Phase Transitions in Artificial General Intelligence: Scaling Laws, Predictability Limits, and Singularity

Abstract We model AGI emergence as a critical transition in large-scale learning systems and propose a quantitative framework connecting scaling laws, dynamical stability, and safety-relevant control. Instead of treating the singularity as a date forecast, we define a measurable transition regime in terms of scaling efficiency, transfer generalization, recursive self-improvement depth, and governance latency. The analysis combines bifurcation-style phase-transition proxies, Lyapunov-inspired predictability horizons, information-theoretic diagnostics, and computational irreducibility constraints. We show how rapid capability gains can coexist with finite prediction windows, yielding practical limits on long-horizon control despite deterministic training dynamics. To operationalize the framework, we specify benchmark-linked indicators, threshold tests, and evaluation protocols for detecting critical behavior across model families. We further map these diagnostics to deployment policy through closed-loop safety gates, rollback criteria, and audit latency targets. The resulting perspective offers a cs.AI-oriented methodology for studying AGI transitions with empirically testable claims, reproducible measurements, and explicit interfaces to safety and governance.