The unambiguity conjecture for substitution-system refinement

A substitution system is a tiling system with finitely many tile types and a substitution rule, and Algorithm~ is the paper's refinement procedure that augments each tile type with information about its surrounding tile types. A system is unambiguous when the refined tile types contain enough information to distinguish the relevant local configurations. Unambiguity conjecture. For any substitution system, there exists $n\geqslant 0$ such that applying Algorithm~ $n$ times makes it unambiguous. Repeated refinement records information from progressively larger neighborhoods and is sufficient in the examples discussed, but the general assertion is left as a conjecture.