Modified Gravity Theory I: On the Modification of General Relativity by Special Relativity

We examine a consistency requirement in many-body general relativity. At a reception event \(p_A\), special relativity assigns no observer-independent simultaneous position to a source \(B\); the source relevant to \(A\) is selected instead on the past light cone of \(p_A\). General relativity adds that this light cone and the relation between the two bodies depend on the inherited metric. When that metric changes, the retarded event of \(B\) and its physical relational position in the receiving frame of \(A\) change with it. We call the self-consistent record obtained by repeating this update the order history. A covariant composition of local Einstein solutions gives one computable realization. Its metric and lapse deformations accumulate through the active frame and the gravitational normal function. Under the stated coherence hypotheses, this history produces a scale-dependent geometric contribution to the outer gravitational field. We derive the corresponding closure equation, its continuum memory, and its application to Galactic rotation curves and source-family scaling. No additional matter component is introduced; in the ordered model the effective missing-gravity term is the observable difference between the closure-complete history and its order-blind comparison. Keywords **General relativity; special relativity; many-body gravity; causal order; order geometry; active-frame composition; spacetime memory; Galactic rotation curves; missing gravity; baryonic Tully–Fisher relation**