Classical scaling laws model AI performance as monotonically improving with model size. We challenge this assumption by deriving the Institutional Scaling Law, showing that institutional fitness -- jointly measuring capability, trust, affordability, and sovereignty -- is non-monotonic in model scale, with an environment-dependent optimum N*(epsilon). Our framework extends the Sustainability Index of Han et al. (2025) from hardware-level to ecosystem-level analysis, proving that capability and trust formally diverge beyond critical scale (Capability-Trust Divergence). We further derive a Symbiogenetic Scaling correction demonstrating that orchestrated systems of domain-specific models can outperform frontier generalists in their native deployment environments. These results are contextualized within a formal evolutionary taxonomy of generative AI spanning five eras (1943-present), with analysis of frontier lab dynamics, sovereign AI emergence, and post-training alignment evolution from RLHF through GRPO. The Institutional Scaling Law predicts that the next phase transition will be driven not by larger models but by better-orchestrated systems of domain-specific models adapted to specific institutional niches.