A Minimal Physics of Systemic Rupture: Control, Field Dynamics, and Multiplicative Loss Across Domains

Most systems do not fail when shocks occur. They fail when recoverability collapses faster than intervention can respond. This work introduces a minimal, cross-domain framework for understanding systemic failure—not as isolated events, but as trajectories governed by measurable structural decay, loss of control, and post-rupture amplification. Positioned at the convergence of critical transition theory and control theory, the paper advances beyond early-warning detection to address a central question: when does a system become uncontrollable—and what happens next? Core Thesis Systemic rupture is governed by three coupled quantities: - Recoverability Half-Life (τ₁/₂) — rate at which a system loses its ability to absorb perturbations - Control Ratio (Λ = IW / τ₁/₂) — whether intervention remains possible - Amplification Factor (μ) — whether losses dampen or compound after rupture Together they define a universal failure trajectory: τ₁/₂ ↓ ⇒ Λ ↓ ⇒ control collapses ⇒ μ > 1 ⇒ Lₜail ≫ Lᵣupture What This Paper Does This work does not attempt to predict events. It defines the conditions under which prediction no longer matters. Key Contributions 1. Controllability, Not Probability Systems are classified by whether they can still be steered: - Glacial (Λ ≫ 1): controllable - Brittle (Λ ≈ 1): unstable - Flash (Λ 1 amplification, making total loss dependent on persistence rather than the initial trigger. 4. Cross-Domain Invariance Analysis of SVB (2023), ERCOT (2021), and Enron (2001) reveals the same structure: collapse of controllability (Λ → 1), seam-localized rupture, and amplification-dominated tails. 5. Rupture Phase Space A two-dimensional mapping of invariant system dynamics (vertical) and institutional perspective (horizontal) shows how identical failures manifest differently across roles: - Reinsurer: loss stacking - Asset manager: portfolio contagion - Operator: loss of control - Regulator: systemic crisis Why This Matters Current systems detect risk too late, act without a control boundary, and underestimate tail consequences. This framework enables early detection of control collapse, cross-domain comparability, and measurement of intervention viability. Who This Is For Reinsurers, asset managers, sovereign funds, infrastructure operators, and policymakers managing systemic risk and regime transitions. Final Claim Systemic risk is not governed by shocks. It is governed by the rate at which recoverability disappears. When control is lost, the tail—not the event—determines the outcome.