Removing decoder assumptions from the generic non-universality argument

Develop an argument establishing generic non-universality of diffeomorphisms without imposing any conditions on the decoder, or at least only assuming a shrinking decoder, thereby extending the periodic-point/Kupka–Smale-based proof that currently requires a hierarchically shrinking decoder and constant slowdown.

Background

The authors prove a generic non-universality result (Theorem 4.6) for diffeomorphisms under strong assumptions on the decoder (hierarchically shrinking) and a constant slowdown function, using a periodic-point argument and the Kupka–Smale theorem.

They explicitly state that they do not know how to adapt this argument when those decoder conditions are weakened or removed, leaving open the problem of extending the result to broader classes of decoders.