Frobenius valuation conjecture for monotone symplectic manifolds

Let $M$ be a monotone symplectic manifold, let $\theta$ be a $(p-1)$-st root of unity, and let $\Phi(\theta)$ be the evaluation at $\theta$ of the Frobenius structure predicted by the Gamma-class overconvergence conjecture. Denote by $b_j(M)$ the Betti number in degree $j$ and by $\operatorname{val}$ the $p$-adic valuation.

Frobenius valuation conjecture. The valuations of the eigenvalues of $\Phi(\theta)$ are nonpositive integers; among them, listed with multiplicities, the number of times that each integer $k$ occurs equals

$$b_{-2k}(M).$$

This predicts that the specialized Frobenius eigenvalues recover the Betti numbers of $M$ from their $p$-adic valuations. The supplied text does not state whether this prediction has been proved or refuted.