  We examine the global structure of scalar field critical collapse spacetimes
using a characteristic double-null code. It can integrate past the horizon
without any coordinate problems, due to the careful choice of constraint
equations used in the evolution. The limiting sequence of sub- and
supercritical spacetimes presents an apparent paradox in the expected Penrose
diagrams, which we address in this paper. We argue that the limiting spacetime
converges pointwise to a unique limit for all r>0, but not uniformly. The r=0
line is different in the two limits. We interpret that the two different
Penrose diagrams differ by a discontinuous gauge transformation. We conclude
that the limiting spacetime possesses a singular event, with a future removable
naked singularity.
