Z-Irreversibility: Under Finite Correction Constraint

Most complex systems measure output variables. Few measure remaining correction capacity. We formalize structural irreversibility within bounded dynamical systems using Lyapunov framing and functional analysis. A system evolving in a Banach space with finite correction rate admits a critical threshold beyond which restoration to equilibrium becomes asymptotically impossible. The result is independent of domain semantics and follows directly from bounded control constraints under cumulative deviation growth.
We then construct a diagnostic framework that operationalizes this theorem through measurable quantities: risk ratio R*, stability margin M, and uncertainty penalty U. The framework reveals that opacity directly accelerates irreversibility through structural mechanisms, not moral arguments.