Large-9 limit for winding Wilson loops on compact surfaces

Let $\Sigma$, $U$, $C$, $a$, and $c=\operatorname{area}(\Sigma)-a$ be as in the preceding conjecture, with $C$ a simple closed curve in the topological disk $U$. For $n\in\mathbb{Z}$, let $C^{(n)}$ be the loop obtained by traveling $n$ times around $C$. The winding Wilson-loop conjecture. For every $n\in\mathbb{Z}$, the limit

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

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

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

This strengthens the simple-closed-curve conjecture to loops with arbitrary integer winding and is intended to support the analysis of all topologically trivial loops with simple crossings. The supplied text does not state whether this extension has been resolved.