Control Laws for Hierarchical Kinetics: Design Principles and Intervention Strategies for Multi-Timescale Systems

Hierarchical systems with mismatched timescales fail in predictable ways. Paper 1 established the spectral stability condition ρ (M) < 1; Paper 2 derived the kinetic phase boundaries that produce metastability when temporal mismatch Δt exceeds critical thresholds. This paper completes the trilogy by answering: What can we actually do about it? We prove that only a specific class of interventions—those acting on temporal mismatch Δt, spectral radius ρ (M), or coupling topology G—can restore coherence once a system crosses phase boundaries. We call these Tier-1 moves. Interventions on derived quantities (coupling strength α, barrier shape Φ, hysteresis amplitude Aₕyst) cannot move systems between regions; we call these Tier-2 moves and prove them insufficient for coherence restoration. The central result is the Δt Management Criterion: A hierarchical system maintains persistent identity if and only if ρ (M) < 1, Δt < Δtc (α, G), and αΦ (Δt) ≫ 1. We derive piecewise control laws for each kinetic region, provide measurement algorithms for all primitives, demonstrate architecture-specific strategies across six canonical topologies, and illustrate application through worked examples spanning AI systems, institutions, markets, and platforms. The framework is falsifiable: we specify observable signatures for each region, predict intervention responses, and identify invariants that must hold across all domains. Violation of any prediction would refute the theory.