  Models of inflation in which non-Gaussianity is generated outside the
horizon, such as curvaton models, generate distinctive higher-order correlation
functions in the CMB and other cosmological observables. Testing for violation
of the Suyama-Yamaguchi inequality tauNL >= (6/5 fNL)^2, where fNL and tauNL
denote the amplitude of the three-point and four-point functions in certain
limits, has been proposed as a way to distinguish qualitative classes of
models. This inequality has been proved for a wide range of models, but only
weaker versions have been proved in general. In this paper, we give a proof
that the Suyama-Yamaguchi inequality is always satisfied. We discuss scenarios
in which the inequality may appear to be violated in an experiment such as
Planck, and how this apparent violation should be interpreted. We analyze a
specific example, the "ungaussiton" model, in which leading-order scaling
relations suggest that the Suyama-Yamaguchi inequality is eventually violated,
and show that the inequality always holds.
