Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Lower bounds on the lowest spectral gap of singular potential
  Hamiltonians
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph