Finite-diameter conjecture for the entropy metric on outer space

Let $r\geq 4$ and consider the outer space of rank-$r$ free groups equipped with the entropy metric. Finite-diameter conjecture. The entropy metric has finite diameter on the outer space for all ranks $r\geq 4$. This conjecture concerns the global geometry of the entropy metric; the source presents it as an unproved conjecture motivated by the incompleteness and completion results discussed above.