8 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.…

Let the graphs in the paper's Figure 2 be indexed by $k$, with the parameter restricted to $k>1$. Haagerup graph conjecture. For every $k>1$, neither graph in the relevant pair is…

The paper considers Haagerup's candidate graphs, with the parameter $n$ indexing the graphs in the family described in the paper. Haagerup graph obstruction conjecture. None of the…

Paley type $II$ principal-graph conjecture. Paley type $II$ Hadamard matrices yield subfactors with $A_\infty$ principal graphs.

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 $\Gamma(\mathcal B)$.

Non-$A_\infty$ subfactor classification conjecture. These two subfactors are the only non-$A_\infty$ subfactors, of any supertransitivity, with index in $(5,3+\sqrt{5})$.

Let $a$ satisfy $|a|=1$, and let $F_4(a)$ be the one-parameter family of complex Hadamard matrices of dimension $4$. Let the associated subfactor have principal graph denoted by…