Nondegenerate multistationarity conjecture for the sequestration networks

Let $K_{m,n}$ be the sequestration network with $n$ reactions and $n$ species, and let $\widetilde K_{m,n}$ denote its fully open extension. A steady state is nondegenerate when its Jacobian has the appropriate nonsingularity property for the steady-state equations. Nondegenerate multistationarity conjecture. For positive integers $n \ge 2$ and $m \ge 2$, if $n$ is odd, then $\widetilde K_{m,n}$ admits multiple nondegenerate steady states. This would show that the networks $\widetilde K_{m,n}$ are CFSTR atoms of multistationarity. The claim is stated to be true for $n=3$ and $m=2$, while the general case remains open.