Status (work package A).

(work package A).{ Constructed (proved): on $\Omega :={\mathbb{R}}^4\setminus \{0\}$,

with $Q(z)=\eta (z,z)$, $\eta =\mathrm{diag}(1,-1,-1,-1)$, including across the nonzero null cone (Theorem thm:wpA-Sbv). Constructed: convention ledger (wpA/kernel_conventions.json); symbolic and numerical cross-checks (wpA/kernel_identification_checks.py); local boundary-value lemma for the variable regulator (Lemma lem:wpA-varreg). Predecessor status: the formula is printed in XVI-J, eq:rational (with $S=-d$, XVI-J, eq:DF); this subsection is a written check of it, not a new extension.

Non-claims: the predecessor $S$ is globally defined (XVI-J); what is not established here is its position-space identification at the origin; no $i\epsilon$ Feynman contour is introduced as a definition; the massive case is not needed for this edge; nothing about M-C, Ward or BV. Gate S-bv / Input (S-bv) is discharged by the theorem below, with the explicit constant $c=1/(4{\pi }^2)$ and boundary side $Q-i0$. The Euclidean calculation of Remark rem:Sbv-motivation remains a motivation only; it is not the certification. }