Lusztig's revised character formula conjecture

Let $\mu$ be $p$-regular, let $x\in\Wa$ satisfy $x\pdot\mu$ dominant, and let $X_1^p$ denote the restricted region in the weight lattice. Let $\operatorname{LCF}$ denote Lusztig's character formula from the preceding statement. Lusztig's revised conjecture. If $p\ge h$, then $\operatorname{LCF}$ holds whenever $x\pdot\mu\in X_1^p$. This stronger version seeks a uniform character formula throughout the restricted region, beyond the weights directly covered by Jantzen's condition. Its resolution status is not specified in the supplied text.