A3: recorded, not opened

XIII-C's four obligations (Input statement input:XIIIC) remain the gate in front of any quantum gauge defect. $s_0$ and $s_{\mathrm{ext}}$ are not applied to ${R_1}^{(1)}$; no $R_1$ coefficient is formed; no Hadamard line is contracted against ${\mathcal{J}}_{\mathrm{D}}$.

X-G's reciprocity theorem is a non-identification: the sheet selected in A0 is density switched, and X-G's mixed map is not its field map. Had A0 selected the source-switched sheet, the master equation would already be blocked by X-G's definition of an exact upgrade; that ending would concern that upgrade only.

The convolution defect $S_{\epsilon }\xi \ne \xi$ is a different coordinate prescription; it is not identified with the ramp edge and is not an input to Theorem thm:breaking.

${{\mathcal{J}}^{\mathrm{D}}}_{g,{\sigma }_{\epsilon }}({\varphi }_m)=\varnothing$ stands. The slot $r_{\mathrm{D}}+r_g$ solves a gauge-fixed forcing equation; it does not fill the invariant coupled jet, and the empty jet is not a failure of $\mathcal{O}$.

The XI-G classes with covectors $\pm (k_1,k_2,0)$, $k_1+k_2=2\mathrm{d}t$, remain excluded; $\mathcal{O}$ is not a representative.

No reduced algebra, physical cohomology class, state, loop, antibracket on ${\mathcal{E}}_H$, interacting differential on ${\mathcal{E}}_H$, or $\epsilon \to 0$ limit is constructed. The antibracket of Section sec:A1 is the classical off-shell antibracket on local functionals of $\mathfrak{F}$ and ${\mathfrak{F}}_W$.