Shelah's saturation characterization conjecture for dependent theories

Let $T$ be a first-order theory, let $M$ be a model of $T$, and let $\kappa$ be an infinite cardinal. A sequence $\langle a_\alpha:\alpha<\delta\rangle$ in $M$ is indiscernible when its order-indiscernibility is preserved over parameters from $M$; a sequence can be continued when it has an indiscernible extension, and a cut is a partition of its index order at which such continuation is considered. Saturation characterization conjecture. $M$ is $\kappa$-saturated if and only if it is $|T|^+$-saturated and every indiscernible sequence $\langle a_\alpha:\alpha<\delta\rangle$ of elements of $M$ with $\delta<\kappa$ can be continued, with the analogous condition holding for cuts. The claim proposes a characterization paralleling the stable-theory case; the source gives no resolution or further hypotheses beyond the displayed formulation.