Andersen's conjecture on modular and quantum tilting characters

Let $G$ be a semisimple, simply connected algebraic group with root system $\Phi_{\rm f}$ over an algebraically closed field of characteristic $p$, let $A_0$ be the dominant weights in the interior of the fundamental $p$-alcove, and let $\prescript{p}{}{W}$ denote the relevant set of dominant elements for the $p$-dilated dot action. For a dominant weight $\lambda$, write $T(\lambda)$ for the indecomposable modular tilting module and $T_p(\lambda)$ for the corresponding quantum tilting module.

Andersen's conjecture. Suppose Lusztig's conjecture holds for $G$ in characteristic $p$. For $\lambda \in A_0$ and dominant $x \in \prescript{p}{}{W}$, one has

$$\operatorname{ch} T(x \cdot_p \lambda)=\operatorname{ch} T_p(x \cdot_p \lambda).$$

This conjecture predicts equality between modular and quantum tilting characters in the region governed by Lusztig's conjecture, strengthening Andersen's general lower-bound observation. The supplied text does not state whether it has been resolved.