Clifford algebra implying three fermion generations revisited

The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure rootp(2) --> Gamma((N)) . p works, leading to a sequence N = 1, 2, 3,... of Dirac-type equations, where four Dirac-type matrices Gamma(mu)((N)) are embedded into a Clifford algebra via a Jacobi definition introducing four "centre-of-mass" and (N - 1) x four "relative" Dirac-type matrices. These define one "centre-of-mass" and N - 1 "relative" Dirac bispinor indices. Secundo, the "centre-of-mass" Dirac bispinor index is coupled to the Standard Model gauge fields, while N - 1 "relative" Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to "relative" Dirac indices. This allows only for three Dirac-type equations with N = 1, 3, 5 in the case of N odd, and two with N = 2,4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3 x 3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is m(tau) = 1776.80 MeV, when the input of experimental m(e) and m(mu) is used.