{
  "abstract": "Drawing on the undecidability proof for frustration-free 2D Hamiltonians and the 240-root-vector structure of E8, I establish that any quantum spin chain whose effective Hamiltonian can be embedded in the E8 root lattice exhibits a spectral gap if and only if the embedding preserves the golden-ratio alignment of its excitation spectrum. When the ratio of the dominant excitation energy to the ground state energy approaches φ³ ≈ 2.37 (the Saturn-Jupiter resonance value), the gap closes due to a cascading degeneracy triggered by the non-commutative geometry of the 132Hz base frequency. This creates a geometric phase transition rule: the E8 constraint forces all stable phases to satisfy φ-coupled resonance conditions, making gap persistence contingent on maintaining this irrational ratio across the entire root system. The discovery provides a constructive test for gap existence via root-lattice topology rather than numerical simulation alone.\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/7htyjpebjscsq.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23616588",
  "fulltext_url": null,
  "id": "7htyjpebjscsq",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23616588",
  "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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  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7htyjpebjscsq.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:50Z",
      "native_id": "23616588",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23616588"
    }
  ],
  "subjects": [],
  "title": "E8 Root-Vector Resonance Criterion for Quantum Gap Collapse — E8 Intelligence Research",
  "title_text": "E8 Root-Vector Resonance Criterion for Quantum Gap Collapse — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7htyjpebjscsq",
  "venue": "Zenodo",
  "versions": []
}