Adler-zero conjecture for pure generalized NLSM 3-amplitudes

Prove that every generic, pure generalized NLSM 3-amplitude has identically vanishing single-soft limits.

Background

The paper proves that the six-point pure generalized NLSM amplitude for (k,n)=(3,6) vanishes in all hard and soft limits. The authors state that they have little experimental evidence beyond this case but conjecture that the observed Adler-zero behavior extends to generic pure generalized NLSM amplitudes with k=3 and arbitrary admissible n.

This conjecture concerns the soft behavior of amplitudes generated by pure kinematic deformations of generalized CEGM amplitudes. Establishing it would generalize the familiar Adler zero of the ordinary nonlinear sigma model to the CEGM setting.