Sphere packings, V.

The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program, a proof that the local density of a certain combinatorial arrangement, the pentahedral prism, is less than that of the face-centered cubic lattice packing. We prove various relations on the local density using computer-based interval arithmetic methods. Together, these relations imply the local density bound.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130708/2/9811077.pd