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Generalized BMS (gBMS) is the Lie group of the asymptotic symmetries at nullinfinity, and is proposed to be a symmetry of the quantum S-matrix. Despitemuch progress in understanding the symplectic structure at null infinityconsistent with the gBMS symmetries, the construction of a radiative phasespace where all the physical soft modes and their conjugate partners areidentified remains elusive. We construct just such a radiative phase space forlinearized gravity by a systematic constraint analysis. In addition, wehighlight the difficulties that arise in extending this analysis to thenon-linear case. In order to analyze the difficulties we face in extendingthese ideas to the non-linear setting, we consider a toy model in which wegauge the action of the Weyl scaling in the Weyl BMS group. We find thatsupertranslations are no longer well-defined symmetries on the reduced phasespace of the gauged Weyl, as Weyl scalings do not commute withsupertranslations. In this restricted case we obtain the symplectic form andderive the reduced phase space.

The Radiative Phase Space for the Dynamical Celestial Metric