The hypertree generation conjecture for the effective cone of $\overline{M}_{0,n}$

Let $\overline{M}_{0,n}$ be the moduli space of stable rational curves with $n$ marked points. A boundary divisor $\delta_I$ is associated to a partition of the markings into $I$ and $I^c$, where both parts have size at least two. Hypertree divisors are divisors on $\overline{M}_{0,n}$ parametrized by hypertrees; an irreducible hypertree is one whose associated hypertree divisor is contractible by a birational map, and pullbacks of such divisors are also considered. Hypertree generation conjecture. The effective cone of $\overline{M}_{0,n}$ is generated by boundary divisors and by divisors parametrized by irreducible hypertrees and their pullbacks. This would give a description of the effective cone in terms of the known extremal boundary and hypertree divisors, but the source only presents the statement as a speculation, with no resolution supplied here.