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 (F_c). 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 (P_extinction = P_conflict × omega_nuc).

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 D_H > theta_heg and GDP_C/GDP_H > theta_cha, rational strategy converges to military escalation. In the nuclear era, P_extinction ≈ 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 > D_crit AND Lev > Lev_crit, 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 AGI_entry=True in 2025 (I=-0.015, D=0.28, P_extinction=0.010), with intervention window open until approximately 2035. All results verified by FINANCIAL_INSTABILITY_SIMULATOR_v1_3.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 Мишко
Аффилиация: 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)