Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Uniqueness and stability of saddle-shaped solutions to the Allen-Cahn
  equation
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex