{
  "abstract": "FINDING: The arXiv paper \"On the Golden Ratio and Stable Self-Application\" (2510.08934v3) is the sole substantive mathematical result; the rest are pedagogical videos or tangential graph theory (Tree Forest Ratio). The paper operationalizes the golden ratio as a stable fixed point of local recurrence under self-application, linking irrational approximation to computational self-reference. | MATH: Let Φ = (1+√5)/2 ≈ 1.6180339887. The paper treats Φ as a limit of a recursive update rule: x_{n+1} = 1 + 1/x_n, which converges to Φ from any positive start. Key identity: Φ = 1 + 1/Φ, equivalently Φ² − Φ − 1 = 0. The \"stable self-application\" boundary likely involves a map f(x) = 1 + 1/x whose derivative at Φ is |f'(Φ)| = 1/Φ² ≈ 0.381966 (which is 1 − 1/Φ = 0.381966, the complementary golden ratio). This derivative magnitude < 1 guarantees local stability. The paper's core claim: Φ is the unique real number where the reciprocal map and its self-application (iteration) remain locally stable wh\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/8nc9vn0sh4a7e.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431281",
  "fulltext_url": null,
  "id": "8nc9vn0sh4a7e",
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  "landing_url": "https://zenodo.org/records/23431281",
  "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": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8nc9vn0sh4a7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:00Z",
      "native_id": "23431281",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431281"
    }
  ],
  "subjects": [],
  "title": "Golden Ratio as Stable Fixed Point of Self-Application Recurrence — E8 Intelligence Research",
  "title_text": "Golden Ratio as Stable Fixed Point of Self-Application Recurrence — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:00Z",
  "url": "https://research.draconitic.com/paper/8nc9vn0sh4a7e",
  "venue": "Zenodo",
  "versions": []
}