Morrison–Peters conjecture on subfactor planar algebras below index $3+\sqrt{5}$

A subfactor planar algebra is non-Temperley–Lieb if it is not the Temperley–Lieb subfactor planar algebra. The index is the Jones index of the corresponding subfactor. The quantum-group subfactor planar algebras are denoted by $\mathfrak{su}(2)_5$ and $\mathfrak{su}(3)_4$.

Morrison–Peters conjecture. There are exactly $2$ non-Temperley–Lieb subfactor planar algebras with index in $(5,3+\sqrt{5})$: the unique $\mathfrak{su}(2)_5$ subfactor planar algebra and the unique $\mathfrak{su}(3)_4$ subfactor planar algebra.

The conjecture is known for exactly $1$-supertransitive subfactor planar algebras, and classifications at index $3+\sqrt{5}$ provide substantial progress toward the broader enumeration. The supplied source does not state that the full conjecture has been resolved.