The generalized admissible triple convergence conjecture for graded graphs

Let $\Gamma$ be a graded graph and let $\mu$ be an ergodic central measure on the path space $T(\Gamma)$. Let $\rho=\rho_0$ be a metric on $T(\Gamma)$ such that $(T(\Gamma),\rho,\mu)$ is an admissible triple. The sequence of spaces $(T(\Gamma),\rho_n,\mu)$ is then expected to converge to a generalized admissible triple. If $\Gamma$ is standard, the limit is, by definition, an admissible triple; if the tail filtration associated with a central measure on a nonstandard graph is not standard, the limit is generalized but not an ordinary metric triple. Generalized admissible triple convergence conjecture. Under these assumptions, $(T(\Gamma),\rho_n,\mu)$ converges to a generalized admissible triple, with the stated distinction between standard and nonstandard graphs. This describes how generalized metric spaces arise as limits of metric structures associated with graded graphs and relates standardness of the tail filtration to whether the limiting triple is ordinary or generalized. The supplied text does not indicate whether this claim has been proved.