Hefetz's acyclic-set conjecture for planar digraphs

Let $D$ be a simple planar digraph on $n$ vertices. An acyclic set is a vertex set inducing no directed cycle in $D$. Hefetz's conjecture. Every simple $n$-vertex planar digraph has an acyclic set of size at least

$$\tfrac{3n}{5}.$$

The conjecture is cited as supporting evidence for the broader 2-colorability problem, but no resolution is given in the source.