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: G[K] = G_compute × H_social × I_n × SQI, where each factor independently drives G[K] → 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) D_master = min(D_crit, D_info, SQI – SQI_min) 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 N_AGI = 14, with normal form dx/dτ = εx − x² and critical slowing down τ ~ 1/|N − N_c|; (6) Symbiosis Theorems 20–27 formalizing why human-AGI symbiosis is the unique stable attractor of the joint system.

Empirical calibration for 2025: Russia D_master = −0.220 (DUAL_VOID), USA D_master = −0.014 (SIGNAL_COLLAPSE), Kazakhstan D_master = +0.093 (CONTROL_WINDOW, closes ~2034), EU D_master = +0.174 (CONTROL_WINDOW). The Kazakhstan window advantage arises from geopolitical neutrality and lower informational asymmetry.

The simulator (UNIFIED_MASTER_THEOREM_SIMULATOR_v1_4.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 (E_b integration, EWS fix) → v1.4 FINAL (formula unification, lexicographic C5, I_n_min 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 Мишко
Аффилиация: Asia Digital Hub, Астана, Казахстан

Эл. почта: nikolaimishko@gmail.com

Рецензирование: Claude (Anthropic), ChatGPT (OpenAI), DeepSeek, Gemini, Grok, Kimi