Diagnostics and the exclusions that remain

reduction. Replace the metric by a prescribed classical background $r$ before taking the scalar response. Its first response is $-{{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{R}}{\mathsf{V}}_{1,g}[r]\varphi$, and its completed second coefficient is (eq:A2). Setting that background to zero gives the zero specialization of those response maps. Setting an external quantum metric configuration to zero after the graviton response does not remove $\mathcal{T}$, which has no such external argument.

gauge. The correct identities are

whereas

need not vanish. A pure-gauge background is not a vanishing test for a tree sourced by scalar stress.

empty Einstein jet. The response $r_g$ and its divergence exist. Above the ramp,

for a free scalar. The named input gives a nonzero source. The tree propagates this de Donder violation; it does not set it to zero or restore the ungauge-fixed Einstein equation.

loop. No scalar Hadamard bisolution, covariance matrix, or retarded quantum product is selected. No mixed-loop expression is multiplied, extended, or subtracted. Missing loop data are an unresolved stop, not a no-go theorem for the classical tree.

gravitational interaction. No cubic Einstein vertex is contracted. Its classical role in nonlinear identities has not disappeared. A future interacting master identity must account for the appropriate gravitational, scalar, ghost, and antifield terms.

and width. The initial coordinate data remain frozen at $\Sigma$. No boundary algebra, boundary charge, reflected-residue subtraction, or $\epsilon \to 0$ limit is constructed.