This study investigates whether gravity-like geometric structurecan arise from projection-based order dynamics without assumingspacetime as a primitive background. Building on earlier results showing that spatial distance geometrycan emerge from low-dimensional projection cores, we examine whetherthe same projection dynamics admits a distinct gravity-like phase. Within this phase the system exhibits Poisson-type response togetherwith inverse-square force behavior. Additional diagnostics,including Gauss-law consistency, approximate curl-free structure,action–reaction symmetry, and Kepler-type two-body dynamics,confirm that the interaction behaves consistently with theNewtonian limit. Using projection-generated order fields, we construct an inducedlocal metric and evaluate the associated Levi–Civita connectionand parallel-transport holonomy. The holonomy angle exhibitsarea scaling consistent with curvature, indicating the emergenceof a metric–connection hierarchy within the projection framework. The analysis is performed entirely within a discrete projectionmodel and does not derive Einstein’s field equations. Instead,it provides a structural investigation of how gravitationalgeometry can appear as an ordered phase of projection dynamics. Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own.
John Jude Hathway (Wed,) studied this question.