  We investigate an economical explanation for the $(g-2)_\mu$ anomaly with a
neutral vector boson from a spontaneously broken $\mathrm{U}(1)_X$ gauge
symmetry. The Standard Model fermion content is minimally extended by 3
right-handed neutrinos. Using a battery of complementary constraints, we
perform a thorough investigation of the renormalizable, quark flavor-universal,
vector-like $\mathrm{U}(1)_X$ models, allowing for arbitrary kinetic mixing.
Out of 419 models with integer charges not greater than ten, only 7 models are
viable solutions, describing a narrow region in model space. These are either
$L_\mu-L_\tau$ or models with a ratio of electron to baryon number close to
$-2$. The key complementary constraints are from the searches for nonstandard
neutrino interactions. Furthermore, we comment on the severe challenges to
chiral $\mathrm{U}(1)_X$ solutions and show the severe constraints on a
particularly promising such candidate.
