General method to prove coprimeness for lattice equations

Develop a completely general method to prove the coprimeness property for lattice equations (or their initial value problems), independent of the concrete form of the equation, possibly via Laurentification or alternative techniques.

Background

Coprimeness provides a powerful algebraic reinterpretation of singularity confinement and can justify exact degree calculations by ruling out extraneous singular behavior. The authors note that existing proofs of coprimeness are ad hoc and equation-specific, and a universal method is currently unavailable.