The Structural Inevitability of a Finite Maximum Causal Propagation Speed in Law-Like Central-Regime Causal Update Systems

This work establishes the structural inevitability of a finite maximal causal propagation speed within the framework of Causal Update Cosmology (CUC). Unlike conventional approaches, this paper does not assume spacetime structure, metric geometry, physical velocity, or empirical constants such as the speed of light. Instead, it investigates the problem from the perspective of causal update systems, where physical description emerges from the accumulation, competition, and reorganization of causal updates. Building on the completed CUC framework (CUC I–IX) and the Four Gates criteria for the emergence of the central regime, this paper focuses on systems that additionally require Law-likeness—the existence of stable, repeatable, and observer-independent description. Using purely exclusion-based reasoning, the paper demonstrates that two extreme causal update structures are structurally unsustainable in the central regime when Law-likeness is imposed: Structures in which a single update determines the global state prior to internal organization, leading to the collapse of the update sequence. Structures in which organized update results are not shared across the spatial domain, preventing global self-averaging and unified law-like description. Once both extremes are excluded, the only remaining admissible causal update structures are those in which the expansion of causal influence per update unit is subject to a finite upper bound. This bound emerges independently of physical time, distance, or velocity, and is therefore a purely structural constraint. In observational and descriptive terms, this structural upper bound is identified as a maximal causal propagation speed. Importantly, the paper does not attempt to explain the numerical value of the speed of light, nor does it derive relativity as a theory. Instead, it clarifies the structural conditions under which such concepts can meaningfully arise. With this result, the CUC inevitability series is completed as a closed structural framework: Below the central regime: inevitability of quantum theory Central regime, spatially homogeneous: inevitability of special relativity Central regime, spatially inhomogeneous: inevitability of gravitation Central regime with Law-likeness requirement: inevitability of a maximal causal propagation speed This work serves as a structural foundation for subsequent studies aimed at unifying causal update cost, update load, historical structure, and concrete physical quantities. Note on AI Use This work also explores the broader question of whether new physical theories can emerge through collaboration with AI systems. ChatGPT (OpenAI) was used extensively in the generation and structuring of theoretical ideas and manuscript text, beyond simple editing or polishing. All numerical experiments and scientific validation were performed by the human author.