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Manuscript X-F@1 · X-F.tex · section · f35cc129

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{}1.12

Item	Declaration
Signature, scalar, ramp, $ε$ , $g$ , $U$ , $g_{U}$	As X-E. Separation (eq:separation).
Gravity	Einstein–Hilbert, X-E's sign. The cubic vertex $S_{3}$ is used through its polarized Euler derivative $G_{2} (h_{cl}, \cdot)$ and its quadratic part $\frac{1}{2} G_{2} [h, h]$ .
Gauge	Background de Donder, Definition def:bgf, Feynman weight, through $κ^{1}$ in $h_{cl}$ , quantum graviton only. Replaces X-E's flat de Donder gauge.
Field content	(eq:metric). $k$ is derived, (eq:khat); it is not an independent field. No ghosts.
Transformation	Complete two-jet law on $(h_{cl}, k_{cl})$ ; $ϕ, h$ held fixed. The same frozen action as X-E's Theorem Background gauge identity.
Order	$κ^{2} ℏ^{0}$ , all trees. Target: background identity through $κ^{2}$ modulo $J$ .
Switch	$σ_{ε}$ on the order- $κ$ gravitational and gauge-fixing sources; $g$ on the matter source, as X-E.
Not opened	$ℏ^{1}$ ; ghosts; BRST/BV with switched matter; positivity; the classical self-response; gauge-parameter dependence; $ε \to 0$ ; X-Enter; $κ^{3}$ .