Structural Emergence of Intelligence: A Minimal, Falsifiable Framework for Bounded-Optimum Scaling

This work presents a minimal and directly testable extension of the Structural Emergence of Intelligence (SEI) framework. The central claim is that intelligence does not scale monotonically with system size or raw capacity, but instead emerges only within a bounded structural regime. Systems that are under-structured or over-scaled fail to sustain stable intelligence-like behavior. We formalize this hypothesis using a minimal structural inequality: C⋅Γ⋅dSCdt>Θ (E, S, T) C dSCdt > (E, S, T) C⋅Γ⋅dtdSC>Θ (E, S, T) where structural density, stabilization, and persistence must collectively exceed a context-dependent emergence threshold. To connect theory with empirical evaluation, we introduce an effective ratio: R (E) =C⋅Γ⋅dSC/dtΘ (E) R (E) = C dSC/dt (E) R (E) =Θ (E) C⋅Γ⋅dSC/dt which enables direct model comparison and falsification. The framework makes a clear, testable prediction: intelligence exhibits a non-monotonic, bounded-optimum scaling behavior rather than continuous monotonic growth. We further provide a minimal empirical decision pathway based on model error comparison, allowing the SEI hypothesis to be supported or weakened using observed data. This work is explicitly falsifiable: If intelligence scales strictly monotonically, the framework is weakened If monotonic models outperform bounded models, the framework is challenged All figures are reproducible and included with corresponding Python scripts.