Fakhruddin's conjecture on the \mathfrak{sl}2 conformal block cone of \overline{M}{0,6}

Let $\operatorname{Nef}(\overline{M}_{0,6})$ be the nef cone. A Fakhruddin ray is an extremal ray spanned either by $D(\mathfrak{sl}_2,1,(1,1,1,1,1,1))$ or by one of the 127 pullbacks from the GIT quotients $(\mathbb{P}^1)^n /\!/_{L} \operatorname{SL}_2$ studied in the source. A Fakhruddin orbit is an $S_6$-orbit of Fakhruddin rays, and the Fakhruddin cone is the subcone of $\operatorname{Nef}(\overline{M}_{0,6})$ spanned by Fakhruddin rays. Fakhruddin's conjecture. The cone generated by all $\mathfrak{sl}_2$ conformal block divisors for all levels is equal to the Fakhruddin cone. This conjecture identifies all such conformal block divisors with the specified extremal-ray cone in the nef cone of $\overline{M}_{0,6}$.