Quadratic-category modular data conjecture for odd abelian groups

Let $A$ be a finite abelian group of odd order, and let $\mathcal{C}$ be a quadratic category of type $(\mathbb{Z}_2,A,1)$ whose $\operatorname{Vec}_{\mathbb{Z}_2}$ subcategory has trivial associator. Odd-group quadratic-category conjecture. The modular data of $\mathcal{Z}(\mathcal{C})$ are the stated tensor-product modular data, with $G_e=\mathbb{Z}_2\times\mathbb{Z}_2$, $G_o=A$, and $q_{1,e}(x,y)=(-1)^{xy}$. The conjecture further predicts the three listed cases according to whether $\alpha_1$ lifts to a fermion or boson and whether $\rho$ is self-dual, including the exact counts for $A=\mathbb{Z}_3$; these claims are open in general.