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.
Beck, James (2025) studied this question.