The SYZ mirror-resolution conjecture for Spin(7) orbifolds

Let $(\widehat{X},\widehat{\Phi})$ be an SYZ-fibred $\operatorname{Spin}(7)$-manifold, let $\tau$ be fibrewise multiplication by $-1$, and let $S$ be the compact four-manifold base. Assume there exists a nonvanishing harmonic self-dual two-form $\zeta\in\Omega^2_+(S)$ and a resolving family

$$\rho_{\zeta;t}:(X_{\zeta;t},\Phi_{\zeta;t})\dashrightarrow(X,\Phi)/\tau.$$

Let $(\overline{X},\overline{\Phi})$ be the SYZ mirror and $\overline{\tau}$ its induced involution. The SYZ mirror-resolution conjecture. The quotient $(\overline{X},\overline{\Phi})/\overline{\tau}$ admits a resolving family

$$\rho_{\zeta^*;t}:(\overline{X}_{\zeta^*;t},\overline{\Phi}_{\zeta^*;t})\dashrightarrow(\overline{X},\overline{\Phi})/\overline{\tau},$$

and $(X_{\zeta;t},\Phi_{\zeta;t})$ and $(\overline{X}_{\zeta^*;t},\overline{\Phi}_{\zeta^*;t})$ are mirror dual. This is a proposed compatibility between Spin(7) orbifold resolutions and SYZ mirror symmetry; the source gives no proof.