Refined Kessar–Schaps conjecture for spin blocks

Let $B^{\eta,\rho,d}_{R_p}$ and $B^{\eta,\rho',d'}_{R_p}$ be arbitrary spin blocks of symmetric groups, or let $(B^{\eta,\rho,d}_{R_p})_{0}$ and $(B^{\eta,\rho',d'}_{R_p})_{0}$ be spin blocks of alternating groups. Refined Kessar–Schaps conjecture. The indicated blocks are splendidly Rickard equivalent if and only if

$$d=d' \quad\text{and}\quad |\rho|-h(\rho)\equiv |\rho'|-h(\rho')\pmod 2.$$

This criterion is presented as sufficient to prove the refined Broué conjecture for all spin blocks of the relevant symmetric and alternating groups. The supplied text gives no resolution status for this conjecture.