The generic étaleness conjecture for the Joyce-structure parameter map

Let $\mathcal O=\mathcal O(g,m)$ be the space of data $(C,Q_0,Q_1,Q_2)$ satisfying the prescribed pole, apparent-singularity, and residue conditions, and let $X^\#$ be the corresponding coordinate space. The map $\pi\colon\mathcal O\to M$ sends $(C,Q_0,Q_1,Q_2)$ to $(C,Q_0)$, while $\alpha\colon\mathcal O\to X^\#$ is defined by the coordinates $(z_i,\xi_j)$. Generic étaleness conjecture. The map

$$\alpha\colon\mathcal O\to X^\#$$

is generically étale. This is the first step toward identifying the coordinates $(z_i,\xi_j)$ as local coordinates and constructing the conjectural Joyce structure; the accompanying sketch argues that this should hold generically, but the statement is presented as a conjecture.