Structural Emergence of Intelligence (SEI) v1.3.1: A Unified Structural Framework for Intelligence Across Galaxies, Planets, and Artificial Systems

We present SEI v1. 3. 1 (Structural Emergence of Intelligence), a minimal and falsifiable framework that unifies the emergence of intelligence across natural and 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 A minimal emergence condition is expressed as: C · Γ · (dSC/dt) > Θ Previous versions of SEI established: - galactic spatial constraints (v1. 0), - temporal evolution (v1. 1), - planetary structural conditions (v1. 2). SEI v1. 3. 1 extends this framework to artificial systems and proposes that artificial intelligence emerges only within a bounded structural and temporal regime defined by: - sufficient model capacity, - stable learning fixation, - persistent training dynamics. We introduce two complementary structures: (1) AI Structural Emergence Map (Fig. 10) A phase-space representation showing that intelligence emerges only between insufficient capacity and excessive instability. (2) Training Dynamics (Fig. 11) A temporal model demonstrating that intelligence emerges only during an intermediate training phase between early instability and late overfitting. These results lead to the central claim: Artificial intelligence is not designed directly; it emerges when structural conditions are satisfied. SEI v1. 3. 1 provides: - a minimal structural definition of intelligence, - a unified emergence condition across galaxies, planets, and AI, - a falsifiable prediction that intelligence does not scale linearly with model size, - a structural explanation of overfitting and instability as suppression mechanisms. The framework is explicitly falsifiable if: - intelligence scales purely with model size, - structural balance does not affect emergence, - instability or overfitting does not suppress intelligence, - no bounded emergence regime is observed. This work proposes that intelligence is not arbitrary, but structurally constrained across all systems. A unified structural explanation of intelligence across the universe, Earth, and AI.