Simple examples with three distinct comparison radii

Construct a simple unital C*-algebra A, a discrete group G, and an action alpha:G→Aut(A) such that rc(C*(G,A,alpha))<rc(A,alpha)<rc(A).

Background

The paper gives an example with three distinct radii for a finite group acting on a nonsimple unital C*-algebra. It asks whether the phenomenon can occur in the simple setting.

The authors suggest combining that example with the principal construction of Section \ref{ImportantExample}, but explicitly leave the existence of such a simple example unresolved.

References

Do there exist a simple unital C*-algebra $A$, a discrete group~$G$, and an action $ \colon G \to Aut (A)$ such that

rc \bigl( C* (G, A, \alpha) \bigr) < rc (A, \alpha) < rc (A)?

— The Dynamical Radius of Comparison for C*-Dynamical Systems  (2609.30211 - Asadi-Vasfi et al., 24 Sep 2026) in Problem \ref{Pb_1412_InCatQ}, Section \ref{Sec_4712_Open}