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  "id": "oai:papers.qnfo.org:finite-prime-valuations-in-fundamental-physics-an-adelically-demoted-real-number",
  "slug": "finite-prime-valuations-in-fundamental-physics-an-adelically-demoted-real-number",
  "title": "Finite‑Prime Valuations in Fundamental Physics: An Adelically Demoted Real‑Number Perspective",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Precision high‑energy experiments, quantum‑information platforms, and cosmological surveys all express predictions as real‑valued numbers, assuming that the Archimedean field alone captures physical reality. The gap is the absence of a systematic demonstration that finite‑prime ( p‑adic ) completions are either optional decorations or mathematically required components of any rational observable. We adopt a purely analytical approach: (i) we model selected observables as rational numbers in Planck units, (ii) we compute their p‑adic absolute values | · |_p for the first few primes, (iii) we verify the adelic product formula ∏_v|q|_v=1 and derive the redundancy relation |q|_∞= ∏_p|q|_p^-1, (iv) we estimate the average number of primes that carry non‑trivial valuation data for reduced fractions with numerator and denominator below 10³, and (v) we count the discriminating power of valuation tuples over the primes p≤13. The exact verification for q=6/35 yields a product of $1$, while a second example q=1001/1000 reproduces the same result with larger p‑adic factors. The average number of non‑trivial primes is $3.94$, and valuation tuples over p≤13 distinguish 3.89×10⁵ classes, comparable to the 3.04×10⁵ reduced fractions with denominator ≤10³. These results imply that the Archimedean place carries no independent information for rational observables; consequently, ultra‑precise measurements of constants such as the fine‑structure constant α become direct probes of hidden p‑adic structure. Adoption of adelic modelling would therefore reshape theoretical design choices in collider physics, quantum‑information engineering, and cosmology.",
  "abstract_markdown": "Precision high‑energy experiments, quantum‑information platforms, and cosmological surveys all express predictions as real‑valued numbers, assuming that the Archimedean field alone captures physical reality. The gap is the absence of a systematic demonstration that finite‑prime ( $p$‑adic ) completions are either optional decorations or mathematically required components of any rational observable. We adopt a purely analytical approach: (i) we model selected observables as rational numbers in Planck units, (ii) we compute their $p$‑adic absolute values $|\\,\\cdot\\,|_{p}$ for the first few primes, (iii) we verify the adelic product formula $\\prod_{v}|q|_{v}=1$ and derive the redundancy relation $|q|_{\\infty}= \\prod_{p}|q|_{p}^{-1}$, (iv) we estimate the average number of primes that carry non‑trivial valuation data for reduced fractions with numerator and denominator below $10^{3}$, and (v) we count the discriminating power of valuation tuples over the primes $p\\le13$. The exact verification for $q=6/35$ yields a product of $1$, while a second example $q=1001/1000$ reproduces the same result with larger $p$‑adic factors. The average number of non‑trivial primes is $3.94$, and valuation tuples over $p\\le13$ distinguish $3.89\\times10^{5}$ classes, comparable to the $3.04\\times10^{5}$ reduced fractions with denominator $\\le10^{3}$. These results imply that the Archimedean place carries no independent information for rational observables; consequently, ultra‑precise measurements of constants such as the fine‑structure constant $\\alpha$ become direct probes of hidden $p$‑adic structure. Adoption of adelic modelling would therefore reshape theoretical design choices in collider physics, quantum‑information engineering, and cosmology.",
  "date": "2026-10-19",
  "first_published": "2026-10-19",
  "last_revised": "2026-10-19T00:00:00Z",
  "modified": "2026-10-19T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/finite-prime-valuations-in-fundamental-physics-an-adelically-demoted-real-number",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Finite‑Prime Valuations in Fundamental Physics: An Adelically Demoted Real‑Number Perspective"
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    ],
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    "publicationYear": "2026",
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        "description": "Precision high‑energy experiments, quantum‑information platforms, and cosmological surveys all express predictions as real‑valued numbers, assuming that the Archimedean field alone captures physical reality. The gap is the absence of a systematic demonstration that finite‑prime ( p‑adic ) completions are either optional decorations or mathematically required components of any rational observable. We adopt a purely analytical approach: (i) we model selected observables as rational numbers in Planck units, (ii) we compute their p‑adic absolute values | · |_p for the first few primes, (iii) we verify the adelic product formula ∏_v|q|_v=1 and derive the redundancy relation |q|_∞= ∏_p|q|_p^-1, (iv) we estimate the average number of primes that carry non‑trivial valuation data for reduced fractions with numerator and denominator below 10³, and (v) we count the discriminating power of valuation tuples over the primes p≤13. The exact verification for q=6/35 yields a product of $1$, while a second example q=1001/1000 reproduces the same result with larger p‑adic factors. The average number of non‑trivial primes is $3.94$, and valuation tuples over p≤13 distinguish 3.89×10⁵ classes, comparable to the 3.04×10⁵ reduced fractions with denominator ≤10³. These results imply that the Archimedean place carries no independent information for rational observables; consequently, ultra‑precise measurements of constants such as the fine‑structure constant α become direct probes of hidden p‑adic structure. Adoption of adelic modelling would therefore reshape theoretical design choices in collider physics, quantum‑information engineering, and cosmology.",
        "descriptionType": "Abstract"
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