The orbit-lattice fixed-point category conjecture

Let $g\in O(\Lambda)$ be an element whose frame shape equals the type of an orbit lattice $N(Z)$, and let $\Lambda_g=(\Lambda^g)^\perp$. Choose a lift $\hat g$ to an automorphism of the lattice vertex operator algebra $V_{\Lambda_g}$. Set

$$W=V_{\Lambda_g}^{\langle\hat g\rangle}.$$

Let $(A,q)$ be the discriminant space of $N(Z)$, and let $\mathcal{Q}(A,-q)$ be its associated modular tensor category with quadratic form $-q$. Fixed-point category conjecture. The algebra $W$ is a vertex operator algebra whose modular tensor category satisfies

$$\mathcal{T}(W)\cong\mathcal{Q}(A,-q).$$

This claim is used to describe the eleven relevant genera of orbit lattices and their associated fixed-point vertex operator algebras. The source does not specify whether it has been proved.