The mixed ramp coefficient

Applying the map to the first frozen test gives

Indeed, $⟨c_1,{\rho }_{1,g}⟩=⟨{\partial }_{\mu }(f{{\mathsf{X}}_1}^{\mu }),{\rho }_{1,g}⟩$. Equation (eq:mixed) is the copied classical mixed term, with the scalar replaced by the free field through its test action. The minus insertion sign is fixed; the plan's plus sign is rejected.