Institutional Degradation Trap: Formal Dynamical Model of Corruption Autocatalysis, Rule of Law Collapse, and Depravity Equilibrium — Work 17, Omega-u Civilizational Framework

We present a formal 7-dimensional dynamical systems model of Civilizational Trap #8 — Institutional Degradation — characterized by autocatalytic corruption growth (Cₐ) coupled with rule of law erosion (Rₗ) through a positive feedback loop of the second order. The model introduces the Benquo three-phase framework (guilt → shame → depravity) as a mathematically rigorous piecewise dynamical system with a transcritical bifurcation at the shame threshold (Iq = 0. 40) and a saddle-node collapse at the depravity threshold (Iq = 0. 20). The depravity phase formalizes Sartre's bad faith as a Nash equilibrium: when Iq Idep is lexicographically prior to all other AGI transition conditions. Kazakhstan is identified as being in the shame phase (Iq=0. 48, Cₐ=0. 45) with the intervention window open until approximately 2032. All results verified by INSTITUTIONALDEGRADATIONSIMULATORᵥ1₂. py (13/13 tests pass, including T2b controllability rank and R1b alphaca stress test). Part of Omega-u Civilizational Framework series, canonical DOI: 10. 5281/zenodo. 19112296. Николай МишкоАффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: nikolaimishko@gmail. com теория v1. 2 + симулятор v1. 2 Рецензирование организаций: Claude (Anthropic), ChatGPT (OpenAI), DeepSeek, Gemini (Google DeepMind), Кими (01. AI), Grok (xAI)