  We prove that soft theorems uniquely fix scattering amplitudes in a wide
range of theories, including Yang-Mills, gravity, the non-linear sigma model,
Dirac-Born-Infeld, dilaton effective theories, extended theories like
NLSM$\oplus \phi^3$ or BI$\oplus$YM, as well as some higher derivative
corrections to these theories. We conjecture the same is true even when
imposing more general soft behavior, simply by assuming the existence of soft
operators, or by imposing gauge invariance/the Adler zero only up to a finite
order in soft expansions. Besides reproducing known amplitudes, this analysis
reveals a new higher order correction to the NLSM, and two interesting facts:
the subleading theorem for the dilaton, and the subsubleading theorem for DBI
follow automatically from the more leading theorems. These results provide
motivation that asymptotic symmetries contain enough information to fully fix a
holographic S-matrix.
