Füredi–Jiang–Kostochka–Mubayi–Verstraëte conjecture for ordered hypergraph forests

Let $F$ be an $r$-uniform forest with interval chromatic number $r$. Füredi–Jiang–Kostochka–Mubayi–Verstraëte conjecture. The maximum number of edges in a vertex-ordered $r$-uniform hypergraph with no subgraph order-isomorphic to $F$ is

$$O\bigl(n^{r-1}\log^{c(F)}n\bigr)$$

for some constant $c(F)$. This extends the Pach–Tardos conjecture from ordered graphs to ordered uniform hypergraphs; the case $r=2$ is stated to be equivalent to it.