  I show that breaking $B-L$ by one unit of this charge is suitable for
neutrino mass generation through an inverse seesaw mechanism, stabilizing a
dark matter candidate without supersymmetry, as well as solving the muon
anomalous magnetic moment and the $W$ mass deviation via dark field
contributions. The new physics is governed by the residual $Z_3$ symmetry of
$B-L$ isomorphic to the center of the color group, instead of the well-studied
matter parity.
