Manuscript XV-F@3 · XV-F-v3.tex · section · d4e74afa

Frozen ledger

Frozen ledger · lines 1753–1787

Entry	Internal expression	Cross-line factors	Status at $N$
$K_{47}$	(eq:K47), $L$ from (eq:L), $R$ explicit; $A$ , $f$ , $σ_{ε}$ candidates; exists (Theorem thm:exist); not of module form	$C_{cross}$ as (eq:cross); blocks C	Composed on $U_{can}$ only Ijoint.
$K_{5}^{[a]}$ , $K_{5}^{[z]}$	(eq:K5a), (eq:K5z); exists; module form in charts $w_{\pm}$ (Proposition prop:K5chart)	As above	I3 stop Ijoint.
$K_{6}$	(eq:K6); $D$ via $a ˙_{2}$ (candidate (eq:a2dot)); module form in $w_{+}$ ; $supp \subseteq S_{\partial}$	Traces $c_{D, β}$ named	Conditional interface only Jconditional.
$K_{8}$ , $K_{9}$	(eq:K8), (eq:K9); $B$ explicit; $q_{α β}$ of order $\leq 2$ ; $E^{A}_{m}$ candidate (eq:EA); $P$ , $b$ , $g$ undefined; $supp K_{8} \subseteq S_{J^{+}}$ , $supp K_{9} \subseteq S_{\partial}$	Traces named	Conditional interface only.

This is a freeze check, not evidence that the full operation exists. Propagator, pole, regulator, carrier, normalization, and ambiguity class are unchanged; the recovered displays are recorded, not altered.

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section: Frozen ledger