The semiprimitivity characterization of graph-restrictive permutation groups

Let $L$ be a transitive permutation group. It is semiprimitive if each of its normal subgroups is either transitive or semiregular, and it is graph-restrictive if there exists a constant $c(L)$ such that, for every connected locally-$L$ pair $(\Gamma,G)$ and every arc $(u,v)$ of $\Gamma$, one has $|G_{uv}|\leq c(L)$. Semiprimitivity characterization conjecture. A permutation group is graph-restrictive if and only if it is semiprimitive. The conjecture seeks a characterization of graph-restrictive groups and, in the source, is motivated by results extending methods for primitive groups to semiprimitive groups; its resolution is not stated there.