Isomorphism conjecture for the KSBA and semitoric compactifications of $D_{1,6}$-polarized Enriques surfaces

Let $\overline{M}_{D_{1,6}}^\nu$ be the KSBA compactification of the moduli space of $D_{1,6}$-polarized Enriques surfaces, and let $\overline{\mathcal{D}/\Gamma}^\Sigma$ be the semitoric compactification of the quotient of the type IV domain $\mathcal{D}$ by $\Gamma$, associated to the admissible decomposition $\Sigma$. The compactifications share the common open subset $\mathcal{D}/\Gamma$. Isomorphism conjecture. The compactifications $\overline{M}_{D_{1,6}}^\nu$ and $\overline{\mathcal{D}/\Gamma}^\Sigma$ are isomorphic. This would identify the KSBA compactification with the semitoric compactification whose boundary strata have the same dimensions and intersection relations; the paper establishes these boundary correspondences and a local isomorphism over the odd $1$-cusp of type $2$, but leaves the global isomorphism conjectural.