We prove that the finite quotients of a fibered hyperbolic 3-manifold group detect the taut polynomials of fibered faces of the Thurston norm balls, whenever the monodromy map is fully-punctured. To this end, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials. As an application, we identify specific one-cusped hyperbolic $3$-manifolds that are profinitely rigid among $3$-manifold groups, by a strategy using normalized dilatations and the veering census; notably, the taut polynomials distinguish a pair of mapping tori sharing the fiber and the dilatation. This talk is based on joint work with Tamunonye Cheetham-West, Jun Ueki, and Youheng Yao.
