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A perfect cuboid is a rectangular parallelepiped. Its edges, its facediagonals, and its space diagonal are of integer lengths. None of such cuboidsis known thus far, though the system of Diophantine equations describing themis easily written. The cuboid characteristic equation is a twelfth degreeDiophantine equation derived from the initial cuboid equations and equivalentto them. In the case of the second cuboid conjecture it reduces to a tenthdegree equation. This equation comprises two parameters. Previously variousasymptotics for roots of this equation were studied as its parameters tend toinfinity either separately or simultaneously provided some linear combinationof them is preserved finite. In the present paper this linear combination isreplaced by a certain nonlinear expression.

Asymptotic estimates for roots of the cuboid characteristic equation in the nonlinear region