Ribbon equivalence conjecture for the even induction functor

Let $\mathrm N$ be the parameter specifying the number of symplectic fermion pairs, let $\beta$ be the scalar used in the ribbon structure, and let $\big(\widehat{-}\big)_\mathrm{ev}$ denote the even-part induction functor from the relevant category associated with the symplectic fermion ribbon quasi-Hopf algebra. Ribbon equivalence conjecture. For the choice

$$\beta=e^{-\mathrm{i}\pi\mathrm N/4},$$

$\big(\widehat{-}\big)_\mathrm{ev}$ is an equivalence of $\mathbb{C}$-linear ribbon categories. This conjecturally refines the known $\mathbb{C}$-linear inclusion to a ribbon equivalence and is used to relate the algebraic category to the even symplectic fermion theory; the necessary coherence isomorphisms are referred to in the cited work.