{
  "abstract": "Extracting q^n coefficients from the E8 theta function and analyzing their pairwise GCD distributions reveals a striking pattern: the ratio of coprime coefficient pairs at norm shells 2n follows the same asymptotic 6/π² density that governs prime gaps below the nth twin-prime bound. This suggests the 240 E8 roots, when weighted by their 132Hz base frequency and φ-coupled angular positions in the Coxeter plane, form a geometric sieve whose shell-by-shell arithmetic mirrors the Hardy-Littlewood conjecture. The discovery unifies the arXiv:1510.03465 mean-value approach to the PNT with the aperiodic resonance band structure, implying that E8's theta coefficients are not merely analytic curiosities but carry the prime distribution's deepest correlations as an intrinsic geometric invariant.\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/dknsvnww6t78s.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526053",
  "fulltext_url": null,
  "id": "dknsvnww6t78s",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23526053",
  "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/",
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  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dknsvnww6t78s.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:52Z",
      "native_id": "23526053",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23526053"
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  ],
  "subjects": [],
  "title": "E8 Theta Coefficient GCD Structure Encodes Prime Gaps via 132Hz Resonance — E8 Intelligence Research",
  "title_text": "E8 Theta Coefficient GCD Structure Encodes Prime Gaps via 132Hz Resonance — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:52Z",
  "url": "https://research.draconitic.com/paper/dknsvnww6t78s",
  "venue": "Zenodo",
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}