A Stability-Theoretic Foundation of Artificial General Intelligence

AbstractThis work proposes a formal foundation for Artificial General Intelligence (AGI) basedon stability theory and geometric control. We introduce a framework in whichintelligence is defined not as optimization of reward, imitation of cognition, or pursuitof stimulus variation, but as the capacity of a system to preserve viable trajectoriesunder conditions of dynamic instability and environmental uncertainty. The central object of the theory is an instability functional ( (S) ) defined over astate manifold (M), together with a dimensionless stability invariant: G (S) = C + D, where () denotes adaptive capacity, (C) structural complexity, () systemload, and (D) accumulated structural deviation. The condition (G (S) 1) defines theadmissible domain of operation, while (G (S) < 1) characterizes collapse-prone regimes. Within this framework, intelligence is formalized as a control process: u (t) = -k (S (t) ), which enables the system to maintain trajectories inside the stability domain despiteperturbations. We demonstrate that behaviors commonly associated with intelligentsystems—adaptation, exploration, learning, and generation of new structuredstates—emerge as consequences of stability-constrained motion in the state space, rather than as primary objectives. In particular, we show that the drive toward state-space expansion and variation is notfundamental, but arises as a secondary effect of navigating instability gradients underbounded control resources. This result unifies previously disconnected paradigms, including reward-based learning, unsupervised adaptation, and stimulus-drivenbehavioral variation, as restricted regimes within a broader stability-theoretic structure. The proposed framework provides a rigorous definition of AGI as a system capable ofsustaining admissible trajectories across open-ended environments. It furtherestablishes explicit conditions for collapse, limits of controllability, and measurableindicators of system viability. These results position stability-preserving control as thefundamental principle underlying general intelligence across artificial, biological, andsocio-technical systems.