{
  "abstract": "FINDING: The search results are a scattered collection of educational videos and an unrelated arXiv paper on scalar curvature — no primary research on the Lagrange spectrum or golden-ratio Diophantine approximation is directly presented. The only substantive mathematical anchors are the golden ratio's continued fraction [1;1,1,1,…] and the Rogers–Ramanujan continued fraction, both of which are classical. | MATH: Golden ratio φ = (1+√5)/2 = 1.6180339…; its continued fraction is φ = [1;1,1,1,…], the *slowest* converging simple continued fraction (all partial quotients = 1). Lagrange spectrum: the Markov constant for φ is 1/√5 ≈ 0.4472, the *worst* possible for any irrational — this is Hurwitz's theorem: |α − p/q| < 1/(√5 q²) is optimal, and φ (and its equivalents) saturate it. Rogers–Ramanujan continued fraction: R(q) = q^(1/5)/(1 + q/(1 + q²/(1 + q³/(…)))), which at q = e^(−2π) yields closed forms involving φ and √5. | CONNECTION: The Lagrange spectrum's *first* gap is exactly the inter\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/23jq50kyaca7k.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553638",
  "fulltext_url": null,
  "id": "23jq50kyaca7k",
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  "landing_url": "https://zenodo.org/records/23553638",
  "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/",
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  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23jq50kyaca7k.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:20Z",
      "native_id": "23553638",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23553638"
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  ],
  "subjects": [],
  "title": "Search Results Lack Primary Research on Lagrange Spectrum and Golden Ratio — E8 Intelligence Research",
  "title_text": "Search Results Lack Primary Research on Lagrange Spectrum and Golden Ratio — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:20Z",
  "url": "https://research.draconitic.com/paper/23jq50kyaca7k",
  "venue": "Zenodo",
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}