Uniqueness of limit models of different lengths in abstract elementary classes

Let $\operatorname{\mathcal{K}}$ be an abstract elementary class, let $\operatorname{Hanf}(\operatorname{\mathcal{K}})$ and $LS(\operatorname{\mathcal{K}})$ denote its Hanf and Löwenheim–Skolem numbers, and let a $(\mu,\sigma)$-limit over $M$ be a limit model of cardinality $\mu$ and length $\sigma$. Uniqueness conjecture for limit models. Suppose that $\operatorname{\mathcal{K}}$ is categorical in some $\lambda\geq\operatorname{Hanf}(\operatorname{\mathcal{K}})$ and $LS(\operatorname{\mathcal{K}})\leq\mu<\lambda$. If $\sigma_1$ and $\sigma_2$ are limit ordinals less than $\mu^+$ and $M_1$ and $M_2$ are respectively $(\mu,\sigma_1)$- and $(\mu,\sigma_2)$-limits over $M$, then $M_1$ is isomorphic to $M_2$ over $M$. The source presents this as a challenging uniqueness question and does not state that it has been resolved.