W16 v2.2 — Financial Instability Trap: Debt Autocatalysis, Leverage Cycles, Thucydides Trap as Nash Equilibrium, and Civilizational Extinction Risk — Formal Dynamical Model with W20 v8.3 Alignment, Kodex Priority Ordering, and SCF Basin Topology

This working paper presents Work 16 v2.2 of the Omega-u Civilizational Framework — a formal dynamical model of the Financial Instability Trap, updated for full structural alignment with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). The document models the civilizational financial layer as a 7-dimensional state vector X = [D, Lev, F_c, G_s, C_b, u, I_q], capturing sovereign debt ratio, leverage, financial capture index, inequality, central bank independence, uncertainty, and institutional quality. The core mathematical framework — established in v2.1 — is fully preserved: triple autocatalytic instability (debt, leverage, and financial capture self-reinforcing feedbacks), the Thucydides Trap formalised as a Nash equilibrium under financial stress (first formal integration with AGI civilizational framework), piecewise Minsky switch dynamics (runaway feedback above leverage threshold D5=25), P_extinction as lexicographic barrier (P_extinction > 0.10 overrides all other stability conditions), path-dependent war and bubble memory (M_war and B_bubble dynamics, T15–T16 confirmed), and triadic control architecture with Alpha/Beta/Gamma roles (Layer 16). All 19 verification tests pass. Version 2.2 introduces three alignment layers absent in v2.1: (i) W20 State Space Bridge (Layer 0b) establishing the formal mappings R_fisc = (1−D/D_safe)·C_b·(1−F_c) → W20 Z[6], M_war(W16) = P_conflict(X) → W20 Z[9], and B_bubble(W16) = normalised excess leverage → W20 Z[10], with explicit formalisation of the lexicographic property: P_extinction > 0.10 overrides ALL other W20 Z components simultaneously, making W16 the only work in the Ω-u series with a civilizational-scale lexicographic collapse condition; (ii) Kodex Priority Ordering Map (Layer 0c) identifying P_extinction as the unique Tier 0.1 violation that is lexicographically prior to all other series violations, Thucydides Nash equilibrium as Tier 0.2 (catastrophic harm), financial oligarchy as Tier 0.4 (anti-concentration), with u_agi_audit and u_cb_independence as the two AGI-native levers; (iii) SCF Basin Topology Map (Layer 0d) classifying eight W16 phases into the three-basin SCF structure, with EXTINCTION_RISK uniquely mapped to Total_Collapse_lexicographic — the only phase in the entire series where basin exit overrides all parallel stability computations. A fourth parallel AGI_FROZEN path is documented (financial channel: M_war → Phi → H_social → 0), joining the W17 institutional, W18 compute paradox, and W19 signal starvation paths previously identified. Country analysis confirms Kazakhstan as the only case in Symbiotic Stability basin (D = 0.28, P_extinction ≈ 0.02), while the USA model places in EXTINCTION_RISK territory at current parameter calibration (D = 1.22, F_c = 0.55), demonstrating the urgency of fiscal stabilisation before AGI deployment. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.2 + симулятор v2.2 Рецензирование организаций: Клод (Anthropic)