Finiteness of the number of collisions in a hard sphere particle system in all space, II: Arbitrary diameters and masses

Consider a system of N hard spheres of radii d i > 0 and masses m i < 0, i = 1,…, N. The spheres may interact through elastic pair collisions but move freely otherwise in all of R3. It is shown that (with the exception of a set of initial states of measure zero) there are at most finitely many collisions for any given initial state of the system.