Main existence conjecture for pluriclosed flow

Let $(M^{2n},g_0,J)$ be a compact complex manifold with pluriclosed metric, and let $\tau^*(\omega_0)$ be the formal cohomological existence time defined by the condition $[\omega_0]-t c_1\in\mathcal P$. Main existence conjecture. The maximal smooth solution of pluriclosed flow with initial condition $g_0$ exists on $[0,\tau^*(\omega_0))$. This predicts that the cohomological upper bound is sharp, although the supplied passage gives no resolution of the conjecture.