The bounded-Loewner-representation conjecture

Let $S^0(\mathcal D_n)$ be the normalized Loewner class, and let $\varphi_{s,t}$ be an evolution family associated with an $\mathcal M(\mathcal D_n)$-Herglotz vector field. Bounded-Loewner-representation conjecture. If $G\in S^0(\mathcal D_n)$ is bounded by $M>0$, then there exist $t\geq0$ and such an evolution family for which

$$\frac{1}{M}G=\varphi_{0,t}.$$

The source attributes this as Conjecture 2 of the cited work and presents it as open.