Kontsevich-Segal-Witten and the no-boundary wave function

The Kontsevich-Segal-Witten (KSW) criterion offers a novel theoretical framework to distinguish well-behaved complex metrics from pathological ones. In this talk, I will discuss implications of applying this criterion to the semiclassical no-boundary wave function. By completing the observable phase of slow-roll inflation with a no-boundary origin and imposing a phenomenologically viable number of e-folds, the KSW criterion translates into constraints on the inflationary potential. The criterion also excludes highly anisotropic configurations in the Bianchi IX model and, in particular, configurations with negative spatial curvature. In both cases, configurations deviating too strongly from de Sitter space are effectively excluded. I will also provide an updated perspective on the validity of the KSW criterion.