Manuscript XVI-M@1 · XVI-M.tex · section · 7346c909

Normalization table

M.0 Dependency, normalization, gates, and target ledger › Normalization table · lines 232–259

XVI-L determines the combinatorial graph factor $(1/2!) \cdot 2 = 1$ and leaves coupling and loop weights undetermined (XVI-L, prop:Lnorm). No number is invented below.

Item	Value / source	Status
Metric fluctuation	$q_{μν} = η_{μν} + κ γ_{μν}$ (XII-C)	Imported
Residual $h$ vs $γ$	Dummy of the same species; no rescaling (XVI-I, prop:Ft)	Imported
$ℓ_{3}$ vs action	$ℓ_{3}$ is the coefficient of $κ$ in the unintegrated signed EH density; $S_{EH} = - \frac{2}{κ ^{2}} \int - q R$ ; $S_{grav, D} = S_{EH} + κ \int (σ - 1) ℓ_{3}$ (XII-C)	Imported
Graph vertex	$V (h) = \int χ_{I} ℓ_{3} (h)$ , $χ_{I}$ independent of $σ_{ε}, f, g$ (XVI-I, prop:second)	Imported; relation of $χ_{I}$ to $κ \int σ ℓ_{3}$ Unresolved
Kinetic operator	$K = - □ P = A + 2 D^{*} D$ , $A = 2 G_{lin}$ (XII-C; XVI-I)	Imported
Propagator	$D_{F} = H + i G^{A} = - P (h_{0} + i E_{0}^{A})$ , $K D_{F} = i id$ (XVI-J, eq:DF, quoted in XVI-K, eq:J-DF); “with $h_{0} = - W_{0}$ (XI-E.tex, eq:h)” (XVI-K, K.0); $S = h_{0} + i E_{0}^{A} = - Δ_{F}^{FR}$ (XVI-J, lem:identify)	Imported
Position-space form of $S$ on $R^{4} ∖ {0}$	$S = c (Q - i 0)^{- 1}$ with $c = \frac{1}{4 π ^{2}}$ , boundary side $Q - i 0$ (Theorem thm:wpA-Sbv); $W_{0} = - \frac{1}{4 π ^{2}} (Q - i 0 sgn z^{0})^{- 1}$ , $E_{0}^{A} = \frac{1}{2 π} θ (- z^{0}) δ (Q)$	Certified (Gate S-bv; written check of XVI-J, eq:rational); Euclidean motivation is not the certification; $S$ is global (XVI-J), its position-space identification at $z = 0$ is not established
$S^{2}$ residue and scale units	$r = - 2 i π^{2} c^{2} = - \frac{i}{8 π ^{2}}$ (Theorem thm:M6-S2); top-order scale residues in units $i π^{2} c^{2} = \frac{i}{16 π ^{2}}$ (Section sec:wpB)	Constructed; not a beta function
Powers of $κ$	Action cubic carries $κ$ ; $a_{λ}$ and the graph factor carry none	Overall order Unresolved
Powers of $ℏ$	“No power of $ℏ$ is assigned” (XVI-I, prop:sector)	Unresolved
Factors of $i$	$i$ in $D_{F}$ fixed by $K D_{F} = i id$ ; vertex factors not assigned	Partial; remainder Unresolved
Insertion	$F_{t} (h, ϕ) = ⟨ t_{D}, h \otimes h \otimes ϕ ⟩$ ; $D_{h}^{2} F_{t} [a, c] = 2 ⟨ t_{D}, a \otimes c \otimes ϕ ⟩$ (XVI-I)	Imported
Loop order	“A count of one cycle is not a loop order of an interacting observable” (XVI-I)	Unresolved
Variational contract	Gate V (Section sec:gates)	Chosen Phase II convention; not certified by this table