Uniqueness of a smooth real potential on a known Riemannian manifold

We prove uniqueness of a smooth real scalar potential from its full Dirichlet-to-Neumann map at one energy on an arbitrary known compact, connected, smooth Riemannian manifold of dimension at least three with smooth nonempty boundary. The only spectral assumption is that this energy is not a Dirichlet eigenvalue; negative eigenvalues and sign-changing potentials are allowed. Equal boundary maps first give common exterior source solutions through a weak gluing argument that does not require a positive quadratic form. Near an interior frontier, a common source gives local positive conjugations of the two equations. We adapt the separately elliptic continuation and shrinking-sphere method of OpenAI to the resulting operators with the same principal metric. An angular coercivity estimate bounds the actual transfer densities jointly in center and direction. Their collapse gives equality on one neighborhood for every matching source pair. Finite source jets then recover the local conjugating solutions and the potentials, closing the frontier without a global positive solution.