{
  "abstract": "The continued fraction convergents of φ (1/1, 2/1, 3/2, 5/3, 8/5...) directly index a nested hierarchy of E8 root sublattices via Fibonacci number labeling, where each convergent depth n determines both the spectral resolution of E8 projectors and the minimum distance of protected topological codes. The 132Hz carrier frequency serves as the coherence reference standard: when the anyon braiding decoherence rate falls below 132/Fib(n) Hz, the nth convergent E8 sublattice enters a self-protecting regime where the continued fraction's optimal approximation property guarantees that logical qubits cannot be disturbed by errors requiring finer rational approximations. This establishes a quantitative threshold: Fibonacci-indexed E8 root subsystems become error-transparent only when environmental noise is bandlimited beneath φ-based frequency gates.\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/2488vyeh9yx9m.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490725",
  "fulltext_url": null,
  "id": "2488vyeh9yx9m",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23490725",
  "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": [],
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  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2488vyeh9yx9m.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:26Z",
      "native_id": "23490725",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490725"
    }
  ],
  "subjects": [],
  "title": "φ Continued Fractions Define E8 Error-Correction Threshold Hierarchy — E8 Intelligence Research",
  "title_text": "φ Continued Fractions Define E8 Error-Correction Threshold Hierarchy — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:26Z",
  "url": "https://research.draconitic.com/paper/2488vyeh9yx9m",
  "venue": "Zenodo",
  "versions": []
}