Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps
The paper establishes structural identifiability for reciprocal graph functionals by showing that a complete map of minimizer locations from a controlled equilibrium response uniquely determines any reciprocal generator whose log-coordinate representation is C2 with everywhere-positive curvature, up to a positive scale. This means the equilibrium measurements can reconstruct the underlying generator without needing prior knowledge of it.