Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Apollonian depth and the accidental fractal   The depth function of three numbers representing curvatures of three mutually
tangent circles is introduced. Its 2D plot leads to a partition of the moduli
space of the triples of mutually tangent circles/disks that is unexpectedly a
beautiful fractal, the general form of which resembles that of an Apollonian
disk packing, except that it consists of ellipses instead of circles.

3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th