Beauville's weak splitting conjecture for hyper-Kähler manifolds

Let $X$ be a projective hyper-Kähler manifold. Consider the cycle class map from the Chow ring $CH^*(X)$ to cohomology. Beauville's weak splitting conjecture. The cycle class map is injective on the subalgebra of $CH^*(X)$ generated by divisors. This is a weak form of Beauville's proposed multiplicative splitting of the Bloch–Beilinson filtration; the source distinguishes it from Voisin's extension involving Chern classes.