Would the following hypothetical algorithm match somehow the expectation of Temporal-Pooler.
Not the feedback part, only the requirement of stable unique output part.

Let say the TM generate sequence of SDR’s : s1, s2, s3, s4, s5, …

The algorithm is very simple every step we pick randomly 50% of the ON bits of the two neighboring SDRs. f.e. ( let f50() be the operation pick 50% of the ON bits)

i.e. TP-SDR is a trailing SDR, because f.e. TP2 has 25% of s1, 25% of s2 and 50% of s3 … TP3 has 12.5% of s1, 12.5% of s2 , 25% of s3 and 50% of s4 … and so on …

I’ve studied this in depth. I too came to your hypothetical solution, tested it, and found that it does not work. The problem is that the overlap** between any two consecutive SDRs should be determined by the underlying data. At the extremes: you could have a stationary input (which should yield nearly 100% overlap); or a completely different input (which should yield very low overlap). But this hypothetical solution has a constant hardcoded overlap, regardless of the situation.

However this does shed light on how to correctly analyze the stability of a temporal pooler.

no… I think of it as … it is using overlap to decide how many bits to copy from both SDR’s … to the final SDR i.e. what portion stays the same and what changes.
if they are similar it changes a little, if they differ then it changes alot …