{
  "abstract": "FINDING: Lawvere's categorical fixed-point theorem unifies Cantor, Turing, Tarski, and Gödel via a single diagonalization schema; substructural logics further generalize it. | MATH: Lawvere's theorem: If \\( \\exists f: A \\to B^A \\) (exponential object) is surjective, then every endomorphism \\( \\alpha: B \\to B \\) has a fixed point. Contrapositive yields diagonal argument: no surjection \\( A \\to B^A \\) if \\( \\alpha \\) lacks fixed points. Fixed-point combinator: \\( \\Delta(x) = \\alpha(f(x)(x)) \\), with \\( d = f(a) \\) giving \\( d(d) = \\alpha(d(d)) \\). Substructural weakening: replace cartesian closed with symmetric monoidal closed + relevant logic — fixed point exists if \\( \\alpha \\) is \"pointed\" (has a distinguished element). | CONNECTION: The diagonal map \\( \\Delta: A \\to A \\times A \\) is a self-pairing — structurally analogous to the golden ratio's self-similarity \\( \\phi = 1 + 1/\\phi \\), where the fixed point equation \\( x = 1 + 1/x \\) yields \\( \\phi = (1+\\sqrt{5})/2 \\approx 1.618 \\). Th\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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        0
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/fvn65dn8djtns.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635367",
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  "published": "2026-10-25",
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  "ris": "https://research.draconitic.com/paper/fvn65dn8djtns.ris",
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  "title": "Categorical Fixed-Point Theorem Unifies Diagonalization Across Logic — E8 Intelligence Research",
  "title_text": "Categorical Fixed-Point Theorem Unifies Diagonalization Across Logic — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/fvn65dn8djtns",
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