The Law of Autocatalytic Inevitability:\\ Network Self-Organization via Bifurcation and Stability Analysis

This article introduces the Law of Autocatalytic Inevitability (\( \mathbf{N}(\mathbf{I}) = \mathbf{k}^{\mathbf{\Lambda}} \mathbf{I} \)), a foundational framework for network self organization. Under specific architectural conditions, the law guarantees the deterministic emergence of decentralized, cooperation based social networks. Mathematical treatment of the empathic dynamics reveals bifurcation structures that mark the NAVPAKI threshold where the empathic economy structurally exceeds traditional systems and Lyapunov exponent evaluations confirm global stability throughout the growth process. Contrary to conventional probabilistic models, this result verifies that global cooperation is inevitable, not merely an ideal objective. Implemented through DSI Exodus 2.0, this model avoids trust dependency, structurally prevents exploitative interactions, and drives exponential network growth toward Economy 3.0—a post-monetary, reputation-based economy for solving global problems.