Structural Emergence of Intelligence (SEI) v1.3: Structural Conditions for the Emergence of Artificial Intelligence

We present SEI v1. 3 (Structural Emergence of Intelligence), a minimal and falsifiable framework that extends the emergence of intelligence from natural systems to artificial systems. In SEI, intelligence is not treated as a directly designed property, but as an emergent phenomenon arising from the self-referential stabilization of structured information under persistent differentiation. The framework is defined by three key variables: - structural density C (x, t) - information fixation rate Γ (x, t) - structural persistence dSC/dt Intelligence is proposed to emerge when these variables simultaneously exceed critical thresholds. Previous versions of SEI established: - spatial constraints at galactic scales (v1. 0), - observational mapping and temporal evolution (v1. 1), - planetary-scale structural conditions (v1. 2). In SEI v1. 3, we extend the same framework to artificial systems and propose that artificial intelligence emerges only within a bounded structural region defined by: - sufficient model capacity, - stable learning fixation, - persistent training dynamics. We introduce two complementary structures: (1) Structural Emergence Map (Fig. 10) A structural phase space showing that intelligence emerges only within a bounded region between insufficient capacity and excessive instability. (2) Training Dynamics (Fig. 11) A temporal model showing that intelligence emerges only during an intermediate training regime between early instability and late overfitting. These results lead to a central claim: Artificial intelligence is not designed directly; it emerges when structural conditions are satisfied. SEI v1. 3 therefore provides: - a minimal structural definition of intelligence, - a unified condition spanning natural and artificial systems, - a falsifiable prediction that intelligence does not scale linearly with model size, - a structural explanation of why overfitting and instability suppress intelligence emergence. The framework is explicitly falsifiable if: - intelligence scales linearly with model size alone, - structural balance does not affect emergence, - instability or overfitting does not suppress intelligence, - no bounded emergence regime is observed during training. This work proposes that intelligence is not arbitrary, but structurally constrained across all systems. A unified structural framework explaining intelligence across galaxies, planets, and artificial systems