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  "slug": "completion-invariance-of-physical-ontology-the-rational-base-field-in-quantum-fo",
  "title": "Completion-Invariance of Physical Ontology: The Rational Base Field in Quantum Foundations",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "We propose and formalize a principle of completion-invariance for physical ontology: since all recorded measurement outcomes are rational numbers, the archimedean completion R and the non-archimedean completions Q_p of the rational base field Q are equally instrumental constructs, and any claim that the continuum is physically real must, to be consistent, extend equal reality-status to every completion of the same base field. We develop a finite-precision (rational) formulation of quantum mechanics in which amplitudes are restricted to rationals of bounded denominator and prove an explicit error bound: for a d-dimensional system with amplitudes approximated at n-bit precision, the deviation of every Born-rule probability from its standard value is at most (2+δ)√d δ with δ = 2^-n-1, which for d=4 and n=64 is ≈ 1.08× 10^-19 — far below any operational discrimination. [...]",
  "abstract_markdown": "We propose and formalize a principle of completion-invariance for physical ontology: since all recorded measurement outcomes are rational numbers, the archimedean completion $\\mathbb{R}$ and the non-archimedean completions $\\mathbb{Q}_p$ of the rational base field $\\mathbb{Q}$ are equally instrumental constructs, and any claim that the continuum is physically real must, to be consistent, extend equal reality-status to every completion of the same base field. We develop a finite-precision (rational) formulation of quantum mechanics in which amplitudes are restricted to rationals of bounded denominator and prove an explicit error bound: for a $d$-dimensional system with amplitudes approximated at $n$-bit precision, the deviation of every Born-rule probability from its standard value is at most $(2+\\delta)\\sqrt{d}\\,\\delta$ with $\\delta = 2^{-n-1}$, which for $d=4$ and $n=64$ is $\\approx 1.08\\times 10^{-19}$ — far below any operational discrimination. [...]",
  "date": "2026-10-10",
  "first_published": "2026-10-10",
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  "url": "https://papers.qnfo.org/papers/completion-invariance-of-physical-ontology-the-rational-base-field-in-quantum-fo",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Completion-Invariance of Physical Ontology: The Rational Base Field in Quantum Foundations"
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        "description": "We propose and formalize a principle of completion-invariance for physical ontology: since all recorded measurement outcomes are rational numbers, the archimedean completion R and the non-archimedean completions Q_p of the rational base field Q are equally instrumental constructs, and any claim that the continuum is physically real must, to be consistent, extend equal reality-status to every completion of the same base field. We develop a finite-precision (rational) formulation of quantum mechanics in which amplitudes are restricted to rationals of bounded denominator and prove an explicit error bound: for a d-dimensional system with amplitudes approximated at n-bit precision, the deviation of every Born-rule probability from its standard value is at most (2+δ)√d δ with δ = 2^-n-1, which for d=4 and n=64 is ≈ 1.08× 10^-19 — far below any operational discrimination. [...]",
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