Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A revision of the proof of the Kepler conjecture   The Kepler conjecture asserts that no packing of congruent balls in
three-dimensional Euclidean space has density greater than that of the
face-centered cubic packing. The original proof, announced in 1998 and
published in 2006, is long and complex. The process of revision and review did
not end with the publication of the proof. This article summarizes the current
status of a long-term initiative to reorganize the original proof into a more
transparent form and to provide a greater level of certification of the
correctness of the computer code and other details of the proof. A final part
of this article lists errata in the original proof of the Kepler conjecture.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org