Generalised uniqueness conjecture for generalised Markov triple-graphs

Let $T_{\mu,\nu}$ be a generalised Markov triple-graph, and let a generalised Markov number be a number associated with this graph. A maximal (middle) element is the middle entry of a Markov triple in $T_{\mu,\nu}$. Generalised uniqueness conjecture. Every generalised Markov number appears exactly once as a maximal (middle) element in a Markov triple in $T_{\mu,\nu}$. The paper formulates this as a generalisation of the classical uniqueness conjecture, but the supplied status evidence indicates that it has a counterexample and is therefore disproved.