The tangent-sheaf cohomology dimension claim for boundary s.l.c. sextic surfaces

Let $S$ be a semi-log-canonical (s.l.c.) sextic surface lying in any boundary divisor of the closure $\overline{M}^{\operatorname{sextic}}$ of the Gieseker moduli stack of sextic surfaces. The cohomology groups of its tangent sheaf are $H^1(S,T_S)$ and $H^2(S,T_S)$. Tangent-sheaf cohomology dimension claim. The dimensions are

$$\dim H^1(S,T_S)=68; \quad \dim H^2(S,T_S)=6.$$

These dimensions describe the deformation-theoretic behavior of the boundary surfaces in the proposed KSBA compactification. The supplied text does not indicate whether the claim has been proved or remains open.