Release and proof boundary

and proof boundary{ Frozen (A0): cubic-only sheet, inverse $-1$, inert $g$ and ${\sigma }_{\epsilon }$, ${\mathfrak{g}}_W$, observable $\mathcal{O}$. One route: relative symmetry.

Constructed: antifield sector and antibracket; the exact breaking functional $(S_{\mathrm{ext}},S_{\mathrm{ext}})=\kappa \int c^{\nu }{\mathcal{K}}_{\nu }$; the relative master equation on ${\mathfrak{F}}_W$ and its nilpotent differential; gauge fixing by XI-B's fermion; the evaluation identity on ${\mathcal{C}}_W$ with the auxiliary pairing printed; the identification of the relative free differential of $\mathcal{O}$ with that pairing.

Proved obstructed: the unrestricted master equation for every extension in the frozen kinematic class ${\mathfrak{S}}_{\mathrm{kin}}$ (nonzero ${\hslash }^0$ breaking); unqualified invariance of $\mathcal{O}$ on ${\mathcal{C}}_{\mathrm{sol}}$ (copied witness); completion inside ${\mathfrak{K}}_{\mathrm{loc},\mathrm{R}}$ (copied from XIII-D).

Outside the claim: a completion of the auxiliary pairing in any class not frozen here; ${R_1}^{(1)}$; a quantum gauge defect; a reduced algebra; an interacting differential on ${\mathcal{E}}_H$; a spurion or density-switched variational sheet; $\epsilon \to 0$.

Ending for the frozen relative sheet: Constructed. The unrestricted sheet is Proved obstructed and is recorded as the boundary of the claim. The release is relative; it is not an interacting quantum algebra.}