Lemma: Lemma 10, field-only projection

Let $A_0=\int (h^{\star \mu \nu }{U}_{\mu \nu }+{\varphi }^{\star }V+{c^{\star }}_{\mu }{W}^{\mu })$ be antifield-linear of ghost numbers $(1,1,2)$, with regular multilocal coefficients and no new inverse operators. Let $P_0$ project to antifield number zero and let $Q_0=(S_0,\cdot )$ be the free differential of the minimal free extended action. Then

and therefore

A graded lattice check is corroboration of the algebra. It is not a substitute for the continuum statement.