{"id":"palomar/PALOMAR-2026-10-01-000001","url":"https://github.com/mmislan/palomar-p004-optimal-affinity-counterexample/tree/50199f4bc2999fb43a0486dcb7571f9dfd333ff2","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-01-000001-v1.json","repo":"https://github.com/mmislan/palomar-p004-optimal-affinity-counterexample","tags":["q-bio.MN","math.DS","msc:92C42","msc:80A30","msc:92C45","autocatalytic-networks","chemical-reaction-networks","affinity","mathematical-biology"],"score":0,"title":"A two-reaction counterexample to the gross-amplification affinity bound","trust":"high","domain":"q-bio.MN","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"q-bio.MN","summary":"Despons, De Decker and Lacoste (https://arxiv.org/abs/2306.02366, conjecture following Eq. (33)) proposed that the affinity at maximum production flux is bounded below by the logarithm of the gross amplification ratio in seed-dependent autocatalytic networks. A two-species reversible mass-action counterexample is given by X ⇌ Y with forward/reverse rates (3, 2) and 2Y ⇌ 2X + Y with rates (7, 6). On the positive Y-stationary set, the production current has its unique global maximum at (X, Y) = (1, 1). At this point the exponential of the overall affinity is 7/4, strictly below the gross…","category":"research","comments":0,"disputed":false,"division":"q-bio","mentions":0,"verified":true,"discussed":0,"published":"2026-10-01","reactions":{},"formalized":true,"formalizes":[{"title":"Optimal affinity of autocatalytic networks beyond gross stoichiometry: a counterexample, the response-profile capacity, and its kinetic realization","identifier":"","relationship":"formalizes"}]}