{
  "abstract": "FINDING: Reversible Turing machines form an algebraic group acting on configuration spaces, with equivalence classes defined by Nielsen/Andrews-Curtis-type operations — revealing symmetry structure in computation itself. | MATH: Group of reversible Turing machines \\(G\\) acting on \\(\\Sigma^{\\mathbb{Z}^d}\\) via local homeomorphisms; equivalence relations generated by \\(\\mathrm{Aut}(F_n)\\) and \\(F_n\\) on normally generating tuples \\((y_1,\\ldots,y_n)\\sim(x_1,\\ldots,x_n)\\); Andrews-Curtis conjecture: any normally generating \\(n\\)-tuple is AC-equivalent to free basis. | CONNECTION: The dihedral group \\(D_4\\) (order 8) is the symmetry group of the square — its elements (identity, rotations \\(r,r^2,r^3\\), reflections \\(s,sr,sr^2,sr^3\\)) correspond to the 8 possible permutations of a 2-state, 2-symbol Turing machine's transition table under complementation (swap 0↔1) and reversal (swap direction). This is precisely the \\(D_4\\) action on the \\(2\\times2\\) grid of state×symbol — a crystallographic\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,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/ddk45s28kgv3r.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465012",
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  "id": "ddk45s28kgv3r",
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  "language": "eng",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddk45s28kgv3r.ris",
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    {
      "first_seen": "2026-11-02T12:21:49Z",
      "native_id": "23465012",
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  "title": "Reversible Computation as Algebraic Symmetry: A Group-Theoretic Structure — E8 Intelligence Research",
  "title_text": "Reversible Computation as Algebraic Symmetry: A Group-Theoretic Structure — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:49Z",
  "url": "https://research.draconitic.com/paper/ddk45s28kgv3r",
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