Through the Helmholtzian factorization of the Helmholtz/Klein-Gordon equation the mass is a sum of squares of a 4-tuple of the four-vector-doublet. The Dirac equation factoring shows that the electron satisfies via a mass-singlet. Thus, in combination, the heavy leptons and quarks are separated as: (0,0,0,mu2080) heavy leptons satisfying the Dirac factoring, and (mu2081,mu2082,mu2083,0) quarks satisfying the Helmholtzian factoring, as pythagorean quadruples. Through the pythagorean quadruple primitives (2,5,14,15)⇒(∓(1/3),∓(5/6),∓(7/3),(5/2)), (±(2/3),±(5/3),±((14)/3),5),charge and color are manifested, plus the mass magnitude |m|² is always the sum-of-squares of the mass-constituents via Klein-Gordon equation. Plus, by establishing the fermion architecture the weak interaction is manifested (including the masses of the Wu207a and Zu2070 , via the fundamental dimensionless physical constant $k$). And continuing the Helmholtzian factorization/Dirac equation factoring analysis, extended through the Helmholtzian factorization to all particle types and interactions (quarks, neutrinos, weaks, heavy leptons).