Assouad dimension conjecture for continuum trees

Let $f$ be an excursion function on $[0,1]$, let $\mathcal{G}_f=\{(t,f(t)):t\in[0,1]\}\subseteq\operatorname{\mathbb{R}}^2$ be its graph, and let $T_f$ be the associated continuum tree. A continuum tree is starry if it has the property intended by the source's terminology.

Assouad dimension conjecture. If

$$\dim_{\mathrm{A}}\mathcal{G}_f>1,$$

then $T_f$ is starry.

This conjecture proposes that the extremal local complexity measured by Assouad dimension forces the associated continuum tree to be starry. The source does not state a resolution.