Analysis extends Koide structure to fermions, revealing near-Koide triples and implications for stability.
We extend the Koide structure analysis of our companion paper beyond the charged lepton sector. A systematic scan of all 220 fermion triples from the Standard Model spectrum reveals 11 near-Koide triples with |Q − 2/3| < 1%, led by the charged leptons (6.2 × 10⁻⁶) and followed by the cross-sector (μ, d, s) at 1.7 × 10⁻³ and the third-generation quarks (c, b, t) at 2.8 × 10⁻³. We show that the (c,b,t) near-miss is stable under QCD running from 2 GeV to 10¹³ GeV. We connect the Koide condition b² = 2 to A₄ flavor symmetry VEV alignment. Radiative stability of Q is established at 1-loop QED, with 2-loop corrections δQ/Q ~ 2 × 10⁻⁶ matching the observed deviation. A Monte Carlo analysis (10⁷ trials) yields p = 1.4 × 10⁻⁵. Companion to: T. Nagy, "Formal Koide Structure: Mass Bounds, Generation Counting, and Neutrino Predictions from the Z_N Ansatz" (DOI: 10.5281/zenodo.19698012).
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Tamás Nagy (2026) studied this question.
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