Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum Braids: A Complete Invariant of Knots and Links   Minimum braids are a complete invariant of knots and links. This paper
defines minimum braids, describes how they can be generated, presents tables
for knots up to ten crossings and oriented links up to nine crossings, and uses
minimum braids to study graph trees, amphicheirality, unknotting numbers, and
periodic tables.

12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio