  We prove a generic smoothness result in rigid analytic geometry over a
characteristic zero nonarchimedean field. The proof relies on a novel notion of
generic points in rigid analytic geometry which are well-adapted to "spreading
out" arguments, in analogy with the use of generic points in scheme theory. As
an application, we develop a six functor formalism for Zariski-constructible
\'etale sheaves on characteristic zero rigid spaces. Among other things, this
implies that characteristic zero rigid spaces support a well-behaved theory of
perverse sheaves.
