= Comma-to-semicolon prescription
{title2=$\partial_a\ \longmapsto\ \nabla_a$}
= Comma goes to semicolon rule
{synonym}
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.
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