Complete Finite-Frequency Nonlinear-Memory Waveform

Determine the complete finite-frequency waveform contribution from the nonlinear gravitational-memory cut, including the regular O(ω^0) term of the six-point amplitude beyond the soft-pole residue.

Background

The paper derives the soft-pole residue of the nonlinear-memory contribution from a 5-point-conjugate-times-6-point cut. The soft factorisation fixes the distributions associated with the measured soft graviton, including the delta-function and principal-value pieces.

However, the derivation does not determine the regular finite-frequency part of the six-point contribution. Consequently, the full waveform at finite frequency remains unresolved.

References

The residue fixes both the πδ(ω) and PV(1/ω) distributions (with sign determined by iϵ), but not the regular O(ω0) six-point term, and therefore the complete finite-frequency waveform remains undetermined.

— Inclusive Radiation and Backreaction from the Phase-Space S-Matrix  (2608.21318 - Moynihan, 21 Aug 2026) in Section 7.2, p. 45