Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Proof of the Matrix-valued P\'olya Positivstellensatz via pure states
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics