Comma-to-semicolon prescription (${\partial }_a⟼{\nabla }_a$)

The prescription replaces partial derivatives in flat-spacetime matter equations by the Levi-Civita connection and the Minkowski metric by the curved metric tensor. It implements minimal gravitational coupling and reproduces flat-spacetime physics at a point in a local inertial frame. It is not a unique rule for rearranged higher-derivative equations: commuting partial derivatives before replacement can conceal a Riemann curvature tensor term afterwards. The derivative-order ambiguity in covariant Maxwell potential equations is an explicit example. The equivalence principle removes uniform gravitational acceleration locally but does not erase tidal curvature over a finite experiment.