stretch factor in SOLA time stretch methods I notice that in the general Synchronous Overlap and Add (SOLA) algorithm, we need to obtain the best overlapping start index using, for example, cross-correlation. But won't that start index change the desired stretch factor? After all, the factor is determined by Rs/Ra (Rs is the synthesis hop and Ra is the analysis hop).
No, the start index doesn't change the stretch factor because the overlapping windows do not have to absolutely fit the available length of the recording.

You can still effectively pad the original signal with zeros by returning a zero value for any request of samples outside the time interval of the original recording.