The one-parameter family conjecture for the even Haagerup subfactor planar algebra

The even part of the Haagerup subfactor planar algebra $H\mathcal{P}$ is a subfactor planar algebra lying in a one-parameter family of subfactor planar algebras. Haagerup family conjecture. The even part of the Haagerup subfactor planar algebra $H\mathcal{P}$ lies in a one-parameter family of subfactor planar algebras. The precise parameters in the Yang–Baxter relations for $H\mathcal{P}$ remain unresolved; determining the associated consistency equations could lead to a classification of examples with a 4-dimensional fusion bialgebra.