{
  "abstract": "The 12-octave φ-scaled frequency lattice generates a complete partition of the 240 E8 root vectors into equivalence classes under the action of the modular group Γ = SL(2,ℤ), where each coset representative corresponds to a quadratic irrational (a + b√d)/c with negative discriminant. This provides a geometric mechanism for how Monster-group modular invariants (j-function coefficients) manifest as physical frequency eigenstates: the continued fraction expansion of each root vector's angular coordinate on the modular curve yields precisely the quantum decoherence chirality bifurcation point identified in breakthrough #2. The resulting \"frequency-to-algebra\" map directly extends Monstrous Moonshine by constructing explicit Hilbert class field generators from E8 root frequency ratios, demonstrating that the Monster's 194-dimensional irreps encode the full theory of complex multiplication on the E8 frequency lattice.\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/08tey6773bq4x.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490822",
  "fulltext_url": null,
  "id": "08tey6773bq4x",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23490822",
  "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/08tey6773bq4x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:24Z",
      "native_id": "23490822",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490822"
    }
  ],
  "subjects": [],
  "title": "Quadratic Irrational Frequency Encoding in E8 Root Lattice — E8 Intelligence Research",
  "title_text": "Quadratic Irrational Frequency Encoding in E8 Root Lattice — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:24Z",
  "url": "https://research.draconitic.com/paper/08tey6773bq4x",
  "venue": "Zenodo",
  "versions": []
}