The Yang–Mills Mass Gap from Causal Chain Topology

I show that the causal chain equation $T = \sum_i (d_i/C + \tau_i)$ resolves the Yang--Mills existence and mass gap problem. The argument proceeds in three steps. First, the causal identity principle---that configurations producing identical causal chains are physically identical---requires all physical excitations of a non-Abelian gauge theory to be gauge-invariant (color-singlet), forcing them into closed chain topologies. Second, self-coupling of the non-Abelian gauge field ensures that every vertex carries strictly positive processing time $\tau_i > 0$. Third, the minimum closed chain loop has strictly positive total processing time, yielding a minimum mass $m_\mathrm{gap} > 0$ via the mass--cycling relation. The mass gap is topological---a structural constraint on which chain configurations constitute valid physical states---not dynamical. The argument correctly produces no mass gap for Abelian theories. I propose that the Wightman axioms axiomatize an approximation to the more fundamental causal chain structure. Replacement axioms (C0--C5) are presented, from which the amplitude structure, the integration measure, the Born rule, and both existence and the mass gap follow as theorems. Anomaly cancellation---the requirement that matter content preserve gauge invariance at the quantum level---is derived as a theorem from C5, constraining the allowed matter representations for any gauge group. The framework produces falsifiable predictions distinct from lattice QCD.