A Formulation of the Kepler Conjecture
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- Hales, T. & Ferguson, S. Discrete Comput Geom (2006) 36: 21. doi:10.1007/s00454-005-1211-1
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.