Intersection-product conjecture for odd-dimensional or Calabi–Yau hypersurfaces

Let $X\subset\mathbb{P}^{n+1}(\mathbb{C})$ be a smooth hypersurface. Assume that either the dimension $n$ is odd, or the degree of $X$ is $n+2$, so that $X$ is Calabi–Yau. Intersection-product conjecture.

$$A^i(X)\cdot A^{j}(X)=\mathbb{Q}[h^{i+j}]\quad\text{for all }i,j>0.$$

This conjecture combines Voisin's theorem for Calabi–Yau hypersurfaces with the preceding product conjecture. Its general validity is not established in the source.