[math-fun] diameter of Rubik's cube puzzle

Has the diameter of the Rubik's cube puzzle been established yet? We now have enough computing power to find & prove the distance- to-start for any particular position, using the obvious square-root meet-in-the-middle algorithm and a big disk. We can search for edge positions by generating random positions and using the exact distance algorithm to guide a hill-climb away from the start position. But this is only heuristic. Rich