Werner's critical-cluster scaling-limit conjecture

For functions $f$ and $g$ depending on the dimension $d$, define

$$(f \boxdot g)(d):=f(d)\mathbb{1}_{d\le 6}+g(d)\mathbb{1}_{d>6}.$$

Here a critical cluster is either a loop cluster of $\widetilde{\mathcal{L}}_{1/2}$ or, when non-empty, a positive cluster $\mathcal{C}^{\ge 0}(v)$; these have the same distribution. For any $3\le d\le 5$ and $d\ge 7$, Werner's conjecture. the scaling limit of critical clusters exists and has fractal dimension

$$\left(\frac{d}{2}+1\right)\boxdot 4.$$

This conjecture concerns the geometry of critical clusters in Gaussian free fields and loop soups. The supplied text does not state whether the conjecture has been resolved.