  We study the relationship between local and global density for sphere
packings, and in particular the convergence of packing densities in large,
compact regions to the Euclidean limit. We axiomatize key properties of sphere
packing bounds by the concept of a packing bound function, and we study the
special case of sandwich functions, which give a framework for inequalities
given by the Lov\'asz sandwich theorem. We show that every packing bound
function tends to a Euclidean limit on rectifiable sets, generalizing the work
of Borodachov, Hardin, and Saff. Linear and semidefinite programming bounds
yield packing bound functions, and we develop a Lasserre hierarchy that
converges to the optimal sphere packing density.
