Vanishing conjecture for the obstruction group of selfdual contact instantons

Let $M$ be a compact Sasakian $7$-manifold with positive transverse scalar curvature, and let ${\bf E}\to M$ be a Sasakian $G$-bundle. Let $A$ be an irreducible selfdual contact instanton on ${\bf E}$. Vanishing conjecture. The second basic cohomology group vanishes:

$$H_B^2=0.$$

This vanishing would remove the relevant obstruction at irreducible selfdual contact instantons and support the study of the corresponding moduli space; the source announces the result while postponing its proof to future work.