{
  "abstract": "FINDING: The Time Hierarchy Theorem uses diagonalization to prove that more time strictly enables more languages to be decided, establishing a strict infinite hierarchy of complexity classes (e.g., DTIME(n) ⊊ DTIME(n²) ⊊ ...). | MATH: For time-constructible f(n) > g(n) log g(n): DTIME(g(n)) ⊊ DTIME(f(n)). Proof: diagonal language L = {⟨M⟩ : M rejects ⟨M⟩ within f(|⟨M⟩|) steps}. Key constants: the logarithmic overhead factor (log g(n)) arises from the universal simulator's tape indexing — a discrete logarithmic scaling. Space analog: Savitch's theorem gives NSPACE(s(n)) ⊆ DSPACE(s(n)²) — a quadratic (power-of-2) blowup, not exponential. | CONNECTION: The strict separation ratio is asymptotic, not a fixed constant. However, the *log factor* in the time hierarchy (g(n) log g(n)) and the *square* in Savitch's theorem echo the 2:1 ratio (0.5, 2.0) seen in crystallographic root systems (B₂, C₂) and the doubling structure of base-60's sexagesimal fractions (1/60, 1/3600 = 60⁻²). The diagonali\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
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/3m5411pka2bdy.bib",
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  "doi": "10.5281/zenodo.23490867",
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  "published": "2026-10-20",
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  "ris": "https://research.draconitic.com/paper/3m5411pka2bdy.ris",
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      "first_seen": "2026-11-03T12:21:24Z",
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  "title": "Diagonalization Proves Strict Infinite Hierarchy of Time Complexity Classes — E8 Intelligence Research",
  "title_text": "Diagonalization Proves Strict Infinite Hierarchy of Time Complexity Classes — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:24Z",
  "url": "https://research.draconitic.com/paper/3m5411pka2bdy",
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