The Koszulity conjecture for Milnor K-theory

Let $K$ be a field and let $l$ be prime such that $K$ contains a primitive $l$-th root of unity. A positively graded algebra $A=k\oplus A_1\oplus A_2\oplus\dotsb$ is Koszul when $\operatorname{Tor}_{ij}^A(k,k)=0$ for all $i\ne j$, with the two subscripts denoting homological and internal grading. Koszulity conjecture. The algebra

$$\mathrm{K}^{\mathrm{M}}(K)/l$$

is Koszul. This conjecture is an approach to the Milnor–Bloch–Kato conjecture and is presented as open in the source.