Castravet–Tevelev's hypertree conjecture for extremal divisors

Let $\overline{\mathcal{M}}_{0,n}$ be the moduli space of stable $n$-pointed genus-zero curves, and let $D_\Gamma$ be the divisor associated with an irreducible hypertree $\Gamma$ of order at most $n$. Castravet–Tevelev's hypertree conjecture. Every extremal ray of

$$\operatorname{Eff}(\overline{\mathcal{M}}_{0,n})$$

is either a boundary divisor or the divisor $D_\Gamma$ of an irreducible hypertree $\Gamma$ of order at most $n$. This is an optimistic converse to the construction of hypertree divisors and predicts a complete description of the extremal rays of the effective cone.