A Triple-Coordinate Framework for Social Dynamics: BRI, SSI, and GPI Derived from Chaos Theory, Attractor Dynamics, and Fractal Self-Similarity

Abstract

This paper proposes a novel triple-coordinate framework for analyzing social instability and development trajectories: the Bimodal Risk Index (BRI v7), the Social Structure Index (SSI), and the Growth Potential Index (GPI). Drawing on chaos theory, attractor dynamics, and fractal self-similarity, we translate mechanical vibration equations into social science metrics capable of measuring a society's instability, structural resilience, and directional velocity simultaneously. BRI v7 operationalizes social pressure through twelve normalized variables organized into three sub-components analogous to mechanical resonance: Pressure, Amplitude, and Frequency. SSI captures attractor strength through damping capacity, resilience, and fractal self-similarity. GPI = 0.5(-ΔBRI/100) + 0.5(ΔSSI/100) functions as a social velocity vector; its cumulative integral serves as an objective leadership performance index. Time-series validation using Sri Lanka (2017-2022) confirms a two-stage lead pattern with approximately two years advance warning. Cross-country analysis of IMF intervention reveals a structural paradox: austerity prescriptions simultaneously elevate BRI while depressing SSI. The framework is offered as a philosophical coordinate system for generating better analytical questions rather than deterministic predictions.

Keywords: O10, C43, E60 Social Instability, BRI, SSI, GPI, Chaos Theory, Attractor Dynamics, Fractal Self-Similarity, Uprising Prediction, Lead Indicator, IMF Paradox, D74

JEL Classification: D74, O10, C43, E60