Zamolodchikov periodicity conjecture for Dynkin Y-systems

Let $\Delta$ and $\Delta'$ be Dynkin diagrams with vertex sets $I$ and $I'$, incidence matrices $A=(a_{ij})$ and $A'=(a'_{i'j'})$, and Coxeter numbers $h$ and $h'$. For variables $Y_{i,i',t}$, where $(i,i')\in I\times I'$ and $t\in\mathbb{Z}$, the $Y$-system associated with $(\Delta,\Delta')$ is

$$Y_{i,i',t-1}Y_{i,i',t+1}=\frac{\prod_{j\in I}(1+Y_{j,i',t})^{a_{ij}}}{\prod_{j'\in I'}(1+Y_{i,j',t}^{-1})^{a'_{i'j'}}}.$$

Zamolodchikov periodicity conjecture. Every solution of this system is periodic in $t$, with period dividing $2(h+h')$. The periodicity conjecture is a central structural statement for $Y$-systems associated with Dynkin diagrams. The supplied source does not state whether the claim is open or resolved.