Three-positive-steady-state bound for the minimally bistable ERK subnetwork

Consider the minimally bistable ERK subnetwork, and let a compatibility class be determined by the conserved quantities of the reaction system. Three-steady-state conjecture. For every choice of rate constants and every compatibility class, the maximum number of positive steady states is $3$. If true, the previously established no-coexistence theorem would imply that Hopf bifurcations and bistability do not coexist in compatibility classes. The bound is presented as a conjecture and remains open.