It's well known in FHI and similar circles, that it's impossible to distinguish an exponential (growth going up wildly) from a sigmoid/logistic curve (exponential growth until a turning point - an S shape) - until well after the turning point.

Which means we can't effectively predict that turning point. And so can't distinguish when a sigmoid will have a turning point, even when we know it must have one.

But this doesn't seem to exist in the statistics literature; and it would be very useful to have such a paper or textbook to point to.

We don't have time to write a full paper ourselves, but is there someone on this list with statistical experience who would like to write or co-write such a paper?

Since this result is important and as yet unpublished, it's plausible that such a publication may get an extremely high number of citations.

Cheers!