Silverman–Morton strong uniform boundedness conjecture

Let $D\ge1$, $N\ge1$, and $d\ge2$. For a number field $K/\mathbb Q$, write $[K:\mathbb Q]$ for its degree, and let $\operatorname{End}_d^N(K)$ be the degree-$d$ endomorphisms of $\mathbb P^N$ defined over $K$. For $f\in\operatorname{End}_d^N(K)$, let $\operatorname{PrePer}(f)$ be its set of preperiodic points. Silverman–Morton strong uniform boundedness conjecture. There is a constant $C_3(D,N,d)$ such that, for every number field $K/\mathbb Q$ with $[K:\mathbb Q]\le D$ and every $f\in\operatorname{End}_d^N(K)$,

$$\#\bigl(\operatorname{PrePer}(f)\cap\mathbb P^N(K)\bigr)\le C_3(D,N,d).$$

This is the expected uniform bound for rational preperiodic points in bounded-degree number fields. The source notes implications for torsion points on abelian varieties and special cases involving twists, but does not give a resolution of the conjecture.