Topological R4 rigidity conjecture for gravitational instantons

Let $(M,g)$ be a gravitational instanton whose underlying manifold $M$ is topologically $\mathbb{R}^4$. Topological $\mathbb{R}^4$ rigidity conjecture. The metric $g$ is either the flat metric or the Taub-NUT metric, up to isometry, scaling, and orientation reversal. The source presents this as a general rigidity expectation and gives no resolution status.