CivOS Safety Kernel: Bounded Stability and Dynamic Risk Mitigation via Commutative Safety Protocols

Modern complex socio-technological and civilizational systems face cascading systemic risks (WR1–WR5), ranging from resource blockades and economic suffocation to infrastructure collapses. Traditional post-hoc governance mechanisms fail to mitigate such adversarial dynamics due to execution-order dependency and cumulative governance latency penalties. This work introduces the CivOS Safety Kernel, a category-theoretic and dynamically adaptive governance architecture that enforces structural safety and bounded stability across multi-layered civilizational systems. By integrating commutative safety protocols with a threshold-triggered re-normalization mechanism, the kernel guarantees invariance of state transitions under adversarial shock permutations when safety strength αₜ = 1.0. Dynamic stress-testing across Constant, Burst, and Ramp attack patterns demonstrates that unprotected systems exhibit unbounded cumulative drift (Δ₍cum₎ → ∞), whereas the CivOS Safety Kernel transforms divergence into strictly bounded sawtooth stability. Furthermore, by rendering attacker payoff strictly negative (Uₐₜₜₐcₖₑᵣ < 0), the kernel establishes a Subgame Perfect Equilibrium where non-attack becomes the unique dominant strategy. This preprint provides the mathematical and operational foundation for civilizational-scale structural deterrence and resilient AI-native OS architecture.