Bulk double soft limits introduce subtleties absent from boundary celestial CFTs, so the full soft expansion of gravitational amplitudes cannot be generated from the first three terms via celestial algebras.
Soft scalars and the geometry of the space of celestial conformal field theories,
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Soft Algebras via Bulk Double Soft Limits
Bulk double soft limits introduce subtleties absent from boundary celestial CFTs, so the full soft expansion of gravitational amplitudes cannot be generated from the first three terms via celestial algebras.