W15 v2.2 — Social Instability Trap: Elite Extraction, Middle Class Erosion, and Civilizational Legitimacy Collapse — Formal Dynamical Model with W20 v8.3 Alignment, Kodex Priority Ordering, and SCF Basin Topology

This working paper presents Work 15 v2. 2 of the Omega-u Civilizational Framework — a formal dynamical model of the Social Instability Trap, updated for full structural alignment with W20 v8. 3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). W15 is the closing work in the W15–W19 alignment series, completing the full structural integration of all five trap layers with the W20 master architecture. The document models the civilizational social layer as a 7-dimensional state vector X = Gₛ, M, Ec, Lₛ, Cₕ, u, Iq, capturing the Gini coefficient, middle class fraction, elite capture index, legitimacy, cognitive capital, uncertainty, and institutional quality. The core mathematical framework — established in v2. 1 — is fully preserved: dual autocatalytic instability (Gₛ and Ec self-reinforcing feedbacks, empirically calibrated from Piketty-Saez and Gilens-Page data), the elite extraction Nash equilibrium (Trap #3 as game-theoretic result: Ec* = max when uₐntitrust = 0), five-level Early Warning System, AGI feedback sigmoid, path-dependent inequality and capture memory (MGini, Mcap), Hₛocial = kappad·Cₕ·M·Lₛ· (1−Ec) as the direct social input to W20's Nₙovelty formula, and triadic control architecture with Alpha/Beta/Gamma roles (Layer 16). All 20 verification tests pass. Version 2. 2 introduces three alignment layers absent in v2. 1: (i) W20 State Space Bridge (Layer 0b) establishing the formal mapping ΦW20 (W15) = Ec + (1−Iq) ·max (0, Ec−0. 30) → W20 Φ component, identifying W15 as the primary driver of W20's trapped institutional fraction; Hₛocial (W15) as the direct social layer input to W20's Nₙovelty computation (T15 confirmed: Hₛocial ratio 6x between low and high capture states) ; and path-dependent memory trap formalised (Dcritₑxt (MGini=0. 72) = −0. 070, T16 confirmed) ; (ii) Kodex Priority Ordering Map (Layer 0c) connecting each failure mode to specific Tier 0 violations — Cₕ+Lₛ simultaneous collapse maps to Tier 0. 1 (Dual Survival) as AGI novelty death, civil war maps to Tier 0. 2 (Catastrophic Harm Prevention), oligarchy phase maps to Tier 0. 4 (Anti-Concentration) as Nash equilibrium result, with uₑdu and uₐgiₐudit identified as the two AGI-native levers; (iii) SCF Basin Topology Map (Layer 0d) classifying eight W15 phases into the three-basin SCF structure, including the PATHTRAP variant of Structural Capture via MGini memory (W15 analog of W17 institutional memory trap), and formally documenting the fifth and final parallel AGIFROZEN path: Cₕ collapse → Hₛocial → 0 → GK → 0 (social channel). Country analysis confirms EU in Symbiotic Stability, Kazakhstan in degrading trajectory (Ec = 0. 48, approaching warning zone), USA in Structural Capture (DEMOCRATICEROSION), Russia in Structural Capture (CLASSFRACTURE trending toward oligarchy). W15 v2. 2 marks the completion of the full W15–W20 alignment series. All five independent AGIFROZEN paths are now formally documented across the series: W15 (social: Cₕ collapse), W16 (financial: Mwar→Φ→Hₛocial), W17 (institutional: Iq→Dcrit→Hₛocial), W18 (technological: Iₙ→φₙovelty→GK), W19 (informational: Signal→Nₙovelty→GK). Together these establish that AGI knowledge growth is simultaneously contingent on social cohesion, financial stability, institutional quality, technological novelty, and information integrity — no single pathway can substitute for the others. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: nikolaimishko@gmail. com теория v2. 2 + симулятор v2. 2 Рецензирование организаций: Клод (Anthropic)