Root-of-unity restricted Q-system conjecture

Fix a level $\ell$ and let $Q^{(a)}_m=\dim_q\mathrm{res}\,W^{(a)}_m$ be the root-of-unity quantum dimensions of the restricted Kirillov–Reshetikhin modules, with $a\in I$ and $\ell_a$ the corresponding restricted boundary. Restricted Q-system conjecture. The quantities $Q^{(a)}_m$ satisfy the level-$\ell$ restricted Q-system and, more strongly, for every $a\in I$,

$$Q^{(a)}_m=Q^{(a)}_{\ell_a-m}\qquad(0\le m\le\ell_a),$$ $$Q^{(a)}_m<Q^{(a)}_{m+1}\qquad\left(0\le m<\left[\ell_a/2\right]\right),$$

and

$$Q^{(a)}_{\ell_a+j}=0\qquad(1\le j\le t_a h^\vee-1).$$

Here $[\ell_a/2]$ is the greatest integer not exceeding $\ell_a/2$. The claim is a proposed level truncation of the unrestricted Q-system at a root of unity; the supplied text gives no resolution.