The moduli-space structure conjecture for stable smooth exploded curves

Let $\mathfrak B$ be an exploded $\mathbb T$ fibration with a closed $2$-form $\omega$. A smooth exploded $\mathbb T$ curve $f:\mathfrak C\longrightarrow\mathfrak B$ is $\omega$-stable if its domain has finitely many strata and the integral of $f^*\omega$ is positive on every unstable fiber over a vertex. For genus $g$ and $n$ marked points, let $\mathfrak M^{sm}_{g,n}(\mathfrak B,\omega)$ denote the moduli space of $\omega$-stable smooth exploded curves.

The moduli-space structure conjecture. The moduli space

$$\mathfrak M^{sm}_{g,n}(\mathfrak B,\omega)$$

has a natural structure of a Fréchet orbifold exploded fibration.

This is part of the proposed perturbation framework for $\omega$-stable holomorphic curves; the source presents it as a rough sketch and gives no resolution evidence.