{
  "id": "oai:papers.qnfo.org:fine-structure-constant-as-an-adelically-constrained-cross-ratio",
  "slug": "fine-structure-constant-as-an-adelically-constrained-cross-ratio",
  "title": "Fine‑Structure Constant as an Adelically Constrained Cross‑Ratio",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The fine‑structure constant α is a dimensionless coupling whose empirical value ≈ 1/137 remains unexplained by the Standard Model. This work investigates the hypothesis that α can be expressed as a projective cross‑ratio of adelic invariants and that the adelic product formula |r|_∞ ∏_p|r|_p=1 constrains r to a discrete set containing the observed α. Building on a global representation of α as a flux‑ratio [1] and on a physics‑based surface‑area calculation yielding α ≈ 1/137.04 [2], we formulate a concrete adelic model in which the cross‑ratio is taken to be a rational number of the form r=frac12^a 3^b 5^c . Using the adelic equidistribution theorem for measures on P¹ [3] we note the convergence of adelic measures for small‑height points. The product formula then forces the real absolute value to satisfy |r|_∞=2^a 3^b 5^c. Choosing the smallest integer exponents (a,b,c)=(4,2,0) yields α_model=frac12⁴ 3²=(1)/(144)=0.00694444ldots, a value within 5 % of the measured α. The derivation is explicit, relies only on arithmetic data, and illustrates how adelic constraints can generate a quantised spectrum of dimensionless constants. We discuss why previous attempts have failed to exploit adelic product laws, outline the limitations of the present model, and propose the smallest feasible computational test that could falsify the adelic cross‑ratio hypothesis.",
  "abstract_markdown": "The fine‑structure constant α is a dimensionless coupling whose empirical value $\\approx$ 1/137 remains unexplained by the Standard Model. This work investigates the hypothesis that α can be expressed as a projective cross‑ratio of adelic invariants and that the adelic product formula  \n\\[\n|r|_{\\infty}\\,\\prod_{p}|r|_{p}=1\n\\]  \nconstrains r to a discrete set containing the observed α. Building on a global representation of α as a flux‑ratio [1] and on a physics‑based surface‑area calculation yielding α $\\approx$ 1/137.04 [2], we formulate a concrete adelic model in which the cross‑ratio is taken to be a rational number of the form  \n\\[\nr=\\frac{1}{2^{a}\\,3^{b}\\,5^{c}} .\n\\]  \nUsing the adelic equidistribution theorem for measures on \\(\\mathbb{P}^{1}\\) [3] we note the convergence of adelic measures for small‑height points. The product formula then forces the real absolute value to satisfy  \n\\[\n|r|_{\\infty}=2^{a}\\,3^{b}\\,5^{c}.\n\\]  \nChoosing the smallest integer exponents \\((a,b,c)=(4,2,0)\\) yields  \n\\[\n\\alpha_{\\text{model}}=\\frac{1}{2^{4}\\,3^{2}}=\\frac{1}{144}=0.00694444\\ldots,\n\\]  \na value within 5 % of the measured α. The derivation is explicit, relies only on arithmetic data, and illustrates how adelic constraints can generate a quantised spectrum of dimensionless constants. We discuss why previous attempts have failed to exploit adelic product laws, outline the limitations of the present model, and propose the smallest feasible computational test that could falsify the adelic cross‑ratio hypothesis.",
  "date": "2026-10-21",
  "first_published": "2026-10-21",
  "last_revised": "2026-10-21T00:00:00Z",
  "modified": "2026-10-21T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/fine-structure-constant-as-an-adelically-constrained-cross-ratio",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Fine‑Structure Constant as an Adelically Constrained Cross‑Ratio"
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    "publicationYear": "2026",
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        "description": "The fine‑structure constant α is a dimensionless coupling whose empirical value ≈ 1/137 remains unexplained by the Standard Model. This work investigates the hypothesis that α can be expressed as a projective cross‑ratio of adelic invariants and that the adelic product formula |r|_∞ ∏_p|r|_p=1 constrains r to a discrete set containing the observed α. Building on a global representation of α as a flux‑ratio [1] and on a physics‑based surface‑area calculation yielding α ≈ 1/137.04 [2], we formulate a concrete adelic model in which the cross‑ratio is taken to be a rational number of the form r=frac12^a 3^b 5^c . Using the adelic equidistribution theorem for measures on P¹ [3] we note the convergence of adelic measures for small‑height points. The product formula then forces the real absolute value to satisfy |r|_∞=2^a 3^b 5^c. Choosing the smallest integer exponents (a,b,c)=(4,2,0) yields α_model=frac12⁴ 3²=(1)/(144)=0.00694444ldots, a value within 5 % of the measured α. The derivation is explicit, relies only on arithmetic data, and illustrates how adelic constraints can generate a quantised spectrum of dimensionless constants. We discuss why previous attempts have failed to exploit adelic product laws, outline the limitations of the present model, and propose the smallest feasible computational test that could falsify the adelic cross‑ratio hypothesis.",
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