Dan Asimov's remark "Finally, the optimality of a sphere packing is determined by the limit of its density in a ball B(R) of radius R, as R -> oo, when this limit exists, which is independent of the center of the ball. This means that any modification of a packing in a bounded region will have no effect on the limiting density." reminds me of a research program currently on my back-burner, awaiting some ideas to make it fully workable. It's a theory in which density is measured not by real numbers but by a richer non-Archimedean number system that allows one to simultaneously consider regular packings, line defects (which are infinitesimal compared to regular packings), and point defects (which are infinitesimal compared to line defects). In this theory, modifying a packing in a bounded region, by removing n spheres and replacing them by n' spheres, changes the "refined density" by an infinitesimal but non-zero amount proportional to n-n'. I can prove some of the basic lemmas in this theory, but what I really want to do in the first article on the theory is to show that, relative to my refined notion of density, the only densest packings of the plane by unit disks are the ordinary densest lattice packings. Maybe one of the existing proofs of Fejes Toth's theorem can be modified to work with refined density, but I don't know how to do this yet. Anyone interested in more details? Jim Propp