The uniform boundedness problem for rational preperiodic points

Let $(X,f,\mathscr L)$ be a polarized dynamical system defined over a number field $K$, with weight $d$, dimension $\dim X$, and polarization degree $c_1(\mathscr L)^{\dim X}$. Uniform boundedness problem. Can the number of $K$-rational preperiodic points of $X$ be bounded solely in terms of $[K:\mathbb Q]$, $\dim X$, $d$, and $c_1(\mathscr L)^{\dim X}$? The question generalizes uniform boundedness for torsion points on abelian varieties. It is known for elliptic curves over $\mathbb Q$ and over arbitrary number fields, while the corresponding question for abelian varieties of dimension at least two remains open.