Paper 0C — The Impossibility of Monolithic Recovery in Systems with Memory: A Zero Leap Theory (ZLT) Formal Result

We prove that in any non-collapsed system with memory where coherence (Φ) has degraded below its pre-degradation baseline (Φ₀), discharge of external intervention alone (V⁻₁) cannot restore Φ. Passive relaxation under V⁻₁ converges to a disordered local equilibrium Φ* < Φ₀; crossing the free-energy barrier to the ordered reference state requires directed reorganization (V⁻₂) that consumes free energy proportional to accumulated structural entropy. We prove that the recovery operations V⁻₁ and V⁻₂ do not commute: reorganization under protected conditions (V⁻₁ first) is strictly more effective than reorganization under active external load. We further establish that V⁻₁ is not a neutral operation: discharge itself can generate irreversible structural entropy when executed outside its admissible intensity-duration window, increasing the cost and reducing the ceiling of subsequent V⁻₂. Six corollaries including Reset Theater detection, minimum recovery cost, quenching risk, and a V⁻₂ taxonomy (endogenous/exogenous/mixed). Validated across 17 empirical domains with deterministic computational proof. Fourth impossibility (I-4) in ZLT's impossibility architecture: cessation of harm is necessary but not sufficient for recovery.