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This paper provides the synthesis. The Theory of Strategic Evolution analyzes strategic replicators: entities that optimize under resource constraints and spawn copies of themselves. We introduce Games with Endogenous Players (GEPs), where lineages (not instances) are the fundamental strategic units, and define Evolutionarily Stable Distributions of Intelligence (ESDIs) as the resulting equilibrium concept.\n  The central mathematical object is a hierarchy of strategic layers linked by cross-level gain matrices. Under a small-gain condition (spectral radius less than one), the system admits a global Lyapunov function at every finite depth. We prove closure under meta-selection: adding governance levels, innovation, or constitutional evolution preserves the dynamical structure. 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Under a small-gain condition (spectral radius less than one), the system admits a global Lyapunov function at every finite depth. We prove closure under meta-selection: adding governance levels, innovation, or constitutional evolution preserves the dynamical structure. 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