Modified Reineke conjecture on maximal stable categories of Dynkin quivers

Let $Q$ be a Dynkin quiver, and let $k$ be the field over which its representations are taken. Write $\mathrm{\mathbf{Rep}}_k(Q)$ for the abelian category of finite-dimensional $k$-representations of $Q$. A maximal stable category is the categorical notion used in the source. Modified Reineke conjecture. The abelian category

$$\mathrm{\mathbf{Rep}}_k(Q)$$

is a maximal stable category. The modified conjecture was proposed after counterexamples to the original Reineke conjecture for quivers of $D$- and $E$-type. The authors state that they do not know whether it is true, even for Dynkin quivers, and note that Juteau and Hille were attempting to prove it.