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Thirty-Two QTM Moves Suffice

I have modified my coset solver to work in the quarter turn metric, and
with 396 cosets solved, I can announce that every cube position can be
solved in 32 or fewer quarter turns.

I am running phase one to a depth of 19 and letting phase two complete
the coset; each run takes about 12 minutes and approximately 63% of
the runs yield an upper bound of 25; the other 37% yield an upper
bound of 26.

No coset I have run yet has required more than 26 moves to solve, and
the possible distance-26 positions that I have run through an optimal
solver have all yielded distances less than 26, so I do not have a