  We study a translation invariant spin model in a three-dimensional regular
lattice, called the cubic code model, in the presence of arbitrary extensive
perturbations. Below a critical perturbation strength, we show that most states
with finite energy are localized; the overwhelming majority of such states have
energy concentrated around a finite number of defects, and remain so for a time
that is near-exponential in the distance between the defects. This phenomenon
is due to an emergent superselection rule and does not require any disorder. An
extensive number of local integrals of motion for these finite energy sectors
are identified as well. Our analysis extends more generally to systems with
immobile topological excitations.
