Unistationarity of Type II_l autocatalytic cores
We prove unistationarity of reversible Type II_l autocatalytic cores with l at least three under strictly positive degradation. The source-minimal wiring forces source exhaustion and unit return tails, allowing comparison of positive stationary states through current ratios, chain reduction and a cyclic determinant argument. The proof includes separated stems and the exceptional coincident three-fork branch, with all internal chain species retained. Exact six- and seven-species reversible mass-action examples show that the minimality assumptions cannot be dropped: both admit two distinct…
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