Erdenberger–Hulek intersection-number vanishing conjecture for principally polarized abelian varieties

Let ${\overline{{\mathcal A}_g}^P}$ be the perfect-cone compactification of the moduli space of principally polarized abelian varieties, let $L$ be the Hodge class, let $D$ be its boundary divisor, and let $g$ and $i$ be integers with $0\leq i\leq g(g+1)/2$. Write $\langle L^iD^{\frac{g(g+1)}2-i}\rangle_{{\overline{{\mathcal A}_g}^P}}$ for the corresponding intersection number.

Intersection-number vanishing conjecture. The intersection number

$$\left\langle L^iD^{\frac{g(g+1)}2-i}\right\rangle_{{\overline{{\mathcal A}_g}^P}}$$

is zero unless $i=\frac{k(k+1)}2=\dim {\mathcal A}_k$ for some $k\leq g$.

The conjecture is motivated by the vanishing pattern of the computed intersection numbers in low genera. The source gives no resolution status.