Declarations

correction. The distinction between factorization of ${\mathsf{T}}_2$ and ordered values of $R_1$ follows from the selected retarded definition. The correction changes neither the inherited causal brackets nor the coefficient $-1$ of the metric inverse.

scope. Properness and tree admission are proved. The two-line extension is expressly unresolved. No failed sufficient wavefront condition is promoted to a theorem that every extension fails.

scope. All constructed outputs use the existing polynomial domain and full-shell quotient. No quotient by ${\mathcal{N}}_W$ is taken. The selected-lift construction is not asserted to descend as a binary operation under arbitrary changes of input representatives.

scope. Only the switched metric–scalar vertex is inserted. The Einstein–Hilbert action remains in the model, but none of its interaction vertices is restored in this selected pair. The empty invariant jet is not used as an interaction functional.

. No successful pdflatex execution, proof-assistant verification, independently executed symbolic computation, independent referee review, or journal acceptance is asserted.