{
  "abstract": "FINDING: Chaitin's Omega (Ω) is a definable real number whose binary expansion is algorithmically random, encoding the halting probabilities of all programs — making it uncomputable and a formal limit to axiomatic mathematics. | MATH: Ω = Σ_{p halts} 2^{-|p|}, where p ranges over self-delimiting programs; Ω is a normal number in every base (Calude, et al. conjecture/partial results), but its bits are irreducible — no finite axiom system can determine more than finitely many bits of Ω (Chaitin's incompleteness theorem). | CONNECTION: The halting probability sum over program lengths 2^{-|p|} mirrors a geometric series with ratio 1/2 — a dyadic analogue of base-60's place-value structure. The \"randomness\" of Ω's bits corresponds to maximal algorithmic entropy, analogous to maximal symmetry-breaking in crystallographic systems (no periodic lattice, no repeating motif). The constant 0.5 (the base of the series) is the dyadic twin of 0.618 — both are fixed points of simple maps (x = 1/2 for\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": [
    {
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        0
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/eayycdssgtdch.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23586994",
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  "id": "eayycdssgtdch",
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  "language": "eng",
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  "published": "2026-10-23",
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  "ris": "https://research.draconitic.com/paper/eayycdssgtdch.ris",
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      "first_seen": "2026-11-06T12:21:55Z",
      "native_id": "23586994",
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  "title": "The Uncomputable Oracle: Chaitin's Omega and the Limits of Mathematics — E8 Intelligence Research",
  "title_text": "The Uncomputable Oracle: Chaitin's Omega and the Limits of Mathematics — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:55Z",
  "url": "https://research.draconitic.com/paper/eayycdssgtdch",
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