Weak monodromy nilpotency conjecture for degenerations of irreducible symplectic manifolds

Let $\pi:\mathcal X\to\Delta$ be a degeneration of an irreducible symplectic $2n$-fold. For each $m$, let $T_m$ be the associated monodromy operator on $H^m(\mathcal X_t,\mathbb C)$, and put $N_m=\log T_m$. Assume that $T_{2k}$ is unipotent for $k\leqslant n$. Weak monodromy nilpotency conjecture. For $k\leqslant n$, one has

$$\operatorname{nilp}(N_{2k})\in\{0,k,2k\}.$$

This is presented as a weak version of the preceding monodromy nilpotency conjecture and gives a restricted set of possible nilpotency indices. The source does not specify whether it has been proved or disproved.