q-deformed uniqueness conjecture for mirror Markov triples

Consider triples in the mirror deformation of the Markov tree, with each triple consisting of mirror deformed Markov numbers and with degree taken in the deformation parameter $q$. The maximum-degree polynomial of a triple is the polynomial among its entries having largest degree. q-deformed uniqueness conjecture. Two mirror deformed triples cannot have the same maximum-degree polynomial. This is presented as an open conjecture extending the classical uniqueness phenomenon to the mirror deformation.