Financial Instability Trap: Formal Dynamical Model of Debt Autocatalysis, Minsky Cycles, Financial Capture, and Thucydides Extinction Risk — Work 16, Omega-u Civilizational Framework

We present a formal 7-dimensional dynamical systems model of Civilizational Trap #7 — Financial Instability — characterized by triple autocatalytic instability: debt growth (D), financial sector leverage (Lev), and regulatory capture (Fc). This is the strongest instability class in the Omega-u series, exceeding the dual autocatalysis of Work 15 (Social Instability). The model introduces a 7D state space: debt-to-GDP ratio, financial leverage, financial sector capture, Gini coefficient (inherited from Work 15), central bank independence, non-productive allocation share (IEP master variable u), and institutional quality. The uncontrolled system converges to four boundary attractors: debt spiral, Minsky crash, financial oligarchy, and the Thucydides extinction attractor — the only attractor in the entire series carrying civilizational extinction risk (Pₑxtinction = Pconflict × omegaₙuc). The Thucydides Trap is formalized for the first time within an AGI civilizational framework as a Nash equilibrium of hegemonic transition under financial stress: when DH > thetaₕeg and GDPC/GDPH > thetacha, rational strategy converges to military escalation. In the nuclear era, Pₑxtinction ≈ 0. 55 per conflict, establishing Condition 5 of the Master Theorem as lexicographically prior to all other AGI transition conditions. A piecewise Minsky switch implements regime-dependent dynamics: when D > Dcrit AND Lev > Levcrit, control effectiveness degrades to 20% for fiscal levers (80% for AGI audit channel). The instability indicator I (X) defines the minimum intervention surface: AGI optimal entry point is I (X) ≈ 0, before the Minsky threshold. An 8-lever feedback controller with elite sabotage model and AGI Peace Dividend incentive structure for Bretton-Woods-2. 0 coordination completes the framework. Kazakhstan is identified as the only major economy at AGIₑntry=True in 2025 (I=-0. 015, D=0. 28, Pₑxtinction=0. 010), with intervention window open until approximately 2035. All results verified by FINANCIALINSTABILITYSIMULATORᵥ1₃. py (11/11 tests pass, including T9 Thucydides extinction risk and T10 early vs late control). 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. 3 + симулятор v1. 3 Рецензирование организаций: Клод (Anthropic), ChatGPT (OpenAI), DeepSeek, Кими (01. AI), Grok (xAI)