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| Médium: | Recurso digital |
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Zenodo
2026
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| On-line přístup: | https://doi.org/10.5281/zenodo.18724352 |
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- <h2><strong>Addendum IV: Irreversibility, Legitimacy Erosion, and Collapse Dynamics</strong></h2> <p>This document presents Addendum IV in the VXPP structural series, formalizing irreversibility and legitimacy erosion in autonomous optimization systems.</p> <p>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.</p> <p>The core results establish:</p> <p>– Monotonic legitimacy decay under non-negative pressure <br>– A finite-time collapse condition when cumulative pressure exceeds initial legitimacy margin <br>– Structural conditions for absorbing failure states <br>– A formal definition of (T,p)-irreversibility <br>– A consistency bridge to Non-Action Stability (NAS) introduced in Addendum II </p> <p>The framework shows that optimization pressure alone is sufficient to drive structural collapse, independent of adversarial intent.</p> <p>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.</p>