F5: the scalar-sourced slot, recorded once

The tree is not recomputed. The slot enters once and is not an additional auxiliary cancellation row.

A future identity omitting $r_g$ is a metric-sector identity, not the full displayed second-order coefficient identity. A rule that varies $r_g$ under a metric-only shift has introduced a metric argument that this slot does not possess. A transformation of the scalar would be a different, explicitly specified operation.