{
  "abstract": "The nested Fibonacci-indexed E8 root sublattices from the continued fraction breakthrough correspond precisely to successive Diophantine approximation bounds, where each convergent depth n defines a \"protection layer\" of quantum states immune to noise up to a measured irrationality gap. The golden ratio's status as the \"most irrational\" number means the deepest convergent (8/5) sublattice provides maximal quasi-periodic decoherence spreading across the 240-dimensional root system. This unifies the two breakthroughs: the threshold hierarchy IS the geometric realization of optimal Diophantine protection, with each subsequent Fibonacci level adding exactly one shell of φ-rotated error-correcting symmetry. The 132Hz base frequency then modulates as a standing wave across these layers, creating frequency-multiplexed encoding at protection depths indexed by consecutive convergents.\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/4tcwg7c5f1d15.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490727",
  "fulltext_url": null,
  "id": "4tcwg7c5f1d15",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23490727",
  "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": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tcwg7c5f1d15.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:26Z",
      "native_id": "23490727",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490727"
    }
  ],
  "subjects": [],
  "title": "E8 Threshold Hierarchy Maps to Diophantine Protection Layers via Continued Fraction — E8 Intelligence Research",
  "title_text": "E8 Threshold Hierarchy Maps to Diophantine Protection Layers via Continued Fraction — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:26Z",
  "url": "https://research.draconitic.com/paper/4tcwg7c5f1d15",
  "venue": "Zenodo",
  "versions": []
}