{
  "id": "oai:papers.qnfo.org:physical-instantiation-as-selection-of-relational-structure-a-statistical-framew",
  "slug": "physical-instantiation-as-selection-of-relational-structure-a-statistical-framew",
  "title": "Physical Instantiation as Selection of Relational Structure: A Statistical Framework for Pre-Discovery in Mathematics",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Mathematics developed without physical motivation repeatedly finds core physical application: complex numbers in quantum mechanics, fiber bundles in gauge theory, and max-plus algebra in optimal control. The standard explanation—unreasonable effectiveness—treats this as a philosophical puzzle rather than a measurable phenomenon. The gap addressed here is the absence of any quantitative test of whether physical instantiation of pre-existing mathematical structures is statistically non-accidental and predictable from structural features alone. We formalize the conjecture that physics selects a subset of an autonomous relational grammar by defining an invariant-overlap isomorphism measure between algebraic relational skeletons and dynamical systems, and by constructing a retrospective selection test over a registry of historically pre-physical structures. Under explicit assumptions (a pool of $N = 20$ structures, $k = 6$ later physically instantiated, a chance rate $p = 0.15$), the binomial tail probability is P(X ≥ 6) ≈ 0.067, and a feature-conditioned split (5 of 8 symmetry-bearing structures instantiated versus 1 of 12 without) yields a one-sided Fisher exact probability of ≈ 0.018. Both computations are shown in full and are sensitive to the assumed counts: lowering the chance rate to $p = 0.10$ moves the binomial tail to ≈ 0.011, while losing one instantiation moves it to ≈ 0.170. The framework converts a metaphysical claim into a falsifiable registry study, gives mathematics-ontology projects a concrete curation target, and proposes a minimal next test: an expert-annotated registry of pre-1850 structures scored against the same null model.",
  "abstract_markdown": "Mathematics developed without physical motivation repeatedly finds core physical application: complex numbers in quantum mechanics, fiber bundles in gauge theory, and max-plus algebra in optimal control. The standard explanation—unreasonable effectiveness—treats this as a philosophical puzzle rather than a measurable phenomenon. The gap addressed here is the absence of any quantitative test of whether physical instantiation of pre-existing mathematical structures is statistically non-accidental and predictable from structural features alone. We formalize the conjecture that physics selects a subset of an autonomous relational grammar by defining an invariant-overlap isomorphism measure between algebraic relational skeletons and dynamical systems, and by constructing a retrospective selection test over a registry of historically pre-physical structures. Under explicit assumptions (a pool of $N = 20$ structures, $k = 6$ later physically instantiated, a chance rate $p = 0.15$), the binomial tail probability is $P(X \\geq 6) \\approx 0.067$, and a feature-conditioned split (5 of 8 symmetry-bearing structures instantiated versus 1 of 12 without) yields a one-sided Fisher exact probability of $\\approx 0.018$. Both computations are shown in full and are sensitive to the assumed counts: lowering the chance rate to $p = 0.10$ moves the binomial tail to $\\approx 0.011$, while losing one instantiation moves it to $\\approx 0.170$. The framework converts a metaphysical claim into a falsifiable registry study, gives mathematics-ontology projects a concrete curation target, and proposes a minimal next test: an expert-annotated registry of pre-1850 structures scored against the same null model.",
  "date": "2026-11-10",
  "first_published": "2026-11-10",
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  "url": "https://papers.qnfo.org/papers/physical-instantiation-as-selection-of-relational-structure-a-statistical-framew",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Physical Instantiation as Selection of Relational Structure: A Statistical Framework for Pre-Discovery in Mathematics"
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