  Consider the Cauchy problem for the radial cubic wave equation in 1+3
dimensions with either the focusing or defocusing sign. This problem is
critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and
subcritical with respect to the conserved energy. Here we prove that if the
critical norm of a solution remains bounded on the maximal time-interval of
existence, then the solution must in fact be global-in-time and scatter to free
waves as $t \to \pm \infty$.
