{
  "abstract": "FINDING: Baker-Gill-Solovay (BGS) theorem proves P vs NP cannot be settled by any relativizing proof technique, as oracle worlds exist where P^A = NP^A and P^B ≠ NP^B. | MATH: ∃A: P^A = NP^A; ∃B: P^B ≠ NP^B. Time Hierarchy Theorem: P ⊊ EXPTIME (since DTIME(n^k) ⊊ DTIME(2^n) for all k). Diagonalization relativizes; hence any proof of P ≠ NP must be non-relativizing (e.g., arithmetization, algebraic geometry, or circuit lower bounds). | CONNECTION: The two oracles A and B form a binary opposition — a symmetry breaking between two \"worlds\" that are computationally indistinguishable from within. This mirrors the dichotomy of root systems (e.g., A_n vs B_n) where one is simply-laced and the other has two root lengths — a structural bifurcation that cannot be resolved by local (relativizing) rules. The ratio of separation (P vs NP) is not a numeric constant but an *ordinal gap* — yet the *existence* of two inequivalent oracles echoes the golden ratio's self-similarity: the problem is scale-i\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/8cvcx82jhr95j.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490788",
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  "id": "8cvcx82jhr95j",
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  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cvcx82jhr95j.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:25Z",
      "native_id": "23490788",
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      "url": "https://zenodo.org/records/23490788"
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  "subjects": [],
  "title": "Relativization Barriers and the Non-Relativizing Path to P vs NP — E8 Intelligence Research",
  "title_text": "Relativization Barriers and the Non-Relativizing Path to P vs NP — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:25Z",
  "url": "https://research.draconitic.com/paper/8cvcx82jhr95j",
  "venue": "Zenodo",
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}