At one point the connection vanishes, yet its second derivatives still refuse to cancel. In normal coordinates the Riemann tensor collapses to pure first derivatives of Γ. Differentiate three ways, cycle the indices, and every second-derivative term pairs with an opposite sign. The sum is identically zero — the Bianchi identity. Contract the upper index with one lower index and the leftover object is the Ricci tensor, the exact curvature that sources Einstein’s equation. Geometry alone enforces local energy conservation.