We present an analytical formula that predicts all nine charged fermion masses from the Poisson ratio nu = 0. 4555 of the vacuum condensate established in the companion paper (https: //doi. org/10. 5281/zenodo. 19143779). The first-generation masses are given by mf = v/ (sqrt (2) RFf), where R = kappa/mu = 2 (1+nu) /3 (1-2nu) = 10. 903 is the bulk-to-shear modulus ratio and the exponents Ff are constructed entirely from Casimir operators of SU (3) and SU (4) and the Poisson ratio itself. Higher generations follow from mₙ = m₁ x Rᵃlphaₛ (n-1) ᵍamma, where alphaₛ and gamma depend on weak isospin T₃, hypercharge Y, and the color Casimir CF -- with each coefficient matching a known group-theoretic or geometric constant to better than 0. 7%. The electron mass is predicted to 0. 3%; all first-generation masses agree within 3. 2%. At leading order, all nine masses are reproduced within 28%; next-to-leading-order corrections with simple-fraction coefficients bring all second- and third-generation predictions within 0. 5% of PDG values. The formula contains zero free parameters beyond the two condensate constants nu and v = 246 GeV already fixed in Paper I.
Luqman Omar Mahmood (2026) studied this question.