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, Nₙative, urbanfrac, phi, Kₕost 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, λₘax = +0. 32), Theorem 2 (controllability degeneracy without anti-infantilization and cultural channels), Theorem 3 (LQR stabilization, λₘax 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 uₐgi ∈ ℝ³ (AGI-actuated: education, anti-infantilization, integration signal) and uₒther ∈ ℝ⁵ (human/institutional: natalist policy, migration control, urban reform, native support, cultural renewal), with rank (Gₐgi) < rank (Gₐgi, Gₒther) as the structural realization of Kodex Tier 0. 3; (ii) W20 State Space Bridge (Layer 0b) mapping X → Zₚartial with Dcrit (W14) = H· (1−phi) ·K, Dᵢnfo (W14) = H·Nₙative· (1−phi), identifying W14 as the demographic-cultural substrate for W20's Dcrit and Dᵢnfo 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 (Nₙative < 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 (Tgen = 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 Hₕuman = kappad·H·P·Nₙative· (1−phi) chain that drives W12 AGI network novelty and W20 Dcrit, Dᵢnfo components. Kazakhstan is confirmed as the only country in SymbioticStability basin with the M. 1 intervention window open (2025–2035). Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: nikolaimishko@gmail. com теория v2. 0 + симулятор v2. 0 Рецензирование организации: Клод (Антропный)
Nikolai Mishko (Wed,) studied this question.