G4: what the result is not

Theorem thm:obstruction is a statement about compact distributional kernels and the copied cone exclusion. It is not a no-go for every bimodule, every renormalized product, or every extension preserving XI-B's commutators.

No quantum retarded product of $J_3$ is formed, no cubic source is contracted against a Hadamard line, and no loop is evaluated. The pairings used are classical evaluations on smooth solutions.

No ${\hat{s}}_{\mathrm{int}}$, antibracket, or master identity is constructed. Ghost number zero of ${\mathcal{C}}_3$ is known and is not closure.

The classical ledger $-I+I+0=0$ of XI-F is untouched; it is a coefficient identity on smooth configurations and needs no representative in ${\mathcal{E}}_H$. It is not re-added as $0+I+0$. The Einstein-shell term ${\mathcal{A}}_1[\mathcal{P}{{\mathsf{E}}_0}^{\mathrm{R}}{{\mathcal{L}}^{\mathrm{dens}}}_{\xi }(A\gamma );{\varphi }_0]$ stays named and unevaluated when $D^{\ast }b\ne 0$ on $U$.

The onset is the zero-data truncation of an unramped source, not the ramp layer; no $\epsilon \to 0$ limit is taken, and the two affine numbers $S_{\epsilon }(t)$ and $\epsilon /2$ are not touched.

${\mathcal{C}}_3$ is not identified with ${\mathcal{B}}_f$, with VII-D's or IX-E-2's kernels; only the covector type is compared.

The empty jet ${\mathcal{J}}_g({\varphi }_m)=\varnothing$ is not repaired, and would not have been repaired by a constructed representative either.

No cone, token, or Enter record is imported.