Griess-algebra conjecture for commutants in affine W-algebras

Let $\mathfrak{g}$ be a simple Lie algebra, let $f$ be a nilpotent element, and set

$$V=\operatorname{Com}\bigl(V^k(\mathfrak{g}^\natural),\mathscr{W}^k(\mathfrak{g},f)\bigr).$$

Let $V_2$ be the weight-two Griess algebra of $V$. Griess-algebra conjecture. The algebra $V_2$ is semisimple and associative. This is presented as a general conjecture about the commutant in a universal affine W-algebra; the supplied text gives no proof or resolution.