The Calder\'on problem is an inverse source problem

We prove that uniqueness for the Calder'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\mathrm{\Delta }+V+({\mathrm{\Lambda }}_t^1-q)\otimes ({\mathrm{\Lambda }}_t^2-q)$ defined on $\mathrm{\partial }{\mathcal{M}}^2\times [0,1]$ where $V$ and $q$ are potentials and ${\mathrm{\Lambda }}_t^i$ is a Dirichlet-Neumann operator at depth $t$. This is done by showing that the difference of two Dirichlet-Neumann maps is equal to the Neumann boundary values of the solution to an inhomogeneous equation for said operator, where the source term is a measure supported on the diagonal of $\mathrm{\partial }{\mathcal{M}}^2$.