Extend the Lw_{1+∞} bootstrap beyond the decay region

Determine whether the \mathcal{L}w_{1+∞} Ward identities, together with appropriate analyticity assumptions analogous to those used in the decay region, can recursively generate the stripped single-minus n-graviton amplitude M_{1…n} for kinematics outside the decay region \mathcal{D}_{n,n-1}.

Background

Within a decay-region chamber, the authors show that the \mathcal{L}w_{1+∞} Ward identities, combined with analyticity assumptions, recursively generate single-minus amplitudes from a three-graviton seed, yielding a simple product formula.

They explicitly note uncertainty about extending this construction beyond the decay region, leaving open whether the same symmetry-based recursion can determine amplitudes for general kinematics.