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No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).The geometric phase due to the evolution of the Hamiltonian is a central concept in quantum physics and may become advantageous for quantum technology. In noncyclic evolutions, a proposition relates the geometric phase to the area bounded by the phase-space trajectory and the shortest geodesic connecting its end points. The experimental demonstration of this geodesic rule proposition in di