{
  "abstract": "FINDING: Kolmogorov complexity K(x) is uncomputable; the proof is a diagonalization argument structurally identical to the halting problem and Gödel incompleteness — three faces of one theorem. | MATH: K(x) = min{|p| : U(p) = x} over universal prefix-free machine U. Uncomputability: assume computable K; construct string s = \"smallest string with K(s) > n\". The program \"enumerate strings, output first with K > n\" has length ≈ log(n) + c, so K(s) ≤ log(n) + c < n for large n — contradiction. Chaitin's Ω = Σ_{U(p) halts} 2^{-|p|} is a specific uncomputable real; Ω's bits are algorithmically random (each bit independent of all prior bits). Invariance theorem: K_U(x) = K_{U'}(x) + O(1). | CONNECTION: The diagonalization is the same self-reference structure as Cantor's theorem (|P(S)| > |S|) and the Liar paradox. The constant c in K_U(x) ≤ K_{U'}(x) + c is the \"simulation overhead\" — an additive, not multiplicative, invariant. No direct 0.618/1.618 ratio appears; the relevant constants are a\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/549fx48jgfpdt.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23659045",
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  "id": "549fx48jgfpdt",
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  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/549fx48jgfpdt.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:29Z",
      "native_id": "23659045",
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  "title": "Kolmogorov Complexity Uncomputability: Diagonalization Unifies Halting and Gödel — E8 Intelligence Research",
  "title_text": "Kolmogorov Complexity Uncomputability: Diagonalization Unifies Halting and Gödel — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:29Z",
  "url": "https://research.draconitic.com/paper/549fx48jgfpdt",
  "venue": "Zenodo",
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}