Space of non-Gaussian fields with single-clock bispectra

We develop a mathematical construction of non-Gaussian fields whose bispectra satisfy the single-clock inflation consistency relation. At the same order that our basis for bispectra recovers the two simplest single-clock templates, we also find a third orthogonal template which has the single-clock squeezed limit, peaks in folded configurations, and has very small coupling in the equilateral limit. We explore the map between templates and operators in a very general Lagrangian for single-clock fluctuations and find no significant overlap between the new template and models in the literature. We comment on the physical implications of this conclusion. Our findings add support for the idea that both theory- and data-driven considerations will be best served if next-generation non-Gaussianity constraints are made in a basis that uses the degree of coupling between long- and short-wavelength modes as an organizing principle.