Reineke's stable-weight-system conjecture for Dynkin quivers

Let $Q$ be a quiver of Dynkin type. A weight system $\Theta$ on $Q$ is understood in the sense of stability for representations of $Q$, and a representation is stable with respect to $\Theta$ when it satisfies the corresponding stability condition. Reineke's conjecture. There exists a weight system $\Theta$ on $Q$ such that the stable representations are precisely the indecomposable ones. This conjecture has been proved for quivers of $A_n$-type, whereas computer-found counterexamples exist for quivers of $D$- and $E$-type; thus the original conjecture is refuted in general. It has applications to stratifications of representation varieties and identities involving quantum dilogarithm series.