Untangling conjecture for admissible $qq$-characters

Let $c7$ be an admissible $qq$-character with a dominant monomial. Its graph may be equipped with a supplement satisfying the compatibility condition around every square, and an incomplete square is a configuration in which exactly three vertices of an associated square occur, connected by two arrows. A $qq$-character is untangled when its graph has a supplement and no incomplete squares. Untangling conjecture. Any admissible $qq$-character with a dominant monomial is untangled. This predicts that admissibility and the presence of a dominant monomial rule out incomplete-square obstructions and guarantee the required global edge supplement.