  For the critical focusing wave equation $\Box u = u^5$ on $\R^{3+1}$ in the
radial case, we establish the role of the "center stable" manifold $\Sigma$
constructed in \cite{KS} near the ground state $(W,0)$ as a threshold between
type I blowup and scattering to zero, establishing a conjecture going back to
numerical work by Bizo\'n, Chmaj, Tabor. The underlying topology is stronger
than the energy norm.
