The main temperedness conjecture for quiver A-polynomials

Let $C$ be the adjacency matrix of a quiver, and let $A(x,y)$ be the associated quiver A-polynomial. A polynomial is tempered when all of its face polynomials have roots only on the unit circle.

Temperedness conjecture. Quiver A-polynomials are tempered for every choice of the adjacency matrix.

This is presented as the main conjecture of the paper and asserts the K-theoretic property for the curves underlying all quiver A-polynomials. The source does not state a resolution of the conjecture.