Rognes' algebraic K-theory red-shift conjecture

Fix a prime $p$. Let $R$ be a suitable $\mathbb{E}_1$-ring of fp-type $n$, where fp-type is the chromatic finiteness notion described in the source, and let $\operatorname{K}(R)^{\wedge}_p$ denote its $p$-completion. Rognes' red-shift conjecture. The spectrum $\operatorname{K}(R)^{\wedge}_p$ is of fp-type $n+1$. This conjecture predicts that algebraic K-theory raises chromatic complexity by one; the source attributes it to Guido and Hahn–Wilson and states that it is proved for $\operatorname{BP}\langle n\rangle^{\wedge}_p$ for every $n\geq -1$, but leaves the general suitable-ring case open.