Power-operation conjecture for cyclic A-infinity structures

Let $R$ be an even commutative $S$-algebra, let $x\in R_d$, and let $p$ be a prime such that $n$ is invertible in $R_*$ for every $n<p$. Let $\bar c_n(x)\in\pi_{p(d+2)-2}R/(p,x)$ denote the cyclic obstruction class, and let $\tilde P$ be a power operation. Power-operation conjecture. If $2(p-1)\mid d$, then there is a power operation

$$\tilde P:R_d\longrightarrow R_{p(d+2)-2}R/p$$

such that

$$\bar c_n(x)=\tilde P(x)\pmod{(p,x)}$$

for all $x$. This conjecture concerns the remaining obstruction to extending cyclic $A_n$ structures when $n=p$ is not invertible; the supplied passage gives no resolution.