Rouquier's graded decomposition-number conjecture for v-Schur algebras

Let ${\cal S}_m$ be the $v$-Schur algebra, let $W(\lambda)$ be the Weyl module for a partition $\lambda$ of $m$, and let $L(\mu)$ be the irreducible module corresponding to a partition $\mu$ of $m$. Write $(W(\lambda)^i)_{i\geq 0}$ for the Jantzen filtration of $W(\lambda)$. Rouquier's graded decomposition-number conjecture. For partitions $\lambda,\mu$ of $m$,

$$d_{\lambda'\mu'}(q)=\sum_{i\geq 0}[W(\lambda)^i/W(\lambda)^{i+1}:L(\mu)]q^i.$$

This refines the ungraded decomposition-number conjecture by relating canonical-basis polynomials to the Jantzen filtration. The source says that it has been checked for small $m$ but gives no general resolution.