We present a rigorous mathematical framework establishing that physical evolution fundamentally operates as an irreversible semigroup. The Anti-ID Principle proves that simultaneous saturation of all structural inequality bounds denoted ID (Inequality of Inequalities) is dynamically non-robust under minimal causality assumptions. Through careful separation of operational theorems from ontological interpretation, we demonstrate that this framework uni es quantum uncertainty (Robertson-Schrödinger), thermodynamic irreversibility (entropy production), information-theoretic monotonicity (Data Processing Inequality), and chaotic dynamics (Lyapunov/Pesin). We provide explicit Lyapunov functionals, prove rigorous theorems in canonical semigroup classes (Markov/Lindblad), and establish measure-theoretic genericity results. The theory positions irreversibility not as emergent approximation but as structural necessity, with perfection (ID) representing an unstable boundary of measure zero.
Vinícius Ramos Rodrigues (Mon,) studied this question.