{
  "abstract": "FINDING: BB(5) resolved by collaborative \"Busy Beaver Challenge\"; higher-order Busy Beaver functions linked to oracle machines and decidability of number-theoretic formulas. | MATH: BB(5) = 47,176,870 (known value, confirmed via Coq proof); BB(n) is non-computable, grows faster than any computable function; higher-order BB functions BB^α(n) based on Turing oracle machines — decidability of Π₁/Σ₁ formulas tied to iterated halting oracles (arithmetical hierarchy: ∅^(α)). | CONNECTION: No direct geometric ratio (0.382, 0.618, 1.618) appears. However, the arithmetical hierarchy mirrors a *lattice structure* of truth degrees — each oracle jump corresponds to a new \"axis\" of undecidability, analogous to root system A_n or the recursive ordinal lattice. The value 47,176,870 has no notable modular or base-60 symmetry. | DEPTH: 7 — Profound for metamathematics (limits of formal systems, unprovable truths), but not directly revealing physical constants or geometric harmony. The higher-order exte\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"
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  ],
  "bibtex": "https://research.draconitic.com/paper/bdd3sy8c9z72e.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658199",
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  "id": "bdd3sy8c9z72e",
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  "language": "eng",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bdd3sy8c9z72e.ris",
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      "first_seen": "2026-11-09T12:21:38Z",
      "native_id": "23658199",
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  "title": "The Busy Beaver Challenge: BB(5) Solved, Higher-Order Functions and Oracle Decidability — E8 Intelligence Research",
  "title_text": "The Busy Beaver Challenge: BB(5) Solved, Higher-Order Functions and Oracle Decidability — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:38Z",
  "url": "https://research.draconitic.com/paper/bdd3sy8c9z72e",
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