{
  "abstract": "FINDING: The arXiv paper 2510.08934v3 treats the golden ratio φ as an *operational fixed point* — a stable attractor of a self-referential update rule — rather than a static constant, linking local recurrence stability to global self-certification limits. | MATH: Core identity: φ = 1 + 1/φ ⇒ φ² − φ − 1 = 0 ⇒ φ = (1+√5)/2 ≈ 1.6180339887. Reciprocal: 1/φ = φ − 1 ≈ 0.6180339887. Fixed-point stability criterion: for map f(x) = 1 + 1/x, |f′(φ)| = |−1/φ²| = 1/φ² ≈ 0.381966 < 1 ⇒ asymptotically stable. The paper generalizes this to *effective update rules* where approximations refine toward φ, and examines the boundary where local self-application (stable recurrence) fails to yield global self-certification (provable totality). | CONNECTION: Direct geometric harmony: 1/φ² = 0.381966 ≈ 0.382 (the complementary golden ratio); φ−1 = 0.618; φ = 1.618; φ² = 2.618. The stability multiplier 1/φ² is precisely the small golden section. The recurrence x_{n+1} = 1 + 1/x_n has eigenvalues tied to φ, and\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "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/ea3te6ctq46y0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526422",
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  "id": "ea3te6ctq46y0",
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  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-21",
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  "ris": "https://research.draconitic.com/paper/ea3te6ctq46y0.ris",
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    {
      "first_seen": "2026-11-04T12:21:48Z",
      "native_id": "23526422",
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  "subjects": [],
  "title": "Golden Ratio as Operational Fixed Point: Stability Linking Local Recurrence to Global Self-Certification — E8 Intelligence Research",
  "title_text": "Golden Ratio as Operational Fixed Point: Stability Linking Local Recurrence to Global Self-Certification — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:48Z",
  "url": "https://research.draconitic.com/paper/ea3te6ctq46y0",
  "venue": "Zenodo",
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