Monotonicity of robustness across equilibrium classes

Let $\rho_{i,j}$ denote the maximal robustness of the three-dimensional equilibrium class indexed by $(i,j)$. Equilibrium-class monotonicity conjecture. If $i\geq k$ and $j\geq l$, then

$$\rho_{i,j}\leq\rho_{k,l}.$$

The conjecture is strongly suggested by the stated monotonicity corollary and is consistent with the findings and conjectures reported in the paper, but remains unresolved in the supplied text.