Addendum IV: Irreversibility, Legitimacy Erosion, and Collapse Dynamics

Addendum IV: Irreversibility, Legitimacy Erosion, and Collapse Dynamics This document presents Addendum IV in the VXPP structural series, formalizing irreversibility and legitimacy erosion in autonomous optimization systems. We model the system as a discrete-time Markov Decision Process (MDP) and introduce a scalar legitimacy function L(s) defined over invariant evaluations. Under sustained non-negative optimization pressure P(t), legitimacy evolves monotonically via a cumulative erosion dynamic. The core results establish: – Monotonic legitimacy decay under non-negative pressure – A finite-time collapse condition when cumulative pressure exceeds initial legitimacy margin – Structural conditions for absorbing failure states – A formal definition of (T,p)-irreversibility – A consistency bridge to Non-Action Stability (NAS) introduced in Addendum II The framework shows that optimization pressure alone is sufficient to drive structural collapse, independent of adversarial intent. This addendum extends the formal foundations established in Addenda I–III and provides the mathematical basis for modeling collapse as a structural phenomenon in autonomous systems.