Chern-Ricci flow convergence conjecture for manifolds of general type

Let $M^n$ be a compact complex manifold with nef canonical bundle $K_M$ and Kodaira dimension $\mathrm{Kod}(M)=n$. Let $\omega(t)$ solve the Chern-Ricci flow starting at an arbitrary Hermitian metric $\omega_0$, and let $S$ be the canonical-model singular set and $\omega_{\rm KE}$ the limiting Kähler-Einstein metric on $M\setminus S$. Chern-Ricci flow convergence conjecture. There is a constant $C$ such that, for all sufficiently large $t$,

$$\mathrm{diam}\left(M,\frac{\omega(t)}{t}\right)\leqslant C,$$

and

$$\left(M,\frac{\omega(t)}{t}\right)\longrightarrow (Z,d)$$

as $t\to\infty$ in the Gromov-Hausdorff sense, where $(Z,d)$ is the metric completion of $(M\setminus S,\omega_{\rm KE})$. This predicts the metric-space asymptotics of the flow in the general-type case; the stated convergence and diameter bound are presented as an expected picture, beyond the convergence results known in the ample and previously treated cases.