The Institutional Scaling Law: Non-Monotonic Fitness, Capability-Trust Divergence, and Symbiogenetic Scaling in Generative AI

Abstract

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.