Unified Master Theorem: Civilizational Control, Symbiosis, and the Omega-u Synthesis — Formal Dynamical Model v1.4

This paper presents the Unified Master Theorem synthesizing the complete Omega-u Civilizational Framework (Works 9–19). We formally prove that civilizational AGI-growth potential Omega is governed by a multiplicative six-factor chain: GK = Gcompute × Hₛocial × Iₙ × SQI, where each factor independently drives GK → 0 — the Extended Compute Paradox. Key contributions: (1) Master Theorem Omega-u with seven conditions C1–C7 in lexicographic order (C5: observability is lexicographically prior — corrupted signal makes all other conditions undefined) ; (2) Dₘaster = min (Dcrit, Dᵢnfo, SQI – SQIₘin) as a unified L∞-type controllability metric; (3) Control Window Theorem v2. 0 with rigorous bang-bang proof via Lie derivatives and HJB; (4) Logistic information correction F (Δ) = (Δ + Δ₅₀) / (Δ + Δ₅₀ − Δ²) with five convergence theorems, replacing divergent linear formula; (5) Theorem 22-Strict: Digital Rut as transcritical bifurcation at NAGI = 14, with normal form dx/dτ = εx − x² and critical slowing down τ ~ 1/|N − Nc|; (6) Symbiosis Theorems 20–27 formalizing why human-AGI symbiosis is the unique stable attractor of the joint system. Empirical calibration for 2025: Russia Dₘaster = −0. 220 (DUALVOID), USA Dₘaster = −0. 014 (SIGNALCOLLAPSE), Kazakhstan Dₘaster = +0. 093 (CONTROLWINDOW, closes ~2034), EU Dₘaster = +0. 174 (CONTROLWINDOW). The Kazakhstan window advantage arises from geopolitical neutrality and lower informational asymmetry. The simulator (UNIFIEDMASTERTHEOREMSIMULATORᵥ1₄. py) passes 27/27 stress tests including logistic correction boundedness, transcritical bifurcation structure, EWS ordering, stochastic control window, Lyapunov ordering, and lexicographic condition evaluation. Version history: v1. 0 (synthesis) → v1. 1 (Control Window v2. 0, SDE) → v1. 2 (logistic correction, Digital Rut bifurcation) → v1. 3 (Eb integration, EWS fix) → v1. 4 FINAL (formula unification, lexicographic C5, Iₙₘin sigmoid). ## References (series DOIs) - https: //zenodo. org/records/19112296 (canonical SCF) - https: //zenodo. org/records/19479777 (Work 15) - https: //zenodo. org/records/19498232 (Work 16) - https: //zenodo. org/records/19553915 (Work 17) - https: //zenodo. org/records/19563314 (Work 18) - https: //zenodo. org/records/19570474 (Work 19) - https: //zenodo. org/records/19352775 (MFLS) Николай МишкоАффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: nikolaimishko@gmail. com Рецензирование: Claude (Anthropic), ChatGPT (OpenAI), DeepSeek, Gemini, Grok, Kimi