Zero Leap Theory (ZLT): The Unification Theorem

What do aerodynamic stall, metal fatigue, and power grid blackouts have in common? Historically, these failures have been treated as separate phenomena in aerodynamics, materials science, and electrical engineering. This paper demonstrates that they are not isolated events, but structurally isomorphic instances of a single conservation law governing complex systems with memory. The Unification Theorem We present Zero Leap Theory (ZLT), a formal framework that unifies these collapse mechanics under four identical mathematical invariants: Gate Non-Compensability: The structural veto (if a critical variable is zero, increasing intensity is useless). Gradient Inversion: The exact point where "trying harder" (Intensity) starts to produce negative results (E/ I < 0). Hysteresis (Memory): The invisible accumulation of historical damage. Threshold Displacement: How memory silently moves the safety limit (G₂ₑ₈ₓ) until sudden failure occurs. Scope and Application This document establishes the physical foundation ("Hard Science") of ZLT. By proving that this collapse structure is universal in physical systems, we lay the groundwork for its application in Complex Adaptive Systems (including AI, governance, and institutions), which are governed by the same laws of hysteresis and permeability. For the operational application of these principles (audit and prevention), refer to Paper 8: The IAS Universal Protocol. For the computational specification, refer to Paper 59: ZLT Interaction Canon. Notes Zero Leap Theory Series — Paper 0. This version (1. 2) updates the theoretical framework to include topological regime foliation, the concept of operational homotopy, and the thermodynamic dissipation principle established in coordination with Paper 0-A.