Asymptotics of quantum spin networks at a fixed root of unity

Understand

A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers.

• The standard evaluation of a spin network is an integer number.
• In a previous paper, we proved an existence theorem for the asymptotics of the standard evaluation of an arbitrary classical spin network when the coloring of its edges are scaled by a large natural number.
• In the present paper, we extend the results to the case of an evaluation of quantum spin networks of arbitrary valency at a fixed root of unity.