Law of Structural Precedence under Irreversibility

We present a structural result concerning guarantees in non-ideal dynamical systems subject to irreversibility. The work formalizes the distinction between architectural properties of a system, encoded in its transition relation, and adaptive policies operating over admissible trajectories. Using a robust predecessor operator, we show that if an irreversible failure state is structurally non-avoidable from the initial conditions, then no policy—regardless of adaptivity, intelligence, or reflexivity—can guarantee its avoidance with probability zero. The result establishes that guarantees against irreversible failure are properties of system architecture rather than control or optimization strategies. A dual principle is derived, showing that only structural invariants of the transition relation are guaranteeable, while all other properties are at best optimizable. The formulation explicitly excludes idealized assumptions such as perfect observability and exact control, and applies recursively to higher-order architectures capable of modifying their own transition structures. The law characterizes a fundamental limitation of policy-based approaches in real-world systems and has direct implications for engineering, safety-critical control, and persistent AI systems.