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 dS_C/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