The dominant narrative of artificial intelligence development assumes that progress is continuous and that capability scales monotonically with model size. We challenge both assumptions. Drawing on punctuated equilibrium theory from evolutionary biology, we show that AI development proceeds not through smooth advancement but through extended periods of stasis interrupted by rapid phase transitions that reorganize the competitive landscape. We identify five such eras since 1943 and four epochs within the current Generative AI Era, each initiated by a discontinuous event -- from the transformer architecture to the DeepSeek Moment -- that rendered the prior paradigm subordinate. To formalize the selection pressures driving these transitions, we develop the Institutional Fitness Manifold, a mathematical framework that evaluates AI systems along four dimensions: capability, institutional trust, affordability, and sovereign compliance. The central result is the Institutional Scaling Law, which proves that institutional fitness is non-monotonic in model scale. Beyond an environment-specific optimum, scaling further degrades fitness as trust erosion and cost penalties outweigh marginal capability gains. This directly contradicts classical scaling laws and carries a strong implication: orchestrated systems of smaller, domain-adapted models can mathematically outperform frontier generalists in most institutional deployment environments. We derive formal conditions under which this inversion holds and present supporting empirical evidence spanning frontier laboratory dynamics, post-training alignment evolution, and the rise of sovereign AI as a geopolitical selection pressure.