Singer's unobstructedness conjecture for anti-self-dual four-manifolds

Let $(M^4,g)$ be an anti-self-dual conformal four-manifold. Its Yamabe invariant is the conformal invariant obtained by taking the supremum, over metrics in the conformal class, of the normalized total scalar curvature. The metric is unobstructed when $H^2_{ASD}(M^4,g)=\{0\}$, where $H^2_{ASD}(M^4,g)$ is the cokernel of the anti-self-dual deformation complex.

Singer's conjecture. If the Yamabe invariant of $(M^4,g)$ is positive, then $(M^4,g)$ is unobstructed; equivalently,

$$H^2_{ASD}(M^4,g)=\{0\}.$$

This conjecture concerns the obstruction space for deformations of anti-self-dual conformal structures. Its validity would give a criterion ensuring that the moduli space is locally smooth, and it is attributed to Singer; the supplied source does not state a resolution.