{
  "abstract": "FINDING: The spectral gap problem — determining whether a quantum Hamiltonian's energy spectrum has a gap above the ground state — is provably undecidable in general, linking quantum many-body physics to the halting problem and Gödelian limits. | MATH: The key construction (Cubitt, Perez-Garcia, Wolf, 2015) reduces the halting problem to a family of 2D spin-lattice Hamiltonians \\( H(n) \\) on a fixed lattice, where the spectral gap (difference between ground state energy \\( E_0 \\) and first excited state \\( E_1 \\)) is either \\( \\Delta > 0 \\) (gapped) or \\( \\Delta = 0 \\) (gapless), depending on whether a Turing machine halts. The Hamiltonian is built from translationally invariant local terms with frustration-free ground states; the gap closes as \\( \\Delta \\sim 1/\\text{poly}(n) \\) in the gapless case. No closed-form equation for \\( \\Delta \\) exists — it is algorithmically uncomputable. | CONNECTION: The construction uses a lattice structure (square lattice, 2D) with local interaction ter\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/8qk0garycqh9m.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658246",
  "fulltext_url": null,
  "id": "8qk0garycqh9m",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23658246",
  "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": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8qk0garycqh9m.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:37Z",
      "native_id": "23658246",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658246"
    }
  ],
  "subjects": [],
  "title": "Quantum Spectral Gap Provably Undecidable, Linking Physics to Halting Problem — E8 Intelligence Research",
  "title_text": "Quantum Spectral Gap Provably Undecidable, Linking Physics to Halting Problem — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:37Z",
  "url": "https://research.draconitic.com/paper/8qk0garycqh9m",
  "venue": "Zenodo",
  "versions": []
}