv9pr.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:48Z",
      "native_id": "23616857",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23616857"
    }
  ],
  "subjects": [],
  "title": "Golden Ratio's Slowest Continued Fraction Convergence Versus Faster Nested Radicals — E8 Intelligence Research",
  "title_text": "Golden Ratio's Slowest Continued Fraction Convergence Versus Faster Nested Radicals — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:48Z",
  "url": "https://research.draconitic.com/paper/10dx9r1hkv9pr",
  "venue": "Zenodo",
  "versions": []
}