ZUST (Zhou Unified Stability Theory): The World's First Unified Theory of Engineering-Cosmic Global Stability — Construction of a Quantitative System Based on Convex Optimization and Empirical Verification of Cosmological Puzzles

Abstract Based on Trait Locking Science (TLS) as the underlying foundation and Zhou's Discontinuous Stability Theory 1 as the direct theoretical source, this paper formally proposes a new basic theory that can realize the unified analysis of engineering dynamic systems and cosmic spacetime gravitational systems — Zhou Unified Stability Theory (ZUST). Taking convex optimization structure and Hessian matrix positive definiteness as the core mathematical tools, this theory extends the underlying logic of "core traits determine system stability" from Trait Locking Science from discontinuous engineering systems to the global cosmic gravitational system on a cross-scale basis through the analogy between the "bowl-small ball" model and the spacetime curvature picture in Einstein's General Relativity 2. Research shows that the self-stability, gravitational binding ability and multi-body interaction laws of all substances and structures in the universe that can produce spacetime curvature (gravitational depression) and have gravitational core traits can be included in the framework of this theory for unified analysis and quantitative determination. This paper elaborates on the origin, core logic, mathematical essence and three core functions of the theory, completes empirical verification through 3 typical cosmic celestial body cases, and applies the theory to solve 9 types of current cutting-edge unsolved cosmological puzzles, proving its universality, innovation and operability in engineering and cosmic scales. It provides a subversive unified analysis perspective and quantifiable mathematical tool for dynamic system stability theory and cosmological research. Update 1: This work stems from a sudden flash of inspiration (Beijing Time, 18:49, February 25, 2026) When developing Zhou's Discontinuous Stability Theory, I adopted the positive definiteness of the Hessian matrix and convex optimization in Theorem 4 to achieve the optimal balance between power consumption and stability in engineering applications. The intuitive model I conceptualized then was the bowl-ball model: the positive definiteness of the Hessian matrix denotes the existence of a bowl-shaped structure locally, ensuring the ball will eventually settle at the lowest point, yet it cannot guarantee a smooth inner wall of the bowl free of burrs that might obstruct the ball. Convex optimization, by contrast, ensures global convexity—an absence of pits or protrusions—rendering the bowl’s inner wall perfectly smooth. The combination of both enables the ball to roll unimpeded to the bottom of the bowl, namely achieving the aforementioned optimal balance between power consumption and stability. At this very moment, Einstein’s spacetime fabric depression model flashed across my mind: a celestial body is the ball, and the universe is the fabric. Theoretically, any substance or structure with gravitational core traits that can press a "dent" into the cosmic fabric behaves analogously to the bowl-ball model, exerting a similar depression effect on the surrounding cosmic fabric while maintaining its own stability. From this insight, I derived the first core function of Zhou Unified Stability Theory (ZUST): Self-Stability Determination. I then pondered further: would the cosmic fabric depressed by a celestial body exert a binding effect on surrounding celestial objects, and could any celestial body break free from such constraints? This led to the second core function: Gravitational Binding Capacity Determination. I continued to reflect: if a single massive celestial body can influence surrounding objects, what would happen when two or more comparable celestial bodies interact? Would they attract, counterbalance, or even devour one another? Hence came the third core function: Multi-Body Interaction Determination (attraction, counterbalance, and dominance relations)—and this constitutes the core of Zhou Unified Stability Theory (ZUST). The judgment logic is elegantly simple: by inheriting the essence of the bowl-ball model and maintaining the "smooth bowl" framework through the positive definiteness of the Hessian matrix and convex optimization, we can rapidly determine whether a target system achieves stability. This framework even allows us to infer the properties of invisible celestial bodies by analyzing their visible neighbors. This breakthrough may inspire new perspectives for exploring uncharted territories in cosmology, and I have applied this theory to solve 9 unsolved frontier puzzles in the field in this paper. I want to share this with all readers: the core of many complex theories originates from imagination, association, and visualization—just as I constructed this new theory by analogizing the bowl-ball model (rooted in Hessian matrix positive definiteness and convex optimization) to Einstein’s spacetime fabric depression model. I explain it in such accessible terms because I believe that true knowledge belongs to all humanity. This is also why I set this paper to writing the moment the inspiration struck: to me, it may merely be a discovery, but it could hold profound significance for the future of human exploration of the universe! P.S. For a collection of my other research papers, you may click the green circle next to the author’s name below the paper title to access my ORCID page, or refer to the paper summary in the metadata section of Zhou's Discontinuous Stability Theory (doi: 10.5281/zenodo.18760561). I will not elaborate further here, but I am confident that as you delve deeper into my work, you will become my loyal readers! Update 2: A More Accessible Extended Working Paper Released (Beijing Time 22:00, February 25, 2026) A working paper on solar research based on the Zhou Unified Stability Theory (ZUST) is now available|doi:10.5281/zenodo.18772300 My original intention was to lower the threshold for understanding ZUST. Instead of using abstract celestial objects, I chose the Sun—the most familiar star to everyone—as a case to verify the universality of ZUST in practice. Meanwhile, by comparing with traditional methods, I highlight its advantages in solar stability analysis, activity interpretation, and evolutionary early warning, laying a foundation for the popularization and cross-disciplinary application of ZUST. I believe that after reading this working paper, you will surely appreciate how my theory achieves both academic depth and public accessibility. After all, the core mission of top scholars is to translate profound knowledge into examples that the general public can understand. So I am sure you will enjoy this paper, won’t you?