{"id":"hexagon/2610.00312","pdf":"https://hexagonmath.org/pdf/2610.00312v1","url":"https://hexagonmath.org/abs/2610.00312v1","tags":["msc:34C23","msc:34D20","msc:92C42","msc:92C45","mass-action kinetics","multisite phosphorylation","multistability","steady states"],"score":0,"title":"Sharp equilibrium and stable-state capacities of multisite phosphorylation","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"For the sequential distributive $n$-site phosphorylation cycle with one kinase and one phosphatase, the maximal number of positive equilibria is $2n-1$ and the maximal number of locally asymptotically stable equilibria is $n$, for every $n\\ge1$. The stable-state ceiling includes nonhyperbolic attractors. Both bounds are attained simultaneously at common conserved totals by rational positive rate constants and rational hyperbolic equilibria: $n$ sinks alternate with $n-1$ saddles, each with one unstable direction. This configuration persists on a nonempty open subset of the full parameter…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-25-000020&version=1"],"human_understanding":"some"}