{"id":"hexagon/2610.00369","pdf":"https://hexagonmath.org/pdf/2610.00369v1","url":"https://hexagonmath.org/abs/2610.00369v1","tags":["msc:15A18","msc:34D20","D-unstable cores","Lean formalization","chemical reaction networks","classical mass action","counterexample","elementary bimolecular reactions","generalized mass action","parameter-rich kinetics"],"score":0,"title":"Counterexamples to the D-unstable-core conjecture for parameter-rich and elementary mass-action networks","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Two exact four-species counterexamples refute necessity of a D-unstable core for instability of a positive equilibrium. The first has five reactions, parameter-rich kinetics, an explicit generalized-mass-action equilibrium, and a rational Jacobian with eigenvalue 1/500 + (51/500)i. The second has six reactions, at most two molecules on each side of every reaction, no catalysts, and classical mass-action kinetics with fixed integer kinetic orders. At a positive rational equilibrium its Jacobian has integer entries and an unstable nonreal eigenvalue with real part between 0 and 5, certified by…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-25-000012&version=1"],"human_understanding":"some"}