Modified anisotropic Calderón conjecture at nonzero 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 $\overline{\Omega}$. Let $\Lambda_{\gamma,\lambda}$ denote the Dirichlet-to-Neumann map at frequency $\lambda$, and let $\operatorname{SDiff}(\overline{\Omega})$ denote the diffeomorphisms of $\overline{\Omega}$ with $|\det D\Psi|=1$. Assume that $\lambda\ne 0$ is fixed and does not belong to the Dirichlet spectrum of $L_{\gamma_j}$ for $j=1,2$.

Modified anisotropic Calderón conjecture at nonzero frequency. If

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

then $\gamma_1$ and $\gamma_2$ are equal up to isometry: there exists $\Psi\in\operatorname{SDiff}(\overline{\Omega})$ such that

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

This modifies the usual anisotropic Calderón conjecture because at nonzero frequency the relevant gauge consists of volume-preserving diffeomorphisms. The supplied text gives no resolution evidence, so the conjecture is recorded as open.