Relate star-lattice scarring to the excitable zero-modes

Characterize the relation between the excitable zero-modes constructed for the one-dimensional star-lattice PXP model and the scarring observed in the same model in Ref.~\cite{verde2026engineering}.

Background

The paper establishes an exponentially large manifold of excitable zero-modes and a linear number of finite-energy scarred eigenstates in the one-dimensional star-lattice PXP model. A separate study, cited as Ref.~\cite{verde2026engineering}, had previously reported scarring in this model.

The authors explicitly identify the relationship between these two structures as unresolved. Determining whether the excitable zero-modes generate, organize, or otherwise explain the previously observed scarred dynamics remains an open question.