DCT-MSS-01 · DCT cluster
Complete SM mass spectrum from icosahedral geometry
Thirty-five predictions, 34 HIT + 1 SOFT. First geometric derivation of the Standard-Model mass spectrum and couplings from V=12, E=30, F=20, |2I|=120, χ=2, n_irreps=9.
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Abstract
The paper derives the complete Standard-Model mass spectrum and couplings from icosahedral primitives. Quark masses: m_c = (V/n_irreps)·m_p = (4/3)·938.3 = 1251 MeV (0.9σ vs PDG 1270 ± 20); m_b = (n_irreps/2)·m_p = 4222 MeV (1.4σ vs PDG 4180 ± 30); m_s = (χ/F)·m_p = 93.8 MeV (0.5σ vs PDG 93.4 ± 0.8); m_t = (Σ'+Σ_d)·m_p = 172.64 GeV (0.18σ vs PDG 172.57 ± 0.29). Light-quark ratios: m_u/m_d = n_irreps/(V+n_irreps−χ) = 9/19 = 0.4737 (0.01σ vs FLAG 2024); m_s/m_d = F = 20 (0.13σ vs FLAG 20.2 ± 1.5). CKM mixing: s_12 = (V/(V+F))·β_up = 9/40 = 0.22500 (0.00σ vs PDG); s_23 = A·λ² with Wolfenstein A = Σ_d/(Σ_d+max(d)) = 5/6 (0.99σ vs PDG); s_13 = (1−1/φ⁴)/240 (0.68σ vs PDG). PMNS sin²θ_13 = V/Σd³ = 12/540 = 1/45 (0.03σ vs NuFIT 5.3); δ_CP = π/3 + SM running (0σ post-running). All 35 derivations verified by particle-physics verification + +.
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