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  "id": "oai:papers.qnfo.org:adelic-constraints-on-standard-model-parameters-a-toy-consistency-test",
  "slug": "adelic-constraints-on-standard-model-parameters-a-toy-consistency-test",
  "title": "Adelic Constraints on Standard Model Parameters: A Toy Consistency Test",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The Standard Model (SM) contains dozens of free parameters whose values are measured but not explained. A long‑standing conjecture proposes that if the fundamental law is defined over the rational numbers Q and must be consistent under every completion (the real place R and all p‑adic fields Q_p), then adelic product formulas force the SM constants to be algebraic rather than arbitrary reals. Existing adelic frameworks—adelic line bundles, quasi‑adelic measures, and adelic tori—provide the mathematical machinery for such constraints. We formulate a simplified consistency condition for a single U(1) gauge coupling, derive the adelic product formula 60·2^-2·3^-1·5^-1=1, prove that it holds identically for any rational seed, and verify that rational perturbations of the seed preserve the identity exactly. These explicit arithmetic checks demonstrate that the adelic product identity can be satisfied without fine‑tuning; within this toy framework, any coupling realized as a rational seed is automatically an algebraic number. If the conjecture holds more generally, it would turn the SM parameters into calculable quantities, reshaping model‑building and precision tests of particle physics.",
  "abstract_markdown": "The Standard Model (SM) contains dozens of free parameters whose values are measured but not explained. A long‑standing conjecture proposes that if the fundamental law is defined over the rational numbers $\\mathbb{Q}$ and must be consistent under every completion (the real place $\\mathbb{R}$ and all $p$‑adic fields $\\mathbb{Q}_p$), then adelic product formulas force the SM constants to be algebraic rather than arbitrary reals. Existing adelic frameworks—adelic line bundles, quasi‑adelic measures, and adelic tori—provide the mathematical machinery for such constraints. We formulate a simplified consistency condition for a single $U(1)$ gauge coupling, derive the adelic product formula $60\\cdot2^{-2}\\cdot3^{-1}\\cdot5^{-1}=1$, prove that it holds identically for any rational seed, and verify that rational perturbations of the seed preserve the identity exactly. These explicit arithmetic checks demonstrate that the adelic product identity can be satisfied without fine‑tuning; within this toy framework, any coupling realized as a rational seed is automatically an algebraic number. If the conjecture holds more generally, it would turn the SM parameters into calculable quantities, reshaping model‑building and precision tests of particle physics.",
  "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/adelic-constraints-on-standard-model-parameters-a-toy-consistency-test",
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  "sha256": "17e369b3244f8907bb94d979f9d537cb97d6808ec44d83e1b39ce3fe7859f398",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Adelic Constraints on Standard Model Parameters: A Toy Consistency Test"
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        "description": "The Standard Model (SM) contains dozens of free parameters whose values are measured but not explained. A long‑standing conjecture proposes that if the fundamental law is defined over the rational numbers Q and must be consistent under every completion (the real place R and all p‑adic fields Q_p), then adelic product formulas force the SM constants to be algebraic rather than arbitrary reals. Existing adelic frameworks—adelic line bundles, quasi‑adelic measures, and adelic tori—provide the mathematical machinery for such constraints. We formulate a simplified consistency condition for a single U(1) gauge coupling, derive the adelic product formula 60·2^-2·3^-1·5^-1=1, prove that it holds identically for any rational seed, and verify that rational perturbations of the seed preserve the identity exactly. These explicit arithmetic checks demonstrate that the adelic product identity can be satisfied without fine‑tuning; within this toy framework, any coupling realized as a rational seed is automatically an algebraic number. If the conjecture holds more generally, it would turn the SM parameters into calculable quantities, reshaping model‑building and precision tests of particle physics.",
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