{
  "abstract": "FINDING: Undecidability is not a computational quirk but a structural invariant of formal systems, extending into quantum many-body physics — the halting problem's diagonalization argument mirrors a fundamental incompleteness in any axiomatic description of physical reality. | MATH: Gödel's incompleteness (∃G: ¬⊢G ∧ ¬⊢¬G); Halting problem (∄H: ∀(P,I), H(P,I) terminates ⟺ P(I) halts); Rice's theorem (any non-trivial semantic property of programs is undecidable); Quantum reduction: spectral gap problem shown undecidable for translation-invariant 1D Hamiltonians (Cubitt, Perez-Garcia, Wolf, 2015) — implies no finite algorithm can decide if a physical system has a gap, even with full Hamiltonian specification. | CONNECTION: The diagonalization argument (Cantor's 2^ℵ₀ > ℵ₀) is a combinatorial shadow of the golden ratio's self-similarity — both encode non-well-founded recursion. The undecidability of the spectral gap for translation-invariant systems ties to lattice structures: the proof con\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"
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  "bibtex": "https://research.draconitic.com/paper/aqxzeetd3tbkc.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465410",
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  "id": "aqxzeetd3tbkc",
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  "language": "eng",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqxzeetd3tbkc.ris",
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    {
      "first_seen": "2026-11-02T12:21:44Z",
      "native_id": "23465410",
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  "subjects": [],
  "title": "Undecidability as a Structural Invariant Across Computation and Quantum Physics — E8 Intelligence Research",
  "title_text": "Undecidability as a Structural Invariant Across Computation and Quantum Physics — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:44Z",
  "url": "https://research.draconitic.com/paper/aqxzeetd3tbkc",
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