{
  "abstract": "FINDING: Undecidability is a structural feature of formal systems, not a computational limitation — Gödel's incompleteness and Turing's halting problem reveal that truth and provability diverge within any sufficiently expressive formal system. | MATH: Gödel's first incompleteness theorem: For any consistent, recursively axiomatizable system S capable of expressing arithmetic, ∃ a sentence G such that S ⊬ G and S ⊬ ¬G. Halting problem: No Turing machine H exists such that H(M,x) halts iff M(x) halts — proof via diagonalization: D(M) = loop if H(M,M) halts, else halt; contradiction H(D,D). Reducibility: A ≤ B means solving B solves A; undecidability propagates via many-one reductions (≤m). | CONNECTION: The diagonalization argument mirrors the golden ratio's self-referential structure — φ = 1 + 1/φ — a fixed-point equation. Gödel's G is a fixed point: G ↔ ¬Prov(⌜G⌝). This self-reference is the same algebraic skeleton as φ's continued fraction [1;1,1,1,...]. The incompleteness gap (unprov\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/fprn2a8h23c52.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431059",
  "fulltext_url": null,
  "id": "fprn2a8h23c52",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23431059",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fprn2a8h23c52.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:05Z",
      "native_id": "23431059",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431059"
    }
  ],
  "subjects": [],
  "title": "Undecidability as Structural Truth: Gödel and Turing's Shared Limit — E8 Intelligence Research",
  "title_text": "Undecidability as Structural Truth: Gödel and Turing's Shared Limit — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:05Z",
  "url": "https://research.draconitic.com/paper/fprn2a8h23c52",
  "venue": "Zenodo",
  "versions": []
}