Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Invisible knots and rainbow rings: knots not determined by their
  determinants
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex