Energy measure singularity dichotomy for MMD spaces

Let $(X,d,m,\mathcal{E},\mathcal{F})$ be a MMD space satisfying $\operatorname{VD}$, $\operatorname{PI}(\Psi)$ and $\operatorname{CS}(\Psi)$. Assume further that $(X,d)$ satisfies the chain condition and that

$$\lim_{r \downarrow 0} \frac{\Psi(r)}{r^{2}}=0.$$

Energy measure singularity dichotomy. Then $\Gamma(f,f) \perp m$ for all $f \in \mathcal{F}$. The conjecture predicts singularity of every energy measure under the stated structural and scaling assumptions; the supplied text does not indicate whether it has been proved or disproved.