Shelah's Hanf-number threshold conjecture for categoricity transfer in AECs

Let ${\bf K}$ be an abstract elementary class and let $\lambda=\operatorname{LS}({\bf K})$, its Löwenheim–Skolem number. Shelah's Hanf-number threshold conjecture. The threshold for categoricity transfer is $\beth_{(2^\lambda)^+}$, the Hanf number. The supplied text attributes this conjecture to Shelah and gives no evidence that it has been resolved.