Convergence of discrete $A$-flow to smooth Ricci flow

Fix a smooth Riemannian surface $(M,g)$. Let $(M_n,\mathcal{T}_n,\Phi_n,r_n)$ be a sequence of weighted triangulations of $M$ with initial circle packing metrics $r_n$, and let $r_n(t)$ be the solution obtained by evolving the $A$-flow from $r_n$. Let $g(t)$ be the solution of the smooth Ricci flow starting from $(M,g)$. Assume that the initial Gromov–Hausdorff distance between $(M,g)$ and $(M_n,\mathcal{T}_n,\Phi_n,r_n)$ tends to zero. The convergence conjecture. Then, as $n\to+\infty$, the discrete solutions $r_n(t)$ converge to the smooth Ricci flow $g(t)$ for $t\in[0,+\infty)$. The claim proposes that the discrete $A$-flow approximates smooth Ricci flow under Gromov–Hausdorff convergence of the initial weighted triangulated surfaces; the supplied source does not indicate whether this has been proved or disproved.