Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A hypothetical upper bound on the heights of the solutions of a
  Diophantine equation with a finite number of solutions
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph