Existence of an irreversible Class 4 CA that is locally universal but not globally universal

Prove the existence of a cellular automaton in Wolfram’s Class 4 that is irreversible and locally universal yet not globally universal, thereby strengthening the separation between local and global universality within the Class 4 regime.

Background

Wolfram’s Principle of Computational Equivalence informally suggests Class 4 CAs are typically universal. The authors argue local universality is the appropriate interpretation for such claims and note that reversible CAs pose obstructions to generating order from randomness, complicating universality notions.

They consequently conjecture an irreversible, locally universal but not globally universal Class 4 CA exists, sharpening the universality hierarchy.