Conjecture on super-exponential condensation in analytic iterated function systems

Let an analytic iterated function system (IFS) be a finite family of analytic contractions, and suppose that it has super-exponential condensation, meaning that distinct cylinder maps approach one another super-exponentially, but has no exact overlaps. Let an IFS be sub-conjugated to a self-similar IFS when it is related to a self-similar IFS by the sub-conjugacy notion used in the paper.

Super-exponential condensation conjecture. Any analytic IFS which has super-exponential condensation but no exact overlaps must be sub-conjugated to a self-similar IFS.

The conjecture concerns whether the known self-similar examples with super-exponential condensation and no exact overlaps account for all such phenomena in the analytic setting. Its resolution is not supplied in the source.