Currently I am studying the Schreier-Sims algorithm. To gain a deeper understanding, I am trying to look into applications of this algorithm, among which its use for solving the Rubik's Cube is perhaps the most famous.

However, it seems that there is not a complete, comprehensive algorithm that uses the Schreier-Sims method to solve the Rubik's Cube. Instead, there are only scattered, fragmentary methods, most of which date back over a decade and do not entirely align with the overall framework of the Schreier-Sims algorithm. Does this mean the problem has not been fully resolved?

Is there any simple introduction of using the Schreier-Sims method to solve the Rubik's Cube? If such a guide is not available, is there any examples where the Schreier-Sims algorithm is applied to similar problems? Thanks a lot.

`GroupHomomorphismByImages`

uses a stabilizer chain, although the algorithm is part of GAP $\endgroup$