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It is shown that the infinite tower of tree-level soft graviton symmetries inasymptotically flat 4D quantum gravity can be organized into a single chiral 2DKac-Moody symmetry based on the wedge algebra of w(1+infinity). The infinitetowers of soft photon or gluon symmetries also transform irreducibly underw(1+infinity).

w(1+infinity) and the Celestial Sphere