Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Hard properties with (very) short PCPPs and their applications
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex