The nondegeneracy conjecture for reaction-network steady states

For a reaction network $G$, let $\operatorname{\cap_{pos}}(G)$ be its maximum number of positive steady states and let $\operatorname{\cap_{nondeg}}(G)$ be its maximum number of nondegenerate positive steady states. If

$$\operatorname{\cap_{pos}}(G)<\infty,$$

then

$$\operatorname{\cap_{pos}}(G)=\operatorname{\cap_{nondeg}}(G).$$

Nondegeneracy conjecture. Every network with finitely many positive steady states has the same capacity when capacity is counted using all positive steady states or only nondegenerate positive steady states. The claim concerns the equality of these two capacities; the surrounding discussion notes only the general inequality between them and does not provide a resolution.