Kirillov–Reshetikhin conjecture for normalized characters of KR modules

Let $\mathfrak g_0$ be the finite-dimensional Lie algebra associated with the paper, let $W^{(a)}_m(\zeta)$ be its Kirillov–Reshetikhin module, and let $H$ be the index set of pairs $(a,m)$. If $\operatorname{ch}^{(a)}_m(x)$ denotes the Laurent polynomial representing the $\mathfrak g_0$-character of $W^{(a)}_m(\zeta)$, define its normalized character by

$${\mathcal Q}^{(a)}_m(y):=x_a^{-m}\operatorname{ch}^{(a)}_m(x)\big|_{x=x(y)}.$$

Let $\mathbf Q^{(a)}_m(y)$ be the unique canonical solution of the relevant $Q$-system, meaning the solution whose limit as $m$ tends to infinity exists in the formal power-series ring $\mathbb C[[y]]$.

Kirillov–Reshetikhin conjecture. For every $(a,m)\in H$,

$${\mathcal Q}^{(a)}_{m}(y)=\mathbf Q^{(a)}_m(y).$$

This conjecture identifies normalized $\mathfrak g_0$-characters of Kirillov–Reshetikhin modules with the canonical solution of the $Q$-system. The supplied text does not state whether the conjecture has been resolved.