KSW criterion in large field models

We extend the analytic description of complex no-boundary solutions in the context of inflation to large field models. We discuss the Kontsevich-Segal-Witten (KSW) criterion and find it is satisfied in small field models, while in large field models it depends on an integral involving $V'(\phi)$ over the range of inflation. It follows that the criterion does not truly constrain inflationary phenomenology since one can complete any inflaton potential beyond observable scales so as to satisfy KSW.