Algebraic homomorphism conjecture for the tautological projection on the moduli of abelian varieties

Let $d53c_g$ be the moduli space of principally polarized abelian varieties of dimension $g$, and let $d53c^*(d53c_g)$ be its Chow ring. The homomorphism property means that the tautological projection preserves products of classes in this Chow ring.

Algebraic homomorphism conjecture. The homomorphism property holds for all classes $d6fc,d6fd\in\mathsf{CH}^*(\mathcal{A}_g)$ defined over $d53e$.

This is a weakening of the strong form, motivated by characteristic-$p$ compact subvarieties of the correct codimension. It remains open.