math.DS — Dynamical Systems
Unistationarity of Type II_l and Type V autocatalytic cores with nonnegative degradation
We prove that reversible Type II_l autocatalytic cores with l at least three and Type V cores admit at most one positive stationary state when every degradation rate is nonnegative. The Type II result assumes source-minimality, while the Type V statement uses its literal normal form. Strictly positive reaction rate constants are retained throughout. A reduction to the fork skeleton, source-exhaustion identities and diagonal current criteria control both positive-loss and boundary cases, including internal chains. We also derive determinant estimates and local continuation results, with small-degradation existence and stability under the stated hypotheses. The main nonnegative-degradation uniqueness theorem is registered in Lean 4; the manuscript and supporting claim map distinguish the formal interface from additional conventional results.