3 problems

Let $\Gamma_k$ denote the graphs in the paper's Figure 2. Haagerup graph principal-graph conjecture. For every $k>1$, the graph $\Gamma_k$ is not a principal graph of a subfactor.…

Morrison–Peters conjecture. Any subfactor with index in the range $(5,3+\sqrt{5})$ has principal graphs $(A_\infty,A_\infty)$, the pair of graphs represented in the source by…

Classification conjecture. Any subfactor with index in $(5,3+\sqrt{5})$ has principal graph $A_\infty$, $\Gamma(\mathcal A)$, or $\Gamma(\mathcal B)$.