  There exists a variety of theories of the glass transition and many more
numerical models. But because the models need built-in complexity to prevent
crystallization, comparisons with theory can be difficult. We study the
dynamics of a deeply supersaturated \emph{monodisperse} four-dimensional (4D)
hard-sphere fluid, which has no such complexity, but whose strong intrinsic
geometrical frustration inhibits crystallization, even when deeply
supersaturated. As an application, we compare its behavior to the mode-coupling
theory (MCT) of glass formation. We find MCT to describe this system better
than any other structural glass formers in lower dimensions. The reduction in
dynamical heterogeneity in 4D suggested by a milder violation of the
Stokes-Einstein relation could explain the agreement. These results are
consistent with a mean-field scenario of the glass transition.
