{
  "abstract": "FINDING: Baker-Gill-Solovay (BGS) proves P vs NP cannot be settled by any relativizing proof technique — there exist oracles A and B with P^A = NP^A and P^B ≠ NP^B. | MATH: ∃A: P^A = NP^A; ∃B: P^B ≠ NP^B. Diagonalization (the only known lower-bound method pre-1990) relativizes — hence cannot resolve P vs NP. Time Hierarchy: P ≠ EXPTIME (deterministic), but NP vs P remains open. | CONNECTION: The oracle separation is a *binary symmetry* — two distinct worlds (A and B) that are mirror-opposite in their P/NP relation. This is structurally analogous to a *Z₂ symmetry breaking*: the truth of P=NP is not invariant under oracle perturbation. No golden-ratio or base-60 link; the relevant structure is the *lattice of complexity classes* under relativization — a partial order with incomparable elements, reminiscent of root-system Weyl chambers where different choices of simple roots yield different but equally valid geometries. | DEPTH: 7 — Profound for metamathematics: it shows the *independenc\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,
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  "author_total": 1,
  "authors": [
    {
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      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/4trk0a9rb6mgn.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553620",
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  "published": "2026-10-22",
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  "ris": "https://research.draconitic.com/paper/4trk0a9rb6mgn.ris",
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      "first_seen": "2026-11-05T12:21:20Z",
      "native_id": "23553620",
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  "title": "Oracle Worlds Split: Why Diagonalization Cannot Settle P vs NP — E8 Intelligence Research",
  "title_text": "Oracle Worlds Split: Why Diagonalization Cannot Settle P vs NP — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:20Z",
  "url": "https://research.draconitic.com/paper/4trk0a9rb6mgn",
  "venue": "Zenodo",
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