Nakayama automorphism conjecture for connected Hopf algebras

Let $H$ be a connected Hopf algebra of finite Gelfand–Kirillov dimension, with antipode $S$. The Nakayama automorphism conjecture. The Nakayama automorphism of the coalgebra $H$ is given by $S^2$. This proposes a coalgebraic analogue of a result for Artin–Schelter regular algebras and concerns the Calabi–Yau structure of connected Hopf algebras; its status is not resolved in the source.