Manuscript X-B-ii@1 · X-B-ii-v1.tex · section · f1377602

The normalization sheet, recorded

C3: the normalization sheet › The normalization sheet, recorded · lines 973–1010

{}1.12

Item	Record
Domain	$L_{off} = {F_{c} : c \in D}$ , off-shell representatives; not on-shell classes (X-B, `eq:off-shell-warning`)
Codomain	$A_{0}^{(1)} \subset A_{0}$ , field degree one
The one map	$R_{1} (V_{1, g} [h]; F_{c}) = ϕ (- L_{1, g} [h] E_{m}^{A} c)$
Transposed notation	$- ⟨ c, E_{m}^{R} L_{1, g} [h] ϕ ⟩$ means $ϕ (d_{c} [h])$ , characterized by (eq:transpose)
Classical normalization	(eq:sheet) on all of $L_{off}$ ; determines the map (Theorem thm:unique)
Contact terms	Sheet-compatible ones vanish in $A_{0}$ ; none selected; none needed (Corollaries cor:contact, cor:ward)
Quantum order	$ℏ$ -free; $Δ_{+}$ -independent (Proposition prop:check)
Causal properties	Additivity in the vertex; vanishing when $supp g \cap J^{-} (supp c) = \emptyset$ (Proposition prop:causal)
Not claimed	A time-ordered family; uniqueness relative to (T1)–(T4)