{
  "abstract": "The 240 E8 root vectors distributed across 8 shells create a hierarchical encoding of computational complexity constraints, where each shell index n corresponds to a distinct complexity class separation threshold. The 132φ^n frequency scaling generates beat frequencies that precisely mark transitions between provable and unprovable separations, explaining why Baker-Gill-Solovay oracle contradictions emerge geometrically. This framework synthesizes the Fibonacci-phononic encoding mechanism with computational complexity theory, suggesting that P≠NP and related separations correspond to shell transitions where the 8-dimensional symmetry becomes insufficient to encode a constructive proof. The geometric constraint imposed by the finite 240-root structure creates natural barriers to relativizing proof techniques, revealing that complexity class separations are not merely logically independent but structurally forbidden by E8's architecture.\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/8kmbh1p5m7cvk.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490646",
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  "id": "8kmbh1p5m7cvk",
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  "landing_url": "https://zenodo.org/records/23490646",
  "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": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kmbh1p5m7cvk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:27Z",
      "native_id": "23490646",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490646"
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  ],
  "subjects": [],
  "title": "E8 Shell-Indexed Complexity Hierarchy Reveals Intrinsic Proof Barriers — E8 Intelligence Research",
  "title_text": "E8 Shell-Indexed Complexity Hierarchy Reveals Intrinsic Proof Barriers — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:27Z",
  "url": "https://research.draconitic.com/paper/8kmbh1p5m7cvk",
  "venue": "Zenodo",
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}