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A perfect cuboid is a rectangular parallelepiped whose edges, whose facediagonals, and whose space diagonal are of integer lengths. The second cuboidconjecture specifies a subclass of perfect cuboids described by one Diophantineequation of tenth degree and claims their non-existence within this subclass.This Diophantine equation has two parameters. Previously asymptotic expansionsand estimates for roots of this equation were obtained in the case where thefirst parameter is fixed and the other tends to infinity. In the present paperreverse asymptotic expansions and estimates are derived in the case where thesecond parameter is fixed and the first one tends to infinity. Theirapplication to the perfect cuboid problem is discussed.

Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture