Conjecture on Ricci-positive metrics after connected sum with a homotopy sphere

Let $M$ be a highly connected manifold admitting a positive scalar curvature metric and with vanishing Witten genus. A homotopy-sphere Ricci-positivity conjecture. There exists a homotopy sphere $\Sigma$ such that $M\sharp\Sigma$ admits a Ricci-positive metric. The conjecture proposes that, after connected sum with a suitable homotopy sphere, the obstruction measured by the Witten genus is sufficient for the existence of a positive Ricci curvature metric. Its status is not resolved in the supplied text.