Large-9 limit for Wilson loops around simple closed curves on compact surfaces

Let $\Sigma$ be a surface of area $\operatorname{area}(\Sigma)$, let $U\subset\Sigma$ be a topological disk, and let $C$ be a simple closed curve in $U$. Assign area $a$ to the interior of $C$ and

$$c:=\operatorname{area}(\Sigma)-a$$

to its exterior, with $a<\operatorname{area}(\Sigma)$. In Sengupta's formula for the YangMills measure on $\Sigma$, let $\operatorname{hol}(C)$ denote the holonomy around $C$ and let $\operatorname{tr}$, $\mathbb{E}$, and $\operatorname{Var}$ denote normalized trace, expectation, and variance, respectively. The large-$N$ Wilson-loop conjecture. The limit

$$\lim_{N\rightarrow\infty}\mathbb{E}\left\{\operatorname{tr}(\operatorname{hol}(C))\right\}$$

exists and depends continuously on $a$ and $c$, and

$$\lim_{N\rightarrow\infty}\operatorname{Var}\left\{\operatorname{tr}(\operatorname{hol}(C))\right\}=0.$$

This is the simple-closed-curve case needed to establish the large-$N$ limit and concentration of Wilson loop observables on a general compact surface. The supplied text does not state whether the conjecture has been resolved.