Perron Support Governance formalizes the governing principle that determines admissibility, stability, and control in near-critical positive-operator systems. The paper shows that all admissible actions, perturbations, and observer interactions are constrained by their projection onto the Perron–Frobenius eigenstructure of basin-restricted operators. Governance is reduced to a single geometric condition: non-positive Perron support. This framework unifies stability, drift prevention, gate admissibility, and control limits across physical, semantic, and observer-coupled systems within the Einsteinian Stack.