  Using the recently developed theory of rigorously validated numerics, we
address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic)
level. We show the existence of critical points and local minimizers associated
with "classical" candidates, grain boundaries, and localized patterns. We
further address the dynamical relationships between the observed patterns for
fixed parameters and across parameter space, then formulate several conjectures
on the dynamical connections (or orbits) between steady states.
