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Manuscript X-E@1 · X-E.tex · section · 293fae6a

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{}1.12

Item	Declaration
Signature	$(+, -, -, -)$ . VII-C's opposite signature is comparison only.
Scalar	The same switched density $L = (1 - g) L_{η} [ϕ] + g L_{q} [q, ϕ]$ , same $g$ , same ramp, fixed $ε$ .
Gravity	Einstein–Hilbert, $S_{gr} = - (2 κ^{2})^{- 1} \int - q R$ , conventions of Section sec:E1. Sign fixed by Diagnostic diag:sign. Quadratic part derived in Lemma lem:quadratic.
Gauge	De Donder, $C^{μ} [h] = \partial_{ν} h ˉ^{ν μ}$ , $h ˉ = h - \frac{1}{2} η tr_{η} h$ , Feynman weight $\frac{1}{4} \int C_{μ} C^{μ}$ , for the quantum graviton only. Classical backgrounds remain unconstrained.
Algebra	The same $g_{U}$ . It acts on the classical backgrounds by the complete two-jet law; Proposition prop:residual shows it cannot act on the gauge-fixed graviton.
Field content	$ϕ$ free Klein–Gordon; $h$ free gauge-fixed graviton; $h_{cl}, k_{cl}$ classical, off shell. No second-order quantum metric, no ghosts.
Order	Classical identity through $κ^{2}$ . One tree at $κ^{2}$ , the first order at which $h$ propagates. Quantum-metric background identity through $κ^{1}$ ; the $κ^{2}$ defect is displayed.
Coordinates	X-A's ramp operator (eq:coordinate-equations). Not replaced by the metric equation.
Not opened	Ghost loops; the word $B_{f} ⋆ W_{g} ⋆ B_{f^{'}}$ ; a triangle subtraction; X-Enter; $ε \to 0$ for any kernel; the self-interaction tree; the mixed loop; gauge-parameter dependence.