{
  "id": "oai:papers.qnfo.org:thresholded-readout-of-continuous-classical-fields-a-formalization-and-counterex",
  "slug": "thresholded-readout-of-continuous-classical-fields-a-formalization-and-counterex",
  "title": "Thresholded Readout of Continuous Classical Fields: A Formalization and Counterexample to the Uniqueness Claim for Quantum Mechanics",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "A family of contemporary foundational programs asserts that reality is a continuum of local deterministic fields and that quantum mechanics is the unique calculus bridging this continuum to discrete measurement outcomes. If that uniqueness claim were correct, research seeking additional physical principles behind quantum statistics could stop; if it is wrong, the specific failure localizes where extra structure must be added. This paper formalizes the proposed bridge as a thresholded amplification map M:RtoO and tests uniqueness by construction. Within the axiom class of continuous local deterministic fields plus irreversible discrete readout, we exhibit two distinct calculi — a linear threshold and a quadratic (intensity-like) threshold — that yield detection probabilities $0.1587$ and $0.3174$ respectively for a unit-variance Gaussian field at threshold Θ=1, a structural factor of exactly $2$ that persists at other thresholds. A slope-matched noisy threshold detector with σ_n=√2/π≈0.7978846 reproduces the two-outcome Born rule only approximately, with maximum deviation $0.1050$ and root-mean-square deviation $0.0602$ over a five-point angular grid. We prove the CHSH bound |S|≤2 for every deterministic local thresholded readout, against the quantum prediction |S|=2√2≈2.8284. Uniqueness therefore fails at the level of the readout calculus. A projection shows ≈130 trials per setting suffice to distinguish the two calculi experimentally.",
  "abstract_markdown": "A family of contemporary foundational programs asserts that reality is a continuum of local deterministic fields and that quantum mechanics is the unique calculus bridging this continuum to discrete measurement outcomes. If that uniqueness claim were correct, research seeking additional physical principles behind quantum statistics could stop; if it is wrong, the specific failure localizes where extra structure must be added. This paper formalizes the proposed bridge as a thresholded amplification map $M:\\mathbb{R}\\to\\mathcal{O}$ and tests uniqueness by construction. Within the axiom class of continuous local deterministic fields plus irreversible discrete readout, we exhibit two distinct calculi — a linear threshold and a quadratic (intensity-like) threshold — that yield detection probabilities $0.1587$ and $0.3174$ respectively for a unit-variance Gaussian field at threshold $\\Theta=1$, a structural factor of exactly $2$ that persists at other thresholds. A slope-matched noisy threshold detector with $\\sigma_n=\\sqrt{2/\\pi}\\approx0.7978846$ reproduces the two-outcome Born rule only approximately, with maximum deviation $0.1050$ and root-mean-square deviation $0.0602$ over a five-point angular grid. We prove the CHSH bound $|S|\\le2$ for every deterministic local thresholded readout, against the quantum prediction $|S|=2\\sqrt{2}\\approx2.8284$. Uniqueness therefore fails at the level of the readout calculus. A projection shows $\\approx130$ trials per setting suffice to distinguish the two calculi experimentally.",
  "date": "2026-10-11",
  "first_published": "2026-10-11",
  "last_revised": "2026-10-15T10:30:36Z",
  "modified": "2026-10-15T10:30:36Z",
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  "url": "https://papers.qnfo.org/papers/thresholded-readout-of-continuous-classical-fields-a-formalization-and-counterex",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Thresholded Readout of Continuous Classical Fields: A Formalization and Counterexample to the Uniqueness Claim for Quantum Mechanics"
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        "description": "A family of contemporary foundational programs asserts that reality is a continuum of local deterministic fields and that quantum mechanics is the unique calculus bridging this continuum to discrete measurement outcomes. If that uniqueness claim were correct, research seeking additional physical principles behind quantum statistics could stop; if it is wrong, the specific failure localizes where extra structure must be added. This paper formalizes the proposed bridge as a thresholded amplification map M:RtoO and tests uniqueness by construction. Within the axiom class of continuous local deterministic fields plus irreversible discrete readout, we exhibit two distinct calculi — a linear threshold and a quadratic (intensity-like) threshold — that yield detection probabilities $0.1587$ and $0.3174$ respectively for a unit-variance Gaussian field at threshold Θ=1, a structural factor of exactly $2$ that persists at other thresholds. A slope-matched noisy threshold detector with σ_n=√2/π≈0.7978846 reproduces the two-outcome Born rule only approximately, with maximum deviation $0.1050$ and root-mean-square deviation $0.0602$ over a five-point angular grid. We prove the CHSH bound |S|≤2 for every deterministic local thresholded readout, against the quantum prediction |S|=2√2≈2.8284. Uniqueness therefore fails at the level of the readout calculus. A projection shows ≈130 trials per setting suffice to distinguish the two calculi experimentally.",
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