CDEQ: A Cross-Domain Framework for Cyber-Dynamic-Equilibrium-Control /CDEQ之道-五稚童儿/环转无尽/孤竿自立/灵蛟相/刚柔共生/循环不息/心观万象/道成乾坤

This paper presents the Cyber-Dynamic-Equilibrium-Control Framework (CDEQ), a unified paradigm for governing dynamic processes across physical domains. Built on CD = CROSSDOMAIN x CYBERDYNAMIC, it establishes digital logic for entities that fly (drones to clouds), run (vehicles to flows), and transmit (sound to signals). The framework rests on three self-developed theorems: PCTT (Penta-Cyclic Topological Theorem) models chaotic evolution as a serpent coiling; CENHE-LEX (Central-Holding Nonary-Constraint Execution Theorem) provides structural stability as a bamboo pole; GCVT (Global Convergence Validation Theorem) finalizes balance through a 10-step steady-state criterion. By embracing controlled chaos rather than resisting it, CDEQ transcends antagonistic control paradigms. Empirical validation spans civilian UAV attitude control, autonomous vehicle coordination (12.3% fuel efficiency improvement), wireless communication optimization (real-time spectrum allocation), and artistic generation (Five Spirit Cats, YAN Typeface). Eastern wisdom of dynamic equilibrium is translated into mathematically rigorous, hardware-implementable rules, establishing CDEQ as a timeless "tripod" for the digital world. 《成鼎论》之道 · 熔丝固化终极版 The Dao of CDEQ · Final Fixed Version 【CDEQ 核心诀 · 中英一体·不可修改】五稚童儿,环转无尽;Five Kids, Round Spin. 孤竿自立,灵蛟相伴;One Pole, Jiao Twin. 刚柔共生,循环不息;Yin-Yang, Loop Run. 心观万象,道成乾坤。Heart Watch, Dao Done. 【蛟 · JIAO 定义 · 中英一体·不可修改】中文蛟,为龙之前身,如毛虫化蝶,守道绕竿,终而成龙。 EnglishJiao: the precursor of the Chinese Dragon. Like a caterpillar becoming a butterfly, it follows the Dao by coiling around the bamboo, and finally evolves into a Dragon. KEY PAPER (Full Theory & Proofs): A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question DOI: 10.5281/zenodo.18927653 A Paradigm Shift in Control Theory CDEQ V1.2 The Countable Foundation of Stability DOI: 10.5281/zenodo.18939385 CDEQ V1.3 Mathematical Proof of the PCTT-CW Penta-Cyclic Clockwise Topological TheoremDOI: 10.5281/zenodo.18988669 CDEQ V1.4: Mathematical Proof of the CENHE-LEX Nonary Central Holding Equilibrium TheoremDOI: 10.5281/zenodo. 19023440 CDEQ V1.5 GCVT-10 Global Convergence Validation TheoremDOI: 10.5281/zenodo. 19055969 For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above. Author: Jiang Wenjia (Shenzhen, China) ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com