Remark: Other repairs

Two further substitutions have been excluded:

1. The correct scalar density perturbation is $Q_{\chi h}$. Replacing it by $\chi Q_h$, or omitting its trace–mass term, would change the declared action and the off-shell test calculation.

2. The notation ${\mathcal{O}}_f[g_{\mathrm{cl}}]$ cannot erase the scalar preparation. The exact theorem names both $g_{\mathrm{cl}}$ and ${\varphi }_{\mathrm{cl}}$, and concerns the first coefficient only.