The one-parameter primitive-solution conjecture for non-perturbative spectral $p$-$q$ duality

In the $(p,q)$-system, let $\mathfrak g$ be defined by $2\mathfrak g=(p-1)(q-1)$, and let $\{\theta_a\}_{a=1}^{2\mathfrak g}$ denote the D-instanton and ghost D-instanton fugacities parametrizing the solution space. Primitive-solution conjecture. Non-perturbative completions possessing non-perturbative spectral $p$-$q$ duality are given by a one-parameter family of the primitive solution. In particular, duality-consistent $(p,q)$ minimal string theory is the true vacuum of the system. This conjecture proposes that spectral $p$-$q$ duality selects a one-parameter family of non-perturbative completions and identifies the duality-consistent minimal string theory as the true vacuum; the supplied context does not state whether it has been proved or disproved.