ARC Planetary Framework A Stability-Centered Architecture for Planetary Systems Management Based on Global Complexity Stability Theory (GCST) and Optimal System Dynamics (OSD)

The ARC Planetary Framework is a systems-level architecture for managing planetary-scale stability in an era of accelerating change. Grounded in Global Complexity Stability Theory (GCST) and Optimal System Dynamics (OSD), it models the Earth system as a network of interconnected stability fields Ψ(x,t) governed by the universal equation: ∂Ψ/∂t = D ΔΨ + F(x,t) + k α2/3 − γ Ψ where α denotes the rate of incoming load/change, and γ the recovery/stabilization capacity. ARC integrates six modules — Water, Waste & Materials, Ecology, Urban, Cognitive, and Resource Equilibrium — each designed to increase γ and constrain α within its domain. The framework introduces the Planetary Stability Index (PSI) as a global metric of accumulated instability: PSI = ∫_Ω Ψ(x,t) dV The long-term objective is to drive PSI toward its minimum, achieving a low-debt planetary civilization where recovery mechanisms are structurally embedded and positive stabilization cascades emerge across subsystems.