ARC Planetary Framework A Stability-Centered Architecture for Planetary Systems Management Based on Global Complexity Stability Theory (GCST)

Abstract The ARC Planetary Framework is a systems-level architecture for managing planetary-scale stability in an era of accelerating change. Drawing on the Global Complexity Stability Theory (GCST), it models the planet as an interconnected set of stability fields Ψ (x, t) whose dynamics are governed by: ∂Ψ/∂t = D ΔΨ + F (x, t) + k α^2/3 − γ Ψ where α represents the rate of incoming stress/load, and γ the recovery/stabilization capacity of each subsystem. ARC consists of six integrated modules — Water, Waste & Materials, Ecology, Urban, Cognitive, and Resource Equilibrium — each engineered to increase γ and constrain α in its domain. The framework introduces the Planetary Stability Index (PSI) as an aggregate measure of system-wide instability: PSI = ∫_Ω Ψ (x, t) dV The objective is to minimize PSI through coordinated interventions that create positive feedback loops of stabilization across subsystems. Rather than solving isolated crises, ARC seeks to design a low-debt planetary civilization where recovery mechanisms are embedded in every process.