I have attached a short description of the periodicity sorting matrix, the PSM. I hope this wsriteup answers questions about how it can achieve real-time pitch tracking.
In my previous "definition" of real time pitch I forgot to add that the pitch period respons is synchronous not only with the onset of the waveform, but with each cycle of the waveform. However, yes, there is a delay in periodicity recognition at the onset of a periodic series because there can be no tonal "pitch" until two successive periods occur. From that point on the pitch response is locked to the real zeros of the waveform.
That's the rudimentary case. In general there will be mixed waveforms with mixed zeros. So the PSM's delay line stores all intermixed zeros but responds only to the ones that match a template in the matrix. That's as instantaneous as you can get, and you can separate tonal sounds from each other as well as atonal ones.
Short PSM description.doc
Description: MS-Word document