  We develop the notion of a Kleinian Sphere Packing, a generalization of
"crystallographic" (Apollonian-like) sphere packings defined by
Kontorovich-Nakamura [KN19]. Unlike crystallographic packings, Kleinian
packings exist in all dimensions, as do "superintegral" such. We extend the
Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones
come from Q-arithmetic lattices of simplest type. The same holds for more
general objects we call Kleinian Bugs, in which the spheres need not be
disjoint but can meet with dihedral angles pi/m for finitely many m. We settle
two questions from [KN19]: (i) that the Arithmeticity Theorem is in general
false over number fields, and (ii) that integral packings only arise from
non-uniform lattices.
