All Exponential Stationary Moments for Arbitrary-Dimensional Directed-Dimer Reaction Networks

We prove nonexplosion, geometric ergodicity and all exponential stationary molecule-count moments for a restricted but arbitrary-dimensional family of weakly reversible stochastic mass-action networks. The family permits any strongly connected directed dimer-conversion graph on 2A, A+B and 2B, arbitrary strongly connected unary conversions, and reversible creation of an A+C pair. A factorized dimer-attraction drift, quotient unary-chain contraction and quartic-imbalance exponential Foster function provide the proof. The result extends a previously drafted three-species reversible-exchange example to all dimensions and directed dimer dynamics. It does not resolve arbitrary weakly reversible network recurrence; historical priority and peer review remain unverified.