Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The Rank-One Theorem on $\mathrm{RCD}$ spaces   We extend Alberti's Rank-One Theorem to $\mathrm{RCD}(K,N)$ metric measure
spaces.

5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci