The construction actually undertaken

The supplied plan leaves the interaction unspecified and asks for all residuals to be instrumentable. Neither request is a theorem without further definitions.

We make the following choices before calculating:

1. the interaction is the compact scalar vertex $V_a$ displayed in the abstract;

2. it first occurs at order ${\kappa }^3$;

3. the retained coupling ring is $\mathbb{R}[\lambda ][\kappa ]/({\kappa }^4)$;

4. the classical reference action is specified by finite Taylor extraction from the natural local action;

5. a report concerns a specified real coefficient of a specified representative on supplied smooth data;

6. only finite dictionaries and finite instrument networks are released.

The parameter $\lambda$ distinguishes the additional vertex from the pre-existing gravitational interaction. Setting $\lambda =0$ does not turn off the reference Einstein–scalar interactions. Setting $\kappa =0$ removes every positive-order interaction.

The principal predecessor records are Cheung's X-G, X-G-ST, and X-H-ST XG,XGST,XHST. The free normalization, relative kinematics, and action conventions used here are restated explicitly. The proofs of the new deformation and its report interfaces do not depend on a registry connection.