The degree-four generalized Fujiki constant formula for hyperkähler manifolds

Let $X$ be a hyperkähler manifold of dimension $2n>2$. The generalized Fujiki constant $C(\mathrm{ch}_4)$ and $C(1)$ are defined by integrating the corresponding characteristic classes against powers of the Beauville--Bogomolov form, as in the paper.

Degree-four generalized Fujiki constant conjecture.

$$\frac{C(\operatorname{ch}_4)}{C(1)}=\frac{5(n+1)}{(2n-1)(2n-3)}.$$

This is presented as a precise conjectural relation arising from Rozansky--Witten theory; the supplied text gives no resolution status.