Positselski's Koszulity conjecture for maximal pro-p Galois cohomology

Let $p$ be a prime and let $\mathbb{K}$ be a field containing a root of unity of order $p$. Write $G_{\mathbb{K}}(p)$ for the maximal pro-$p$ Galois group of $\mathbb{K}$, and let

$$H^\bullet(G_{\mathbb{K}}(p),\mathbb{F}_p)=\bigoplus_{n\geq 0}H^n(G_{\mathbb{K}}(p),\mathbb{F}_p)$$

be its $\mathbb{F}_p$-cohomology algebra with the cup product. Positselski's conjecture. The algebra $H^\bullet(G_{\mathbb{K}}(p),\mathbb{F}_p)$ is Koszul. This conjecture proposes a Koszul-algebraic strengthening of the quadraticity supplied by the Bloch–Kato conjecture; its status is not specified in the source.