CDEQ V1.0: The Answer to Lyapunov's Century-Old Question on Chaotic System Stability CDEQ三大定理,回应李雅普诺夫百年之问

THE DAO OF CDEQ《成鼎论之道》 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. Jiao: Chinese: 蛟,为龙之前身,如毛虫化蝶,守道绕竿,终而成龙。 English: Jiao: 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. --- ABSTRACT In 1892, Lyapunov asked: What is stability? He answered with a theorem [1]. But he left unanswered: How to implement it? For 134 years, this gap was unbridgeable. This paper establishes CDEQ: the complete framework for implementing Lyapunov stability in deterministic hardware. The framework is rooted in the eternal Dao of CDEQ and delivered as 32 lines of synthesizable Verilog. Central to this framework is GCVT — which defines the condition of TAI (泰): a state of dynamic harmony achieved when opposing forces reach perfect balance. Hardware validation on an FPGA platform confirms 100% convergence within the theoretical 80-cycle bound. The core PCTT‑W chaos coefficient in this paper was originally derived from a basic parameter designed by the author to regulate the randomness and coherence of the generation process during the development of the standalone offline AI painting software AI-Sage CDEQ Chaotic Blender. In long-term practice, this coefficient has demonstrated strong universality and can stably support artistic creation tasks such as AI painting, music composition, and 3D animation generation. Until recently, the author has clarified that this parameter originating from artistic creation is highly isomorphic to quantum superposition states in mathematical structure and dynamic behavior, and can provide a new engineering approach to Lyapunov's century-old question on the stability of chaotic systems. Based on this discovery, the author proposes the CDEQ unified framework and extends its application to key engineering fields including Bipedal Robot Stability Control, Biopharmaceutical Stability Control, New Energy Vehicle Stability Control, and AI Big Data Stream Stability Control, forming the theoretical and application system presented in this paper. 本文核心的PCTT‑W 混沌系数,最初源自作者研发单机离线AI作画软件《AI画圣混沌搅拌机(AI-Sage CDEQ Chaotic Blender)》时,为调控生成过程的随机性与连贯性所设计的基础参数。在长期实践中,该系数展现出极强的普适性,可稳定支撑 AI 绘画、音乐创作与 3D 动画生成等艺术创作任务。直至近期作者才明确:这一起源于艺术创作的参数,在数学结构与动态行为上与量子叠加态高度同构,并可为李雅普诺夫关于混沌系统稳定性的百年问题提供全新的工程化思路。基于这一发现,作者提出 CDEQ 统一框架,并将其拓展应用于两足机器人稳定控制、生物制药稳定控制、新能源汽车稳定控制、AI大数据流稳定控制等关键工程领域,形成了本文的理论与应用体系。 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 A Paradigm Shift in Control TheoryCDEQ V1.2 The Countable Foundation of StabilityDOI: 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