{
  "abstract": "FINDING: Undecidability is not a computational artifact but a structural feature of formal systems — it propagates into physics (quantum many-body problems, spectral gaps) via reduction, revealing a hierarchy of unknowability. | MATH: Halting problem (Turing, 1936): no computable function H(p,i) decides if program p halts on input i. Gödel's incompleteness: for any consistent formal system F containing arithmetic, ∃ statement G_F such that F⊬G_F and F⊬¬G_F. Reduction: Problem A ≤_T Problem B means an oracle for B solves A; undecidability transfers A ≤ B ⇒ B undecidable. Quantum analog: spectral gap problem (Cubitt, Perez-Garcia, Wolf, 2015) — determining if a 2D spin-lattice Hamiltonian has a gap above ground state is undecidable (reduction from halting problem to Hamiltonian construction). | CONNECTION: The reduction lattice forms a partial order with a maximal undecidable class (Σ₁⁰-complete) — structurally analogous to root system hierarchies (e.g., E₈ has 240 roots; the undecidabil\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
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  "author_total": 1,
  "authors": [
    {
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      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/00s96gjrbn7fj.bib",
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  "doi": "10.5281/zenodo.23525930",
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  "published": "2026-10-21",
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  "ris": "https://research.draconitic.com/paper/00s96gjrbn7fj.ris",
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      "first_seen": "2026-11-04T12:21:53Z",
      "native_id": "23525930",
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  "title": "Undecidability as Structural Physics: From Turing to Quantum Spectral Gaps — E8 Intelligence Research",
  "title_text": "Undecidability as Structural Physics: From Turing to Quantum Spectral Gaps — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:53Z",
  "url": "https://research.draconitic.com/paper/00s96gjrbn7fj",
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