Khesin–Soloviev's dynamical degree conjecture for truly skew pentagram maps

Let $T_{a,b,c,d}$ be a truly skew pentagram map, with parameters $(a,b,c,d)$ as in the paper, and let its dynamical degree be denoted by $\rho(T_{a,b,c,d})$. Khesin–Soloviev's conjecture. All truly skew pentagram maps $T_{a,b,c,d}$ have dynamical degree $4$. The conjecture is motivated by height-growth experiments and the results established in the paper for infinite families of examples; its general validity remains open.