Regularity up to the cohomological time for pluriclosed flow

Let $(M^{2n},g_0,J)$ be a compact complex manifold with pluriclosed metric. Define

$$\tau^*(g_0):=\sup\{t\geq 0\mid[\omega_0]-t c_1\in\mathcal P^{1,1}_{A}\}.$$

Here $\omega_0$ is the fundamental form of $g_0$, $c_1$ is the first Chern class in Aeppli cohomology, and $\mathcal P^{1,1}_{A}$ is the positive Aeppli cone. Pluriclosed-flow regularity conjecture. The unique maximal smooth solution to pluriclosed flow exists on $[0,\tau^*(g_0))$. The preceding upper-bound lemma shows that the maximal smooth existence time cannot exceed $\tau^*(g_0)$; the conjecture asserts equality, but the supplied text gives no resolution status.