Bernstein-generality conjecture for conservative reaction networks

A conservative reaction network is a chemical reaction network in which each species occurs in at least one nonnegative conservation law. Let the mixed-volume bound be the upper bound obtained from the mixed volume of the network's polynomial system, and let the Newton–Okounkov bound be the corresponding upper bound obtained from Newton–Okounkov body theory. Bernstein-generality conjecture. For every conservative reaction network, the mixed-volume bound is equal to the Newton–Okounkov bound; equivalently, conservative networks are Bernstein-general. The conjecture is based on the authors' investigations of non-conservative examples and asserts that conservation prevents the improvement seen there. The supplied text gives no evidence that it has been proved or refuted.