The reverse-braiding realization conjecture for completely rational conformal nets

For a completely rational conformal net $\mathcal{A}$, write $\operatorname{Rep}(\mathcal{A})^{\mathrm{rev}}$ for the unitary modular tensor category obtained by replacing its braiding with the opposite braiding. Reverse-braiding realization conjecture. For every completely rational conformal net $\mathcal{A}$, there exists a completely rational conformal net $\widetilde{\mathcal{A}}$ such that

$$\operatorname{Rep}(\widetilde{\mathcal{A}})\cong\operatorname{Rep}(\mathcal{A})^{\mathrm{rev}}.$$

This asserts closure of the representation categories of completely rational conformal nets under reversal of the braiding. The source presents it as a conjectural consequence or variant of the broader realization problem and does not establish it in general.