Heath, Pemmaraju and Trenk's bounded stack-number conjecture for outerplanar DAGs

Let $G$ be a directed acyclic outerplanar graph, and let $\operatorname{sn}(G)$ denote its stack number. Heath, Pemmaraju and Trenk's conjecture. The stack number of the class of directed acyclic outerplanar graphs is bounded above by a constant.

This was a long-standing question concerning whether stack number is bounded for outerplanar directed acyclic graphs. The present paper proves the conjecture, in fact showing that every outerplanar DAG $G$ satisfies $\operatorname{sn}(G) \leq 24776$.