Classification of all quasi-local invariants

Establish a classification theorem for every quasi-local conserved invariant of the species-flipping three-state interaction-round-a-face cellular automaton, thereby determining whether any conserved directions exist beyond the displayed common quasi-local family and resolving unconditional completeness of its sound-active sector.

Background

The paper constructs a one-parameter family of common quasi-local charges for the species-preserving and species-flipping rules and obtains the restricted sound velocity ±√(3/23) on the span of that family and the three elementary charges.

For the species-flipping rule, the result agrees with a previously reported numerical sound velocity, but the paper does not prove that no additional quasi-local conserved directions exist. Such directions could affect the full hydrodynamic conserved space and the unconditional completeness of the sound-active sector.