Transitivity conjecture for weakly proper pairs of analytic stacks

Let $X$, $Y$, $Z$, and $S$ be analytic stacks. Write $X \Subset_S Y$ when $X$ is weakly proper over $S$ relative to $Y$.

Transitivity conjecture. If $X \Subset_S Y$ and $Y \Subset_S Z$, then

$$X \Subset_S Z.$$

This conjecture asserts transitivity of weak properness for analytic stacks. The paper states that the conjecture will be proved in the complex-analytic case; its general status is not established in the supplied text.