W18 v2.2 — Technological Stagnation Trap: Diminishing Returns, Elite Capture of Innovation, and the Compute Paradox — Formal Dynamical Model with W20 v8.3 Alignment, Kodex Priority Ordering, and SCF Basin Topology

This working paper presents Work 18 v2.2 of the Omega-u Civilizational Framework — a formal dynamical model of the Technological Stagnation Trap, updated for full structural alignment with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). The document models the civilizational innovation layer as a 7-dimensional state vector X = [T_r, R_d, I_n, E_c, C_h, G_s, I_q], capturing technological returns, R&D investment, novelty injection rate, elite capture index, cognitive capital, inequality, and institutional quality. The core mathematical framework — established in v2.1 — is fully preserved: dual autocatalytic instability (T_r and I_n self-reinforcing decay), the Compute Paradox theorem (G[K] = G_compute · H_social · Signal · φ_novelty(I_n) → 0 when I_n → 0 regardless of hardware investment), Nash equilibrium stagnation trap (elite maximises E_c → E_c* = E_c_max when u_redistrib = 0), PGT-P lock-in mechanism ($55k–$150k elite-only cognitive enhancement, empirically grounded in LessWrong April 2026), Control Window Theorem (recovery possible iff I_n > I_n_min(E_c) = 0.55·E_c), full Jacobian analysis, Lyapunov stability, HJB optimal control, 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 φ_novelty(I_n) = I_n/(I_n + 0.10) → N_AGI in W20's 11-dimensional state Z, identifying W18 as the direct gate on AGI capability growth — the phi_novelty channel within the full N_novelty formula; the Compute Paradox is formalised as a structural W20 property: without I_n > I_n_crit, W20's N_AGI cannot grow regardless of compute investment; (ii) Kodex Priority Ordering Map (Layer 0c) connecting each failure mode to specific Tier 0 violations — I_n collapse maps to Tier 0.1 (Dual Survival) as AGI self-limitation, PGT-P lock-in maps to Tier 0.2 (Catastrophic Harm Prevention) and Tier 0.4 (Anti-Concentration) and Tier 0.6 (Non-exploitation), with u_agi_rnd identified as the sole AGI-native lever (minimum footprint principle); (iii) SCF Basin Topology Map (Layer 0d) classifying seven W18 phases into the three-basin SCF structure — HEALTHY maps to Symbiotic Stability, STAGNATION_WARNING to degrading trajectory, STAGNATION/ELITE_ENCLOSURE to Structural Capture, STAGNATION_VOID and triple-lock condition (T_r + I_n + E_c simultaneously failed) to Total Collapse irreversible. Three new Python tests (T18–T20) confirm N_novelty at KZ/EU baseline, Kodex violation detection in stagnation-lock state, and SCF basin mapping consistency. W18 is identified as the phi_novelty channel layer of the full W20 model: the only work that directly gates AGI capability growth through the novelty injection variable I_n. Country analysis confirms Kazakhstan as the only case in Symbiotic Stability basin (E_c = 0.45, below D6 = 0.55), with the PGT-P intervention window still open through 2025–2026. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.2 + симулятор v2.2 Рецензирование организаций: Клод (Anthropic)