{
  "abstract": "FINDING: The convergence of fixed-point theorems, diagonalization, and self-reference forms a unified structural principle underlying Gödelian incompleteness, the halting problem, and Banach contraction mappings — all hinging on the existence or non-existence of invariant points under transformation. | MATH: Banach fixed-point theorem: \\( d(Tx,Ty) \\leq q\\,d(x,y), \\; q \\in [0,1) \\Rightarrow \\exists! x^*: T(x^*) = x^* \\), with convergence rate \\( d(x_n, x^*) \\leq \\frac{q^n}{1-q} d(x_0, x_1) \\). Diagonalization lemma (Gödel/Carnap): \\( \\exists \\phi \\) such that \\( PA \\vdash \\phi \\leftrightarrow \\psi(\\ulcorner \\phi \\urcorner) \\). Halting problem: no total computable \\( h(x,y) \\) with \\( h(x,x)=1 \\) iff \\( \\phi_x(x) \\) halts — proven via self-application \\( \\phi_d(x) = \\text{loop if } h(x,x)=0 \\). | CONNECTION: The contraction constant \\( q \\) is a ratio in (0,1). The golden ratio conjugate \\( 0.618... \\) is the optimal contraction factor for certain Lipschitz maps on intervals (e.g., \\( T(\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": [
    {
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/2cm2szkpyfwpg.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587338",
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  "id": "2cm2szkpyfwpg",
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  "language": "eng",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cm2szkpyfwpg.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:47Z",
      "native_id": "23587338",
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  "subjects": [],
  "title": "The Invariant-Point Principle Unifying Gödel, Halting, and Banach — E8 Intelligence Research",
  "title_text": "The Invariant-Point Principle Unifying Gödel, Halting, and Banach — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:47Z",
  "url": "https://research.draconitic.com/paper/2cm2szkpyfwpg",
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