Riemannian gauge-completeness conjecture for anisotropic elasticity

Consider generic stiffness tensor fields $c_i$, density fields $\rho_i$, and Riemannian metrics $g_i$ in the setting of the stated Riemannian anisotropic elasticity problem, and let $\Lambda_{(\rho_i,c_i,g_i)}$ denote the corresponding Dirichlet-to-Neumann maps. Riemannian gauge-completeness conjecture. If

$$\Lambda_{(\rho_1,c_1,g_1)}=\Lambda_{(\rho_2,c_2,g_2)},$$

then

$$(\rho_2,c_2,g_2)=\left(\mu^{\frac{n}{2+n}}\,\phi_*\rho_1,\mu\,\phi_*c_1,\mu^{-\frac{2}{2+n}}\,\phi_*g_1\right)$$

for some function $\mu$ and diffeomorphism $\phi$. This conjecture proposes that the gauge freedom identified in the Riemannian setting is the entire gauge freedom; the source gives no resolution.