Primality conjecture for invariant ideals in skew power series rings

Let $R$ be a Noetherian ring, complete with respect to a positive filtration topology, and let $(\sigma,\delta)$ be a continuous skew derivation compatible with the filtration. Define the skew power series ring

$$S=R[[x;\sigma,\delta]],$$

with multiplication determined by $xr=\sigma(r)x+\delta(r)$ for $r\in R$. Let $P$ be a prime, $(\sigma,\delta)$-invariant ideal of $R$. Primality conjecture. The ideal $SP$ is a prime ideal of $S$. This conjecture asks when invariant prime ideals remain prime after extension to a skew power series ring; the paper partially addresses it, including reductions to a finite-index problem in characteristic $p$ and preliminary results in the Iwasawa algebra case.