The semiprimeness conjecture for bounded skew power series rings

Let $Q$ be a simple artinian $\mathbb{Z}_p$-algebra carrying a standard filtration $u$. Let $(\sigma,\delta)$ be a commuting skew derivation on $Q$, meaning that

$$sigmadelta=deltasigma.$$

Assume that $(\sigma,\delta)$ is quasi-compatible with $u$, and let $Q^+[[x;\sigma,\delta]]$ denote the bounded skew power series ring.

Semiprimeness conjecture. The ring $Q^+[[x;\sigma,\delta]]$ is (semi)prime.

The bounded skew power series ring is known to exist under these hypotheses. If this conjecture holds, the filtered localisation procedure would imply that every skew power series ring over a complete, filtered prime ring is (semi)prime, answering the corresponding question about Iwasawa algebras positively.