Geometric Parametrization of Flavor Mixing and the Mass Spectrum of Elementary Particles

We propose a geometric parametrization scheme with the electron mass m_e, the fine-structure constant α, π, and √2 as its sole inputs. In the quark sector, the four CKM flavor parameters are given directly by geometric formulas, with all nine matrix elements deviating by no more than 1.4σ; in the lepton sector, within the Normal Ordering with θ23 < 45° framework, the four PMNS flavor parameters are likewise given by geometric formulas, with all nine matrix elements within 1σ. Furthermore, the six quark masses are described by the PMNS/CKM mixing angles and m_e, with deviations below 0.7σ; the two mass-squared differences of the neutrino mass spectrum derived thereby deviate from NuFIT 6.0 by −0.21σ and −0.82σ (both within 1σ), and Δm²21 is confirmed by the higher-precision independent measurement (7.50±0.12)×10⁻⁵ eV² from JUNO 2026 (deviation −0.42σ). The same geometric rule extends to the Higgs boson mass and the glueball candidate X(2370). These results indicate that the flavor mixing angles, the mass spectrum of elementary particles, and the neutrino mass spectrum can be described uniformly by the same set of geometric constants and the master factor (A = (8π+1)/2).