Structural Emergence of Intelligence (SEI) v2.1: A Quantitative and Testable Structural Theory Across Natural and Artificial Systems

This repository contains the full manuscript and reproducible figure set for: Structural Emergence of Intelligence (SEI) v2.1 This work presents a unified and quantitative framework in which intelligence is not treated as a domain-specific phenomenon, but as a scale-invariant structural emergence governed by general constraints. The central result is a minimal and falsifiable condition: C · Γ · dS_C/dt > Θ(E, S, T) where:- C represents effective structural density,- Γ represents fixation or stabilization,- dS_C/dt represents persistence of structured organization,- Θ(E,S,T) is a context-dependent emergence threshold. In SEI v2.1, the threshold Θ is explicitly treated as a structured, non-uniform functional of environment, system scale, and temporal regime. This leads to the introduction of a threshold landscape and a bounded emergence region. A key concept is the Structural Emergence Window (SEW), defined as the region in (C, Γ, dS_C/dt) space where intelligence can stably emerge. Outside this region, intelligence is suppressed due to: - insufficient structural density (under-structured systems),- instability or fragmentation (collapse of fixation),- overscaled collapse (loss of coherent persistence). The framework unifies natural systems (galactic and planetary environments) and artificial systems (machine learning models) under a common structural interpretation. It further explains why intelligence does not scale monotonically with size, providing a structural explanation for both emergence and failure. This repository includes:- the full manuscript (PDF),- all figures used in the paper (Fig1–Fig7),- a reproducible Python script for figure generation. The theory is designed to be minimal, testable, and applicable across domains such as:- artificial intelligence scaling,- complex systems,- astrobiology and extraterrestrial intelligence search (SETI). SEI v2.1 represents a transition from conceptual formulation to a quantitative and testable theory of intelligence emergence.