The Structural Inevitability of Gravitation in Spatially Inhomogeneous Central-Regime Causal Update Systems

Description This paper establishes the structural inevitability of gravitation within the completed framework of Causal Update Cosmology (CUC). Building on prior results demonstrating the inevitability of quantum theory below the central regime and special relativity under spatially uniform central-regime establishment, this work addresses the remaining case: central-regime causal update systems with spatially inhomogeneous establishment. The analysis proceeds entirely through structural elimination, without introducing new physical assumptions. No forces, masses, interactions, field equations, or numerical simulations are employed. Instead, the argument relies solely on the internal causal-update structure of CUC. It is shown that spatial inhomogeneity in the degree of central-regime establishment necessarily generates inhomogeneous causal congestion, which in turn induces reachability gradients. Under these conditions, motion remains locally inertial but becomes globally biased, giving rise to geodesic-like behavior. The paper demonstrates that all force-based and coordinate-based descriptions are structurally excluded under these constraints. As a result, a geometric description in terms of curved spacetime emerges as the only stable and coherent framework capable of accommodating local inertial behavior together with global nonlinearity. General relativity is thus not derived, nor assumed. Rather, it is shown to be the sole surviving descriptive structure once all incompatible alternatives are eliminated. This work completes the third step of the inevitability program within CUC, establishing that: quantum theory is inevitable below the central regime, special relativity is inevitable when the central regime is spatially uniform, and gravitation (general-relativistic description) is inevitable when spatial inhomogeneity arises after central-regime establishment. The results position gravitation not as a fundamental force or interaction, but as the geometric expression of spatial gradients in causal-update structure.The paper concludes by identifying the remaining open question: the origin of a maximal causal propagation speed and its relation to information-processing limits, to be addressed in subsequent work. 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.