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Previously I announced that the 4x4x4 cube could be solved in 79 single-slice turns by solving it in five stages, in a manner similar to the Thistlethwaite 4-stage solution for the 3x3x3. (See The 4x4x4 can be solved in 79 moves (STM).) However, I have now realized my solution to the 2nd stage could have allowed the use of more basic turns than I used. I have realized that:
< U,u,D,d,L²,l²,R²,r²,F²,f,B²,b > = < U,u,D,d,L²,l,R²,r,F²,f,B²,b >
So with l and r replacing generators l² and r², you still can not reach any additional positions. As a result, I should have included the moves { l, l', r, r' } along with the other 24 allowed slice turns for that stage.