Winter–Tikuisis regularity conjecture for simple nuclear C*-algebras

Let $A$ be a simple, unital, separable, nuclear, infinite-dimensional C$^*$-algebra. Winter–Tikuisis regularity conjecture. The following are equivalent:

1. $A$ has finite nuclear dimension.
2. $A$ is $\mathcal{Z}$-stable.
3. $A$ has strict comparison of positive elements.

This conjecture proposes the equivalence of the principal regularity properties used in the classification of simple nuclear C$^*$-algebras. It connects nuclear dimension, $\mathcal{Z}$-stability, and strict comparison, but the supplied source does not establish its resolution.