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The Kepler conjecture asserts that no packing of congruent balls inthree-dimensional Euclidean space has density greater than that of theface-centered cubic packing. The original proof, announced in 1998 andpublished in 2006, is long and complex. The process of revision and review didnot end with the publication of the proof. This article summarizes the currentstatus of a long-term initiative to reorganize the original proof into a moretransparent form and to provide a greater level of certification of thecorrectness of the computer code and other details of the proof. A final partof this article lists errata in the original proof of the Kepler conjecture.

A revision of the proof of the Kepler conjecture