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We prove that the stationary magnetic potential vector and the electrostaticpotential entering the dynamic magnetic Schr\"odinger equation can be Lipschitzstably retrieved through finitely many local boundary measurements of thesolution. The proof is by means of a specific global Carleman estimate for theSchr\"odinger equation, established in the first part of the paper.

Carleman estimate for the Schr\"odinger equation and application to magnetic inverse problems