The nondegeneracy conjecture for positive steady states

Let $G$ be a reaction network, and suppose that $G$ does not admit infinitely many positive steady states in any stoichiometric compatibility class. Recall that $G$ admits $k$ positive steady states if some choice of positive rate constants yields exactly $k$ positive steady states in a stoichiometric compatibility class; it admits $k$ nondegenerate positive steady states if those steady states can be chosen nondegenerate. Nondegeneracy conjecture. If $G$ admits $k$ positive steady states, then $G$ admits $k$ nondegenerate positive steady states. This conjecture asks whether positive steady states can always be realized nondegenerately when the network has no stoichiometric compatibility class with infinitely many positive steady states; the source does not provide evidence resolving it.