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

Decision and final release

Decision and final release · lines 1769–1818

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{}1.12

Gate	Evidence	Status
E1 action	Einstein–Hilbert, sign by TT positivity and Newtonian attraction; Palatini first variation derived	Frozen
E1 equation	(eq:metric-euler-expanded); Noether identity (eq:noether) with switch defect $(\partial g) T$	Proved
E2 invariance	Total Lagrangian exactly $G_{U}$ -invariant; Euler operators covariant; classical identity through $κ^{2}$	Proved
E2 jet	Bianchi identity forces $(\partial_{μ} g) T^{μ}_{ρ} [ϕ_{0}] = 0$	Coupled jet generically empty; observable unaffected
E3 operator	$P_{gr} = - \frac{1}{4} P □$ , $Δ_{R}^{gr} = - 4 P E_{0}^{R}$ , $P^{2} = 1$	Constructed
E3 residual	Compactly supported de Donder residuals vanish	$g_{U}$ acts on backgrounds only
E4 tree	Kernel, support in $J^{-} (K)$ , microcausal admission, classical normalization	Constructed at $ℏ^{0}$
E4 identity	Invariant through $κ^{1}$ ; $κ^{2}$ defect $- κ^{2} A_{1} [L_{ξ} h]$ displayed and nonzero	Order boundary at $κ^{1}$
E5	(E1)–(E4) copied; one line, no $W_{g}$ , no $ℏ^{3}$	Inapplicable, not contradicted
Named	Self-interaction tree; mixed loop; second-order quantum metric; ghosts; $ε \to 0$	Not constructed

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