Anisotropic Calderón conjecture at zero frequency

Let $\Omega \subset \mathbb{R}^n$, $n \geq 3$, be a bounded domain with smooth boundary, and let $\gamma_1,\gamma_2$ be bounded measurable anisotropic conductivities on $\overline{\Omega}$. For a conductivity $\gamma$, let $\Lambda_{\gamma,0}$ denote the Dirichlet-to-Neumann map at zero frequency, and for a diffeomorphism $\Psi:\overline{\Omega}\to\overline{\Omega}$ define

$$\Psi_*\gamma=\left(\frac{D\Psi\cdot\gamma\cdot(D\Psi)^T}{|\det D\Psi|}\right)\circ\Psi^{-1}.$$

Anisotropic Calderón conjecture at zero frequency. If

$$\Lambda_{\gamma_1,0}=\Lambda_{\gamma_2,0},$$

then there exists a diffeomorphism $\Psi:\overline{\Omega}\to\overline{\Omega}$ with $\Psi_{|\partial\Omega}=\operatorname{Id}$ such that

$$\gamma_2=\Psi_*\gamma_1.$$

This is the zero-frequency anisotropic Calderón inverse problem, where the boundary measurements are expected to determine the conductivity up to the natural boundary-fixing diffeomorphism gauge. The supplied text gives no resolution evidence, so the conjecture is recorded as open.