The bounded perfect derived subgroup conjecture for pointwise stabilizers

Let $G$ be a finite primitive group acting on a set, and consider the pointwise stabilizer $H$ of two points in this action.

Bounded perfect derived subgroup conjecture. There exists an absolute constant $c$ such that $H^{(c)}$ is perfect.

This conjecture generalizes the known result for primitive groups with solvable stabilizer, where two points can be chosen so that their pointwise stabilizer has derived length bounded by an absolute constant. The preceding theorem establishes a uniform bound for the derived subgroups of stabilizers in primitive perfect groups, but the stated assertion for all finite primitive groups remains open.