Declarations

scope. All identities are classical, at ${\hslash }^0$, on smooth off-shell configurations or on the named bosonic shell. The antibracket is the classical antibracket of local functionals. No quantum antibracket, quantum master equation, quantum Ward identity, or quantum retarded coefficient is constructed.

scope. The relative master equation is an identity on ${\mathfrak{F}}_W$, whose ghosts are supported where both backgrounds are trivial. Its restriction to XII-A's free shell has trivial ghost sector. The unrestricted master equation in the frozen kinematic class fails by an explicit nonzero ${\hslash }^0$ functional. The observable identity is an evaluation on ${{\mathcal{C}}_{\mathcal{W}}}^{\mathrm{bos}}$, not a quotient and not closure on ${\mathcal{C}}_{\mathrm{sol}}$.

-identification scope. The convolution-regulated sheet, the source-switched sheet with inverse $-4$, and the cubic-only sheet with inverse $-1$ are three different models. Only the third is frozen. No obstruction proved on another sheet is imported as a theorem about this one; the breaking functional is recomputed from XII-C's identity in the present conventions.

scope. XII-C supplies the action, its Euler derivatives, and the changed Noether identity. XI-B supplies the inverse normalization, fermion, ghost normalization, and the compact residual lemma. XII-A supplies the carrier and the frozen free rule. XII-E and XII-F supply the observable, its finite ledger, and the witness value. XIII-A supplies the uniform plateau hypothesis and the evaluation identity. XIII-D supplies the class exclusion. X-G supplies the normalization-independent kinematic nilpotence lemma. The antifield sector, the exact antibracket square, its late-switch witness, the relative master equation, the carrier boundary, and the identification of the relative differential of $\mathcal{O}$ with the auxiliary pairing are proved here.

. No successful pdflatex execution, proof-assistant check, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The witness values are analytic; the value $-8I$ is copied from XII-F and not recomputed.