Homeomorphism and codimension conjecture for Kähler–Ricci flow limits

Let $M^m$ be a compact Kähler manifold with semiample canonical bundle and Kodaira dimension $n=\kappa(M)$ satisfying $0<n<m$. Let $f:M\to N$ be its Iitaka fibration onto a normal projective variety $N^n$, let $N^\circ$ be the complement of the discriminant locus, and let $(Z,d_Z)$ be the metric completion of $(N^\circ,\omega_{\rm can})$, where $\omega_{\rm can}$ is the canonical metric arising from the normalized Kähler–Ricci flow $\frac{\partial}{\partial t}\omega(t)=-\operatorname{Ric}(\omega(t))-\omega(t)$. Kähler–Ricci flow collapse conjecture. In the Kähler–Ricci flow setup, $(M,\omega(t))\to (Z,d_Z)$ in the Gromov–Hausdorff topology. Furthermore, $Z$ is homeomorphic to $N$ and $Z\backslash N^\circ$ has real Hausdorff codimension at least $2$ inside $(Z,d_Z)$. This predicts the topology and metric codimension of the singular set in the limiting space of the normalized Kähler–Ricci flow; convergence to a compact metric completion is known, while the full homeomorphism and codimension assertions remain open in general.