Propagating local agreement to a true Z-test under weaker conditions

Prove that the Local Agreement Theorem for the V-test can be propagated to a true Z-test under conditions weaker than λ-globality, for example under coboundary expansion or other recent topological notions, thereby achieving 1% regime testers on broader classes of complexes.

Background

The paper’s Local Agreement Theorem shows that non-trivial V-test agreement implies local consistency with a global function on many links. The current 1% regime Z-test’s soundness requires λ-globality, a strong condition satisfied mainly by dense systems.

The authors suggest topological notions from recent work (e.g., coboundary expansion) might suffice, and explicitly leave this as an open question.