2011, pp 83-133
Date: 20 Oct 2011

A Formulation of the Kepler Conjecture

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Abstract

This paper is the second in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. The top level structure of the proof is described. A compact topological space is described. Each point of this space can be described as a finite cluster of balls with additional combinatorial markings. A continuous function on this compact space is defined. It is proved that the Kepler conjecture will follow if the value of this function is never greater than a given explicit constant.

Received November 11, 1998, and in revised form September 12, 2003, and July 25, 2005. Online publication February 27, 2006.