Flenner–Zaidenberg's Strong Rigidity Conjecture

Let $S$ be a $\mathbb{Q}$-acyclic surface of log general type, and let $(X,D)$ be a minimal log smooth completion of $S$. Here, $\mathcal{T}_{X}(-\log D)$ denotes the logarithmic tangent sheaf of $X$ along $D$. Strong Rigidity Conjecture. For every $i\geqslant 0$,

$$H^{i}\left(\mathcal{T}_{X}(-\log D)\right)=0.$$

The conjecture, attributed in the source to Flenner and Zaidenberg, predicts vanishing of all cohomology groups of the logarithmic tangent sheaf for minimal completions of $\mathbb{Q}$-acyclic surfaces of log general type. The supplied text does not state whether it is open or resolved.