Theorem: Unrestricted master equation: Proved obstructed in

For every $S^{\prime }\in {\mathfrak{S}}_{\mathrm{kin}}$, the antifield-degree-zero component of $(S^{\prime },S^{\prime })$ equals $\mathfrak{K}$, which is a nonzero functional on $\mathfrak{F}$ at order ${\hslash }^0$. Hence no $S^{\prime }\in {\mathfrak{S}}_{\mathrm{kin}}$ satisfies $(S^{\prime },S^{\prime })=0$ on the unrestricted field space, and no correction beginning at order $\hslash$ changes this conclusion.

Proof. Lemma lem:decomp, Theorem thm:breaking, and Proposition prop:witnessA1. Higher antifield terms and $\hslash$-corrections do not affect the antifield-degree-zero ${\hslash }^0$ coefficient.