All Conventional Large-Scale Solutions of the Einstein Equations Have Been Wrong: A Two-Body Test Imposed by Special and General Relativity

The Einstein equation is correct. The classical method conventionally used to construct a large-scale many-body solution is not. By the classical method we mean the procedure that fixes a source record in a trial geometry and then solves for a different metric without rebuilding that record. At a reception event \(p_A\), retarded propagation selects an event of a second body \(B\), while general relativity makes the selecting light cone, the relational position of that event, its transport, and the receiving frame depend on the metric being solved. Holding these quantities fixed therefore locates \(B\) with one geometry and propagates its field with another. The required order–geometry relation is not a new gravitational field equation; it is the closure rule by which the sources entering Einstein’s equation are identified in the same geometry that they produce. A two-body variation gives a nonzero invariant closure defect for every nondegenerate interacting configuration and proves that an exact classical output is an exact solution of a different, incorrectly posed problem. The defect begins at second order on a short causal link, which explains the local success of the classical method. In the one-dimensional inward radial sector, the exact ordered recursion and the positive retarded self-gravity resolvent show that the omitted contribution remains attractive and grows with causal depth. The resulting radial excess is the geometric term conventionally represented by dark matter. **Keywords** General relativity; special relativity; causal ordering; many-body gravity; order–geometry closure; retarded propagation; relational position; self-gravity; dark matter; galactic rotation curves.