Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic estimates for roots of the cuboid characteristic equation in
  the nonlinear region   A perfect cuboid is a rectangular parallelepiped. Its edges, its face
diagonals, and its space diagonal are of integer lengths. None of such cuboids
is known thus far, though the system of Diophantine equations describing them
is easily written. The cuboid characteristic equation is a twelfth degree
Diophantine equation derived from the initial cuboid equations and equivalent
to them. In the case of the second cuboid conjecture it reduces to a tenth
degree equation. This equation comprises two parameters. Previously various
asymptotics for roots of this equation were studied as its parameters tend to
infinity either separately or simultaneously provided some linear combination
of them is preserved finite. In the present paper this linear combination is
replaced by a certain nonlinear expression.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga