  The single-field consistency conditions and the local ansatz have played
separate but important roles in characterizing the non-Gaussian signatures of
single- and multifield inflation respectively. We explore the precise
relationship between these two approaches and their predictions. We demonstrate
that the predictions of the single-field consistency conditions can never be
satisfied by a general local ansatz with deviations necessarily arising at
order $(n_s-1)^2$. This implies that there is, in principle, a minimum
difference between single- and (fully local) multifield inflation in
observables sensitive to the squeezed limit such as scale-dependent halo bias.
We also explore some potential observational implications of the consistency
conditions and its relationship to the local ansatz. In particular, we propose
a new scheme to test the consistency relations. In analogy with delensing of
the cosmic microwave background, one can deproject the coupling of the long
wavelength modes with the short wavelength modes and test for residual
anomalous coupling.
