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On March the 3rd I finally finished the last coset required to prove that 25 moves suffice.

I have finally finished a draft version of a paper detailing the technique and result:

http://tomas.rokicki.com/rubik25.pdf

The technique uses the coset solver I have described previously here (over the past two years)
but I have also made it faster, and also gotten a new machine that is faster and has more memory to run these cosets more quickly.

In the end, it required about 4,000 cosets to be solved to prove a bound of 25.
By solved, I mean an upper bound on the largest distance in that coset was found;