Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local-global principle for integral bends in orthoplicial Apollonian
  sphere packings   We introduce an orthoplicial Apollonian sphere packing, which is a sphere
packing obtained by successively inverting a configuration of 8 spheres with
4-orthplicial tangency graph. We will show that there are such packings in
which the bends of all constituent spheres are integral, and establish the
asymptotic local-global principle for the set of bends in these packings.

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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: cs