One-dimensional search-space conjecture for the generalized three-color matrix model

Consider the generalized three-color matrix model referred to in the source, with coupling constant $g$. Let $m_2$ denote its second moment, and consider the large-$N$ limit of all moments. The search-space dimension is the number of independent quantities needed to express all such moments.

One-dimensional search-space conjecture. The matrix model has search-space dimension one: all moments in the large-$N$ limit can be written in terms of the coupling constant $g$ and $m_2$.

The conjecture is based on algebraic solutions of the Schwinger–Dyson equations yielding relations among the moments. If true, the model would be essentially solved because an explicit expression for $m_2$ is available. The supplied text gives no resolution.