The Félix--Jessup--Murillo nilpotence conjecture

Let $(\Lambda V,\operatorname{d})$ be a minimal Sullivan algebra with $V^1=0$, and suppose that both the even-degree part $V^{\mathrm{even}}$ and the even-degree cohomology $H^{\mathrm{even}}(\Lambda V,\operatorname{d})$ are finite dimensional. Let $(v_i)_{i\geq 0}$ be a homogeneous basis of $V$. Nilpotent Omnibus Conjecture. Each $v_i$ is nilpotent in the cohomology algebra $H(\Lambda V^{\geq \deg v_i},\bar{\operatorname{d}})$. The source attributes this conjecture to Félix--Jessup--Murillo, presents a slightly weaker form than theirs, and states that it implies Anick's conjecture; no resolution is stated in the supplied text.