Anderson's codimension-two conjecture for the Einstein orbifold boundary

Let $\mathbf{E}(M^4)$ be the moduli space of Einstein metrics on a fixed smooth four-manifold, let $\partial_o\mathbf{E}(M^4)$ denote the subspace of singular Einstein orbifold metrics in its Gromov–Hausdorff completion, and write $\overline{\mathbf{E}(M^4)}_{GH}$ for that completion. Anderson's codimension-two conjecture. The subspace

$$\partial_o\mathbf{E}(M^4)$$

is of codimension $2$ in

$$\overline{\mathbf{E}(M^4)}_{GH}.$$

This is presented as an optimistic conjecture about the size of the singular boundary of the Einstein moduli space. It is false in the asymptotically hyperbolic context, where examples show that the corresponding codimension is $1$.