The universal Calabi–Yau ALE structure conjecture

Let $\kappa:\mathbb{M}\to\Theta_{\operatorname{Im}(\mathbb{C})}$ be the universal Kähler ALE bundle, with vertical forms $\omega_{\mathbb{M};RF}$ and $\operatorname{Re}(\theta_{\mathbb{M};RF})$, $\operatorname{Im}(\theta_{\mathbb{M};RF})$. The universal Calabi–Yau ALE structure conjecture. There exist $\Lambda_{\mathbb{M};RF}\oplus\Xi_{\mathbb{M};RF}\in\Omega^{0,2}\oplus\Omega^{0,(n,0)}(\mathbb{M},\mathfrak{z})$ satisfying the displayed differential identities and the condition $\Lambda_{\mathbb{M};RF}\wedge\omega_{\mathbb{M};RF}=0$:

$$\operatorname{d}\omega_{\mathbb{M};RF}=\operatorname{d}^{0,1}\omega_{\mathbb{M};RF}=\left\langle\kappa^*\theta_{\Theta_{\operatorname{Im}(\mathbb{C})}}\wedge\Lambda_{\mathbb{M};RF}\right\rangle,$$ $$\operatorname{d}\operatorname{Re}(\theta_{\mathbb{M};RF})=\operatorname{d}^{1,0}\operatorname{Re}(\theta_{\mathbb{M};RF})=\left\langle\kappa^*\theta_{\Theta_{\operatorname{Im}(\mathbb{C})}}\wedge\operatorname{Re}(\Xi_{\mathbb{M};RF})\right\rangle,$$ $$\operatorname{d}\operatorname{Im}(\theta_{\mathbb{M};RF})=\operatorname{d}^{1,0}\operatorname{Im}(\theta_{\mathbb{M};RF})=\left\langle\kappa^*\theta_{\Theta_{\operatorname{Im}(\mathbb{C})}}\wedge\operatorname{Im}(\Xi_{\mathbb{M};RF})\right\rangle.$$

These identities are intended to organise the Ricci-flat Calabi–Yau structures into a family over the parameter space; the source supplies no proof.