The paper presents a mathematical model for a society based on pure anarchy without coercion, hierarchies, or governments.It argues that coercive political systems are destined to collapse, while pure anarchy can sustain long-term stability.Theorems in the paper discuss the inevitability of coercive collapse, resource inefficiency in centralized systems, and cascade fragility.The model is supported by historical validations and simulations and proposes decentralized governance models for resilient societies.