  There is no reason why the gauge symmetry extension is family universal as in
the standard model and the most well-motivated models, e.g. left-right symmetry
and grand unification. Hence, we propose a simplest extension of the standard
model -- a flavor-dependent $U(1)$ gauge symmetry -- and find the new physics
insight. For this aim, the $U(1)$ charge, called $X$, is expressed as $X=x B+y
L$ in which $x$ and $y$ are free parameters as functions of flavor index, e.g.
for a flavor $i$ they take $x_i$ and $y_i$ respectively, where $B$ and $L$
denote normal baryon and lepton numbers. Imposing a relation involved by the
color number $3$, i.e.
$-x_{1,2,\cdots,n}=x_{n+1,n+2,\cdots,n+m}=3y_{1,2,\cdots,n+m}\equiv 3z$, for
arbitrarily nonzero $z$, we achieve a novel $U(1)$ theory with implied
$X$-charge. This theory not only explains the origin of the number of observed
fermion families but also offers a possible solution for both neutrino mass and
dark matter, which differs from $B-L$ extension. Two typical models based on
this idea are examined, yielding interesting results for flavor-changing
neutral currents and particle colliders, besides those of neutrino mass and
dark matter.
