Rigidity of graded noetherian down-up algebras under semisimple Hopf algebra actions

Let $A$) be a graded noetherian down-up algebra $\mathbb{D}(\alpha,\beta)$, where $\alpha$ and $\beta$ are scalars in $\Bbbk$ with $\beta\neq 0$. A semisimple Hopf algebra action on $A$ is understood in the sense of.

Rigidity conjecture. The graded noetherian down-up algebras are rigid with respect to semisimple Hopf algebra actions.

This conjecture extends the paper's finite-group-coaction rigidity theorem to semisimple Hopf algebra actions. The supplied text does not indicate whether the conjecture has been resolved.