Global convergence conjecture for pluriclosed flow on surfaces of general type

Let $(M,J)$ be a complex surface of general type, and let $\omega_0$ be a pluriclosed metric. General type convergence conjecture. The solution to pluriclosed flow with initial condition $\omega_0$ exists on $[0,\infty)$, and the solution to normalized pluriclosed flow exists on $[0,\infty)$ and converges exponentially to $\omega_{KE}$, the unique orbifold Kähler–Einstein metric on the associated canonical model. The passage says that this is confirmed for a large class of surfaces of general type, but does not establish it in full generality.