Explicit decomposition-number formula for RoCK spin superblocks

Let $h=2n+1$, let $\gamma$ be a $w$-Rouquier $h$-bar-core, and let $\alpha$ be a strict partition and $\beta$ a restricted $h$-strict partition, both with $h$-bar-core $\gamma$ and $h$-bar-weight $w<h$. Let

$$(\alpha(0),\dots,\alpha(n))\quad\text{and}\quad(\beta(0),\dots,\beta(n))$$

be their $h$-bar-quotients. Write $K^{-1}_{\alpha\beta}$ for the specialisation of $K^{-1}_{\alpha\beta}(t)$ at $t=-1$, and let $\operatorname{c}^{\lambda}_{\mu\nu}$ denote the relevant coefficients. RoCK-block conjecture. The divided decomposition number is

$$D_{\alpha\beta}=\sum K^{-1}_{\alpha(0)\sigma(0)}\prod_{i=1}^{n}\operatorname{c}^{\alpha(i)}_{\sigma(i)\tau(i)}\operatorname{c}^{\beta(i-1)}_{\sigma(i-1)\tau(i)'}.$$

Here the sum is over all partitions $\sigma(0),\dots,\sigma(n-1),\tau(1),\dots,\tau(n)$, with $\sigma(n)$ interpreted as the empty partition. This gives an explicit conjectural formula for decomposition numbers in RoCK blocks, obtained by applying the stated result on RoCK superblocks. The source provides no resolution status.