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  "slug": "non-associative-spectral-triples-and-a-parameter-free-foundation-for-the-standar",
  "title": "Non‑Associative Spectral Triples and a Parameter‑Free Foundation for the Standard Model",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The Standard Model (SM) contains dozens of empirically determined parameters, limiting its predictive power and obstructing unified model building. A concrete gap is the absence of a mathematically grounded mechanism that generates particle masses, coupling constants, and generation structure without external input. We formulate a non‑associative spectral triple based on the octonion algebra O, impose a self‑consistency (autaxys) condition on the Dirac operator, and derive a resonance condition that reproduces the Koide formula for charged leptons. Using the same framework we compute the Compton wavelength of a putative 10^-15 eV ultralight dark‑matter particle, its free‑streaming horizon, and the corresponding oscillation frequency. The Koide ratio evaluates to $0.66665864$, differing from the exact value 2/3 by 8.03×10^-6 (relative deviation 1.2×10^-5), well within experimental uncertainties; the dark‑matter wavelength is 1.23984193×10⁹ m, the free‑streaming horizon is 1.37×10^-5 pc (corresponding to 4.2×10¹1 m), and the oscillation frequency is 0.241791 Hz. These results demonstrate that a non‑associative geometric foundation can yield quantitative SM relations and falsifiable cosmological predictions, opening a pathway toward a parameter‑free theory of fundamental physics.",
  "abstract_markdown": "The Standard Model (SM) contains dozens of empirically determined parameters, limiting its predictive power and obstructing unified model building. A concrete gap is the absence of a mathematically grounded mechanism that generates particle masses, coupling constants, and generation structure without external input. We formulate a non‑associative spectral triple based on the octonion algebra $\\mathbb{O}$, impose a self‑consistency (autaxys) condition on the Dirac operator, and derive a resonance condition that reproduces the Koide formula for charged leptons. Using the same framework we compute the Compton wavelength of a putative $10^{-15}\\,\\text{eV}$ ultralight dark‑matter particle, its free‑streaming horizon, and the corresponding oscillation frequency. The Koide ratio evaluates to $0.66665864$, differing from the exact value $2/3$ by $8.03\\times10^{-6}$ (relative deviation $1.2\\times10^{-5}$), well within experimental uncertainties; the dark‑matter wavelength is $1.23984193\\times10^{9}\\,\\text{m}$, the free‑streaming horizon is $1.37\\times10^{-5}\\,\\text{pc}$ (corresponding to $4.2\\times10^{11}\\,\\text{m}$), and the oscillation frequency is $0.241791\\,\\text{Hz}$. These results demonstrate that a non‑associative geometric foundation can yield quantitative SM relations and falsifiable cosmological predictions, opening a pathway toward a parameter‑free theory of fundamental physics.",
  "date": "2026-11-03",
  "first_published": "2026-11-03",
  "last_revised": "2026-11-03T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/non-associative-spectral-triples-and-a-parameter-free-foundation-for-the-standar",
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        "title": "Non‑Associative Spectral Triples and a Parameter‑Free Foundation for the Standard Model"
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        "description": "The Standard Model (SM) contains dozens of empirically determined parameters, limiting its predictive power and obstructing unified model building. A concrete gap is the absence of a mathematically grounded mechanism that generates particle masses, coupling constants, and generation structure without external input. We formulate a non‑associative spectral triple based on the octonion algebra O, impose a self‑consistency (autaxys) condition on the Dirac operator, and derive a resonance condition that reproduces the Koide formula for charged leptons. Using the same framework we compute the Compton wavelength of a putative 10^-15 eV ultralight dark‑matter particle, its free‑streaming horizon, and the corresponding oscillation frequency. The Koide ratio evaluates to $0.66665864$, differing from the exact value 2/3 by 8.03×10^-6 (relative deviation 1.2×10^-5), well within experimental uncertainties; the dark‑matter wavelength is 1.23984193×10⁹ m, the free‑streaming horizon is 1.37×10^-5 pc (corresponding to 4.2×10¹1 m), and the oscillation frequency is 0.241791 Hz. These results demonstrate that a non‑associative geometric foundation can yield quantitative SM relations and falsifiable cosmological predictions, opening a pathway toward a parameter‑free theory of fundamental physics.",
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