Wall's conjecture for intermediate conformal subnets

Suppose that ${\cal A}\subset {\cal B}$ are conformal subnets with finite index. Let the vacuum representation of ${\cal B}$ carry the action of ${\cal A}$, and let $V$ be the space of bounded maps from this vacuum representation to itself that commute with the action of ${\cal A}$. Wall's conjecture for conformal subnets. The number of minimal, respectively maximal, subnets between ${\cal A}$ and ${\cal B}$ is less than ${\mathrm {\dim}} V$. This is the conformal-net formulation of the intermediate-subfactor conjecture studied in the paper. The source states that the paper verifies the conjecture for four infinite series of conformal inclusions and for Jones–Wassermann subfactors, while the general finite-index conformal-subnet case remains open.