  This is the second in a series of papers giving a proof of the Kepler
conjecture, which asserts that the density of a packing of congruent spheres in
three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This
is the oldest problem in discrete geometry and is an important part of
Hilbert's 18th problem. An example of a packing achieving this density is the
face-centered cubic packing.
  This paper defines a local formulation of the conjecture which is used in the
proof.
