W14 v2.0 — Civilization Dynamics & Control: Unified Control Theory, Game Theory, Bifurcation and MFLS Closure (Aligned with W20 v8.3 Three-Corpus Architecture)

This working paper presents Work 14 v2.0 of the Omega-u Civilizational Framework — a formal control-theoretic model of demographic-cultural civilizational dynamics, fully aligned with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis) and the complete W15–W20 triadic architecture series. The document operates on a 7-dimensional state vector X = [H, I, P, N_native, urban_frac, phi, K_host] capturing human capability index, infantilization dynamics, population sustainability, native cultural carrier fraction, urbanization, enclave formation, and cultural code strength. The core mathematical contributions — established in v1.0 — are fully preserved: Theorem 1 (intrinsic structural instability, λ_max = +0.32), Theorem 2 (controllability degeneracy without anti-infantilization and cultural channels), Theorem 3 (LQR stabilization, λ_max closed-loop = −0.012), Theorem 4 (Trap F as Nash equilibrium), Theorems 5–7 (saddle-node, transcritical, and pitchfork bifurcation structure), and Theorem 9 (Master Theorem: four necessary and sufficient conditions C1–C4 for stable civilizational growth). Monte-Carlo robustness (100 runs), MPC via L-BFGS-B with terminal Riccati cost, and real country cases (Japan, France, Sweden, Kazakhstan) are retained from v1.5. All 17 verification tests pass. Version 2.0 introduces four alignment layers: (i) control decomposition into u_agi ∈ ℝ³ (AGI-actuated: education, anti-infantilization, integration signal) and u_other ∈ ℝ⁵ (human/institutional: natalist policy, migration control, urban reform, native support, cultural renewal), with rank(G_agi) < rank([G_agi, G_other]) as the structural realization of Kodex Tier 0.3; (ii) W20 State Space Bridge (Layer 0b) mapping X → Z_partial with D_crit(W14) = H·(1−phi)·K, D_info(W14) = H·N_native·(1−phi), identifying W14 as the demographic-cultural substrate for W20's D_crit and D_info components; (iii) Kodex Priority Ordering Map (Layer 0c) connecting each theorem to specific Tier 0 violations — Trap F Nash equilibrium maps to Tier 0.4 (Anti-Concentration) and Tier 0.6 (Non-exploitation), cultural extinction (N_native < 0.35) maps to Tier 0.2 (Catastrophic Harm Prevention), uncontrolled collapse maps to Tier 0.1 (Dual Survival); (iv) SCF Basin Topology Map (Layer 0d) mapping all W14 phases to the three-basin SCF structure, and Triadic Control Architecture (Layer 16) with Alpha/Beta/Gamma roles specific to demographic dynamics — including 25-year lag projection protocol (T_gen = 25yr), country-specific triadic status, and Trap F coercive filtering detection hook for W20 skeleton. W14 is identified as the demographic-cultural substrate layer of the full W20 model, providing the H_human = kappa_d·H·P·N_native·(1−phi) chain that drives W12 AGI network novelty and W20 D_crit, D_info components. Kazakhstan is confirmed as the only country in Symbiotic_Stability basin with the M.1 intervention window open (2025–2035). Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.0 + симулятор v2.0 Рецензирование организации: Клод (Антропный)