Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Metric Extension Operators, Vertex Sparsifiers and Lipschitz
  Extendability
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas