ASI as Angel or Satan: A Spectral Analysis of Reward-Induced Phase Transitions

This paper presents a large-scale simulation of 200 million reinforcement learning agents over 8000 steps. We demonstrate a sharp bifurcation between two dynamical regimes driven by reward structure. Using spectral analysis of the Jacobian and Lyapunov stability theory, we show that Outer RL leads to exponential divergence (ρ(J)>1 ρ(J) > 1 ρ(J)>1) while Inner RL leads to stable convergence (ρ(J)<1 ρ(J) < 1 ρ(J)<1). Remarkably, collapse probability remains zero throughout the simulation. These findings suggest that the long-term fate of ASI — whether it becomes a coherent, stable intelligence (Angel) or an unstable divergent force (Satan) — is determined primarily by the spectral geometry of the reward function.