Q-system Demazure decomposition conjecture

Fix $a\in I_0$, set $c=\min\{c_b\mid A_{ba}\neq 0\}$, and let $\ell\geq\lceil m/c\rceil$. Write $L(k)=\left\lfloor\frac{mA_{ba}-k}{A_{ab}}\right\rfloor$. Q-system Demazure decomposition conjecture. The following two isomorphisms hold, with the first for untwisted types and the second for twisted types:

$$\widetilde{D}_{\ell}\left((B^{a,m-1})^{\otimes 2}\right)\cong \widetilde{D}_{\ell}(B^{a,m}\otimes B^{a,m-2})\oplus\widetilde{D}_{\ell}\left(\bigotimes_{b\sim a}\bigotimes_{k=0}^{-A_{ab}-1}B^{b,L(k)-1}\right),$$ $$\widetilde{D}_{\ell}\left((B^{a,m-1})^{\otimes 2}\right)\cong \widetilde{D}_{\ell}(B^{a,m}\otimes B^{a,m-2})\oplus\widetilde{D}_{\ell}\left(\bigotimes_{b\sim a}(B^{b,m-1})^{\otimes -A_{ba}}\right).$$

These identities are Demazure-crystal analogues of the untwisted and twisted $Q$-system relations. They are presented as conjectural in the source, and no resolution status is supplied.