Strict dynamical comparison with positive ordinary radius

Construct a stably finite simple unital C*-algebra A, a discrete amenable group G, and an action alpha:G→Aut(A) such that rc(A)>0 while rc(A,alpha)=0.

Background

The dynamical radius of comparison can be smaller than the ordinary radius in nonsimple examples, while the paper’s main constructions do not resolve whether this phenomenon occurs for stably finite simple unital C*-algebras with amenable group actions.

Examples for G=Zd with positive rc(A) and zero crossed-product radius are identified as promising candidates, but their dynamical radii remain to be computed.

References

Do there exist a stably finite simple unital C*-algebra $A$, a discrete amenable group~$G$, and an action $ $ such that

rc (A) > 0

rc (A, ) = 0?

— The Dynamical Radius of Comparison for C*-Dynamical Systems  (2609.30211 - Asadi-Vasfi et al., 24 Sep 2026) in Problem \ref{Pb_5Z14_Strict}, Section \ref{Sec_4712_Open}