Ciocan-Fontanine–Kim–Sabbah conjecture for quantum abelianisation

Consider a GIT quotient $X_G$ and its abelianisation $X_T$. Fix lifts of cohomology classes from $H^*(X_G)$ to $H^*(X_T)^W$, coordinates $t_i$ in a basis of $H^*(X_G)$, lifted coordinates $\tilde{t_i}$, and the natural specialization map $p$ from the quantum parameters of $X_T$ to those of $X_G$. Let $*_G$ denote the quantum product on $X_G$, and let $*$ denote the quantum product on $X_T$ after specialization via $p$. For classes $\alpha,\alpha'$, let $\zeta,\zeta'$ be the unique classes satisfying

$$\tilde{\alpha}\cup\omega=\zeta*\omega,\qquad \tilde{\alpha'}\cup\omega=\zeta'*\omega.$$

Ciocan-Fontanine–Kim–Sabbah conjecture. For $\alpha,\alpha',\zeta,\zeta'$ as above,

$$(\widetilde{\alpha *_G \alpha'}\cup\omega)(t)=(\zeta*\zeta'*\omega)(\tilde{t}(t),0),$$

where $\tilde{t}(t)$ is an appropriate change of variables. This conjecture relates the quantum cohomology of a GIT quotient to the specialized quantum cohomology of its abelianisation; the source restricts the general big-quantum-cohomology conjecture to small quantum cohomology, and does not state its resolution.