Local-to-global multiplicativity conjecture for perverse filtrations

Let $f:X\to Y$ be a proper flat morphism between smooth algebraic varieties. The perverse filtration associated with $f$ is the filtration defined on the cohomology of $X$ by the perverse truncations of $Rf_*\mathbb{Q}_X$. For every closed point $p\in Y$, the local perverse filtration is the filtration on the cohomology of the fiber $F=f^{-1}(p)$ induced by the stalk at $p$ of these perverse truncations.

Local-to-global multiplicativity conjecture. The perverse filtration associated with $f$ is multiplicative if and only if the local perverse filtrations on all fibers are multiplicative. This conjecture proposes that multiplicativity can be checked fiberwise, reflecting the local nature of perverse sheaves; its resolution is not given in the source.