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  "id": "oai:papers.qnfo.org:operational-axioms-do-not-select-the-standard-model-a-formal-audit-of-a-generali",
  "slug": "operational-axioms-do-not-select-the-standard-model-a-formal-audit-of-a-generali",
  "title": "Operational Axioms Do Not Select the Standard Model: A Formal Audit of a Generalized-Probabilistic-Theory Reconstruction Conjecture",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "A conjecture in the foundations of physics holds that four operational axioms of generalized probabilistic theories (GPTs) — causality, no-signaling, local tomography, and continuous reversibility — extended to systems with infinitely many degrees of freedom, necessarily yield quantum field theory satisfying the Wightman axioms, and that adding Poincaré symmetry uniquely reconstructs the Standard Model Lagrangian. Existing finite-dimensional GPT reconstructions do not address field-theoretic or gauge structures, so the conjecture's necessity claims are untested. This paper tests them by formal analysis: it formalizes the conjecture as three precise statements, counts the structural degrees of freedom the axioms constrain, and analyzes the thermodynamic limit of finite-dimensional reconstructions. We derive that the Standard Model gauge sector carries $12$ Lie-algebra generators and $24$ propagating polarizations in the unbroken counting, while alternative gauge groups such as SU(5) (dimension $24$) and SO(10) (dimension $45$) violate none of the four operational axioms; that one Standard Model generation comprises $15$ Weyl fields ($45$ over three generations), a number no axiom forces; and that under local tomography the GPT state-space dimension grows as d²N-1, reaching approximately 10⁶02060 real parameters for 10⁶ two-level sites, so finite-dimensional reconstructions do not pass to the infinite limit without normalizability constraints the axioms do not supply. The necessity conjecture is therefore unproven and partially refuted at the level of gauge-group uniqueness; we specify the calculations that would settle it.",
  "abstract_markdown": "A conjecture in the foundations of physics holds that four operational axioms of generalized probabilistic theories (GPTs) — causality, no-signaling, local tomography, and continuous reversibility — extended to systems with infinitely many degrees of freedom, necessarily yield quantum field theory satisfying the Wightman axioms, and that adding Poincaré symmetry uniquely reconstructs the Standard Model Lagrangian. Existing finite-dimensional GPT reconstructions do not address field-theoretic or gauge structures, so the conjecture's necessity claims are untested. This paper tests them by formal analysis: it formalizes the conjecture as three precise statements, counts the structural degrees of freedom the axioms constrain, and analyzes the thermodynamic limit of finite-dimensional reconstructions. We derive that the Standard Model gauge sector carries $12$ Lie-algebra generators and $24$ propagating polarizations in the unbroken counting, while alternative gauge groups such as $SU(5)$ (dimension $24$) and $SO(10)$ (dimension $45$) violate none of the four operational axioms; that one Standard Model generation comprises $15$ Weyl fields ($45$ over three generations), a number no axiom forces; and that under local tomography the GPT state-space dimension grows as $d^{2N}-1$, reaching approximately $10^{602060}$ real parameters for $10^{6}$ two-level sites, so finite-dimensional reconstructions do not pass to the infinite limit without normalizability constraints the axioms do not supply. The necessity conjecture is therefore unproven and partially refuted at the level of gauge-group uniqueness; we specify the calculations that would settle it.",
  "date": "2026-11-03",
  "first_published": "2026-11-03",
  "last_revised": "2026-11-03T00:00:00Z",
  "modified": "2026-11-03T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/operational-axioms-do-not-select-the-standard-model-a-formal-audit-of-a-generali",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Operational Axioms Do Not Select the Standard Model: A Formal Audit of a Generalized-Probabilistic-Theory Reconstruction Conjecture"
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        "description": "A conjecture in the foundations of physics holds that four operational axioms of generalized probabilistic theories (GPTs) — causality, no-signaling, local tomography, and continuous reversibility — extended to systems with infinitely many degrees of freedom, necessarily yield quantum field theory satisfying the Wightman axioms, and that adding Poincaré symmetry uniquely reconstructs the Standard Model Lagrangian. Existing finite-dimensional GPT reconstructions do not address field-theoretic or gauge structures, so the conjecture's necessity claims are untested. This paper tests them by formal analysis: it formalizes the conjecture as three precise statements, counts the structural degrees of freedom the axioms constrain, and analyzes the thermodynamic limit of finite-dimensional reconstructions. We derive that the Standard Model gauge sector carries $12$ Lie-algebra generators and $24$ propagating polarizations in the unbroken counting, while alternative gauge groups such as SU(5) (dimension $24$) and SO(10) (dimension $45$) violate none of the four operational axioms; that one Standard Model generation comprises $15$ Weyl fields ($45$ over three generations), a number no axiom forces; and that under local tomography the GPT state-space dimension grows as d²N-1, reaching approximately 10⁶02060 real parameters for 10⁶ two-level sites, so finite-dimensional reconstructions do not pass to the infinite limit without normalizability constraints the axioms do not supply. The necessity conjecture is therefore unproven and partially refuted at the level of gauge-group uniqueness; we specify the calculations that would settle it.",
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