Reinterpreting Motion from Structure: A Connection-Based Formulation of Structural Differentiation Gravity (SDG v1.7)

This work presents a connection-based formulation of Structural Differentiation Gravity (SDG), in which motion, curvature, and propagation are reinterpreted as emergent consequences of structural differentiation. Unlike conventional frameworks where motion is defined within a pre-existing geometric background, SDG proposes that admissible transport is determined by structure itself. In this formulation, the connection governs transport, curvature arises as transport mismatch, and propagation follows connection-guided paths. We demonstrate that:(i) effective motion emerges from connection-based transport,(ii) curvature can be interpreted as closed-loop transport mismatch,(iii) in the weak and smooth regime the connection approximately reduces to the gradient form,(iv) signal propagation can be described as path deformation under structural connection. In the present implementation, the connection reduces to a gradient-based form, providing a minimal realization of the framework while preserving the conceptual structure of connection-based dynamics. The accompanying Python script reproduces all figures in the paper, providing a fully transparent and reproducible visualization of the framework. This work provides a minimal and unified structural interpretation linking motion, curvature, and signal propagation without assuming a fundamental geometric background. Motion is not commanded by geometry; it is selected by structure.