The anisotropic Calderón conjecture for Riemannian manifolds

Let $(M,g_1)$ and $(M,g_2)$ be two compact oriented Riemannian manifolds with smooth boundary and dimension $n\geq 3$. For a metric $g$, let

$$C_g=\{(u|_{\partial M},\partial_{\nu}u|_{\partial M});\,\Delta_g u=0\text{ in }M,\ u\in C^{\infty}(M)\}$$

be the Cauchy data set of harmonic functions. The anisotropic Calderón conjecture. If $C_{g_1}=C_{g_2}$, then

$$g_2=\psi^*g_1$$

for some diffeomorphism $\psi:M\to M$ satisfying $\psi|_{\partial M}=\operatorname{Id}$. This is the geometric formulation of Calderón's inverse problem: boundary measurements determine the Riemannian metric up to a diffeomorphism fixing the boundary. The supplied text does not indicate whether the conjecture was resolved, so its status is left open.