The Zero Leap Theory (ZLT): An Impossibility Theorem for Intensity-Based Intervention in Complex Systems with Memory

This paper postulates the Principle of Conservation of Complex Structures with Memory, a fundamental proposition stating that systems with history actively dissipate intervention energy as structural friction to preserve their topological identity. Against this backdrop, we introduce the Zero Leap Theory (ZLT), a formal framework for executing effective interventions without triggering catastrophic conservation responses. We demonstrate, through a Representation and Impossibility Theorem, that any linear intervention model ignoring this conservation principle—specifically variables of memory (hysteresis), stability, and permeability—is mathematically incomplete and structurally dangerous. Among the axioms, A2 (Non-Compensability) functions as the dominant constraint: no increase in intensity (I) can compensate for vanishing alignment (Φ) or permeability (C). The Ibuprofen Trap. We demonstrate the theory's predictive power through 9 canonical experiments spanning policy (Prohibition, 1920), technology (Windows ME, 2000), and medicine (NSAID fever suppression). The medical case exemplifies dual-channel harm: ibuprofen provides measurable symptom relief (fever reduction) while simultaneously masking infection progression and elevating cardiovascular risk—a pattern mirroring structural failures from Prohibition to digital product launches. The theory's core prediction (A2: Non-Compensability) is validated through Monte Carlo Ordinal Safety Witness (simulateᵦlt. py, n=1, 000 trials, seed=42, Supplement F) —a minimal computational construction demonstrating that under low alignment, escalating intervention intensity concentrates probability mass on collapse outcomes. The witness confirms 98. 4% collapse dominance in low-alignment regimes despite moderate intervention intensity, establishing regime dominance rather than point forecasts. A formal proof of Critical Dominance establishes strict epistemic shielding against tautology. Scientific Position. ZLT is presented as a structural decision framework grounded in systems physics, yielding ordinal and prohibitive predictions verified by falsifiability constraints. The framework predicts intervention regimes (go/no-go classifications), risk orderings (alignment-intensity phase space), and critical dominance conditions—not universal point forecasts of specific outcomes. This ordinal scope ensures predictive rigor while acknowledging irreducible complexity in real-world systems. Importantly, our impossibility result is conditional: it applies to intensity-only intervention models within the domain of systems exhibiting structural memory (hysteresis), where intervention energy is dissipated as preservation friction. The claim is therefore structural and domain-bounded, not a universal forecasting statement about all systems.