Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Diophantine Geometry over Groups X: The Elementary Theory of Free
  Products of Groups
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th