{
  "id": "oai:papers.qnfo.org:computable-real-boundary",
  "slug": "computable-real-boundary",
  "title": "The Computable Real Boundary: Where Physics Ends and Cognitive Fiction Begins",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Every experiment reduces to a finite act of distinction: this reading, not that; this frequency range, not that; this bit string, not its negation. Physics is, at its operational core, a discipline of finite distinguishability. Yet the mathematical architecture physics inherited — the real number field R — is uncountable, containing elements that no finite procedure can approximate or discriminate. This paper argues that the boundary between physics and what lies beyond it coincides exactly with the computable reals R_comp: the set of real numbers that are ε-approximable by a terminating algorithm for any rational ε > 0 [@turing_computable_numbers_1936]. Drawing on Spencer-Brown's Laws of Form [@spencer_brown_lof], its QNFO extension [@qnfo_quantum_laws_of_form], and independent work on the physical Church-Turing thesis [@leshem_physical_ctt; @bolotin_nonconstructive_qm], we define Cognitive Fiction as any formal system that is internally consistent but cannot be reduced to void — cannot be distinguished by any finite measurement procedure — under the two primitive operations that generate all physically accessible distinctions: the mark and the enclosure. We argue that non-computable reals, non-measurable sets, and unfalsifiable formal systems belong to this category, and show through a cross-domain structural translation that this boundary is not unique to physics but recurs as the verifiable/unverifiable cut across six independent disciplines.",
  "abstract_markdown": "Every experiment reduces to a finite act of distinction: this reading, not that; this frequency range, not that; this bit string, not its negation. Physics is, at its operational core, a discipline of finite distinguishability. Yet the mathematical architecture physics inherited — the real number field $\\mathbb{R}$ — is uncountable, containing elements that no finite procedure can approximate or discriminate. This paper argues that the boundary between physics and what lies beyond it coincides exactly with the computable reals $\\mathbb{R}_{\\text{comp}}$: the set of real numbers that are $\\varepsilon$-approximable by a terminating algorithm for any rational $\\varepsilon > 0$ [@turing_computable_numbers_1936]. Drawing on Spencer-Brown's *Laws of Form* [@spencer_brown_lof], its QNFO extension [@qnfo_quantum_laws_of_form], and independent work on the physical Church-Turing thesis [@leshem_physical_ctt; @bolotin_nonconstructive_qm], we define **Cognitive Fiction** as any formal system that is internally consistent but cannot be reduced to void — cannot be distinguished by any finite measurement procedure — under the two primitive operations that generate all physically accessible distinctions: the mark and the enclosure. We argue that non-computable reals, non-measurable sets, and unfalsifiable formal systems belong to this category, and show through a cross-domain structural translation that this boundary is not unique to physics but recurs as the verifiable/unverifiable cut across six independent disciplines.",
  "date": "2026-07-28",
  "first_published": "2026-07-28",
  "last_revised": "2026-07-28T00:00:00Z",
  "modified": "2026-07-28T00:00:00Z",
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  "language": "en",
  "keywords": [
    "computable reals",
    "Laws of Form",
    "Church-Turing thesis",
    "falsifiability",
    "cognitive fiction",
    "Monna-map",
    "ultrametric physics",
    "ontological closure"
  ],
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  "url": "https://papers.qnfo.org/papers/computable-real-boundary",
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  "version_url": "https://papers.qnfo.org/papers/computable-real-boundary/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "The Computable Real Boundary: Where Physics Ends and Cognitive Fiction Begins"
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        "subject": "computable reals"
      },
      {
        "subject": "Laws of Form"
      },
      {
        "subject": "Church-Turing thesis"
      },
      {
        "subject": "falsifiability"
      },
      {
        "subject": "cognitive fiction"
      },
      {
        "subject": "Monna-map"
      },
      {
        "subject": "ultrametric physics"
      },
      {
        "subject": "ontological closure"
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        "date": "2026-07-28",
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        "description": "Every experiment reduces to a finite act of distinction: this reading, not that; this frequency range, not that; this bit string, not its negation. Physics is, at its operational core, a discipline of finite distinguishability. Yet the mathematical architecture physics inherited — the real number field R — is uncountable, containing elements that no finite procedure can approximate or discriminate. This paper argues that the boundary between physics and what lies beyond it coincides exactly with the computable reals R_comp: the set of real numbers that are ε-approximable by a terminating algorithm for any rational ε > 0 [@turing_computable_numbers_1936]. Drawing on Spencer-Brown's Laws of Form [@spencer_brown_lof], its QNFO extension [@qnfo_quantum_laws_of_form], and independent work on the physical Church-Turing thesis [@leshem_physical_ctt; @bolotin_nonconstructive_qm], we define Cognitive Fiction as any formal system that is internally consistent but cannot be reduced to void — cannot be distinguished by any finite measurement procedure — under the two primitive operations that generate all physically accessible distinctions: the mark and the enclosure. We argue that non-computable reals, non-measurable sets, and unfalsifiable formal systems belong to this category, and show through a cross-domain structural translation that this boundary is not unique to physics but recurs as the verifiable/unverifiable cut across six independent disciplines.",
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