May's rational acyclicity conjecture for H-infinity-ring spectra

Let $R$ be an $H_\infty$-ring spectrum, and suppose that

$$R \otimes \mathbb{Q} \simeq 0.$$

May's conjecture. Then $R$ is $K(n)$-acyclic for all $n>0$.

The statement concerns the chromatic acyclicity of rationally trivial structured ring spectra. The paper explains that this conjecture is already known, so it is included as the previously established $n=0$ case underlying the paper's main theorem.