Inoue-surface Chern-Ricci flow convergence conjecture

Let $M$ be any Inoue surface. Let $\omega(t)$ be the Chern-Ricci flow and let $\omega_\infty$ be the closed semipositive $(1,1)$-form representing a multiple of $c_1(K_M)$ described in the source. Inoue-surface convergence conjecture. For any Hermitian initial metric $\omega_0$, without requiring it to be Gauduchon or making an initial conformal change, the convergence

$$\frac{\omega(t)}{t}\to\omega_\infty$$

is uniform; it is in fact $C^\infty$, and there is a constant $C$ such that

$$\left|\operatorname{Rm}\left(\frac{\omega(t)}{t}\right)\right|_{g(t)/t}\leqslant C$$

on $M$ for all sufficiently large $t$. Existing results establish these conclusions for restricted classes of initial metrics, while the fully arbitrary-Hermitian statement remains open.