Equality of the $(g,g,g)$ and $(g,-g,g)$ two-matrix model solutions

Consider the two-matrix models with parameter triples $(g,g,g)$ and $(g,-g,g)$, and impose the positivity constraints on their large-$N$ moments. A solution is called unique if it is the sole solution satisfying those constraints.

Equality-of-solutions conjecture. The $(g,g,g)$ and $(g,-g,g)$ two-matrix models have the same unique solution satisfying the positivity constraints.

The conjecture is motivated by matching bootstrap plots and moment series expansions at zero. No resolution is given in the supplied text.