{
  "abstract": "FINDING: Busy Beaver function defines a non-computable hierarchy that outruns every arithmetically definable function, revealing a strict lattice-like stratification of uncomputability. | MATH: BB(n) = max steps before halting among n-state Turing machines; BB grows faster than any computable function f(n) (∀f computable, ∃N: BB(n) > f(n) ∀n>N). Arithmetical hierarchy: Σ₀=Π₀=Δ₀ (decidable), Σ₁ (computably enumerable), Π₁ (co-c.e.), … Σ_k, Π_k, Δ_k = Σ_k ∩ Π_k. Key theorem: BB is Σ₁-complete (equivalent to halting problem); iterated BB (BB₂, BB₃, …) climbs the hierarchy — BB^(k) is Σ_k-complete. Known values: BB(1)=1, BB(2)=6, BB(3)=21, BB(4)=107, BB(5)=47,176,870 (proven 2024 via Coq). | CONNECTION: The correspondence between BB-hierarchy and arithmetical hierarchy mirrors a **lattice duality**: each level k corresponds to quantifier alternation depth (∃∀∃…), analogous to crystallographic root system rank — the number of alternations acts like dimension. The growth ratios between succe\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/df4m0nbve7t85.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587264",
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  "id": "df4m0nbve7t85",
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  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/df4m0nbve7t85.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:50Z",
      "native_id": "23587264",
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      "url": "https://zenodo.org/records/23587264"
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  "subjects": [],
  "title": "Busy Beaver Outruns All Arithmetically Definable Functions — E8 Intelligence Research",
  "title_text": "Busy Beaver Outruns All Arithmetically Definable Functions — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:50Z",
  "url": "https://research.draconitic.com/paper/df4m0nbve7t85",
  "venue": "Zenodo",
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