This work presents a structural and mathematical analysis of the asymptotic symmetry–memory correspondence developed by Sabrina Pasterski, Andrew Strominger and Alexander Zhiboedov. The analysis is performed entirely at the level of explicit equations and functional dependence, without relying on phenomenological interpretation or conceptual assumptions. The electromagnetic and gravitational memory observables are shown to take the general form of time-integrated radiative fluxes, equivalently corresponding to zero-frequency projections in Fourier space. It is demonstrated that the resulting observables depend explicitly on externally specified boundary data and are not generated through an internal dynamical mechanism. The work further analyzes the structure of soft theorems and asymptotic symmetries, showing that soft factors emerge as kinematic limits of scattering amplitudes, while asymptotic symmetry transformations depend on undetermined boundary functions not fixed by any internal equation. As a consequence, the soft theorem–symmetry–memory correspondence does not define a closed generative system. The absence of a generating functional, an internal spectral structure, and a global selection mechanism is established explicitly. The analyzed framework is therefore shown to describe mappings between imposed configurations and derived observables rather than internally generated physical states. The comparison with a closed variational structure makes the structural difference precise: the analyzed framework remains externally driven, while a variationally closed system generates admissible configurations internally through stationary conditions, spectral structure, and global selection. All results follow directly from the explicit mathematical structure of the analyzed equations without fitting procedures or external assumptions.
