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, updated for structural alignment with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). 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 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. Version 2.0 introduces four alignment layers required for integration with the W20 v8.3 control architecture: (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 (Human Agency in Existential Decisions); (ii) a formal state bridge M: X → Z_partial mapping W14 demographic variables to W20's 11D civilizational state components D_crit, D_info, O_eff, Φ, and Ω_partial; (iii) a Kodex Priority Ordering mapping connecting each major theorem to specific Tier 0 principle violations — Trap F Nash equilibrium maps to Tier 0.4 (Anti-Concentration) and Tier 0.6 (Non-exploitation), cultural extinction maps to Tier 0.2 (Catastrophic Harm Prevention), and uncontrolled collapse maps to Tier 0.1 (Dual Survival); (iv) SCF basin topology alignment mapping all W14 phase classifications to the three-basin structure of the Symbiotic Codes Framework (Symbiotic Stability / Structural Capture / Total Collapse) with Open-Ended Co-Evolution as the goal-path endpoint. A novelty metric N_novelty is added as the W14 demographic analog of W20's MFLS novelty proxy. All 17 verification tests pass (14/14 from v1.0 extended to 17/17 with new W20-alignment tests T13–T17). The paper positions W14 as the demographic-cultural substrate layer of the full W20 civilizational control architecture: W14 drives the D_crit, D_info, O_eff, and Φ components of W20's 11D state vector Z, while W14's Lyapunov matrix P constitutes the demographic component of W20's full Directional Lyapunov Function. Country analysis confirms Kazakhstan as the only case currently in Symbiotic Stability basin with all four Master Theorem conditions met and the intervention window (2025–2035) still open. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.0 + симулятор v2.0 Рецензирование организаций: Клод (Anthropic)