To sort out which GR asymptotic symmetry might represent the Universe, recent simulations suggest that determining which gravitational-wave (GW) memory terms, displacement and spin, would give the best fit to the GW data to be collected in next generation detectors might constrain the three model symmetry scenarios: (a) Poincaré group (no memory); original BMS group (only displacement memory); and (c) extended BMS group (both displacement and spin memories).