Maximum positive and stable steady states in the full ERK network

Consider the full ERK network and the same network with $k_{\mathrm{on}}=0$, and let a positive steady state mean a steady state with all relevant concentrations positive; call a steady state positive stable when it is both positive and stable. ERK steady-state conjecture. For each of these two networks, the maximum number of positive steady states is $3$, and the maximum number of positive stable steady states is $2$. This conjecture concerns the sharpness of the bounds in the table and the stability of the steady states; the surrounding discussion establishes multistationarity for the full network but does not resolve these maxima.