  A classification of irreducible, dynamically non-degenerate, almost
commutative spectral triples is refined. It is extended to include centrally
extended spin lifts. Simultaneously it is reduced by imposing three
constraints: (i) the condition of vanishing Yang-Mills and mixed gravitational
anomalies, (ii) the condition that the fermion representation be complex under
the little group, while (iii) massless fermions are to remain neutral under the
little group. These constraints single out the standard model with one
generation of leptons and quarks and with an arbitrary number of colours.
