D3–D4: the gate is not crossed

Since admission has not been constructed, no antibracket on admitted quantum composites is defined here. XI-B's antifields remain external slots. In particular, there is no claimed Jacobi identity for an unnamed bracket.

There is also no constructed $s_1$ or $s_2$. Saying that $s_1$ is “the variation of $V_{1,g}$” leaves an essential ambiguity. In a canonical BV description, an antifield-free interaction changes the antifield equations through its Hamiltonian vector field; it does not, by itself, specify new transformations of the fields. The necessary antifield-dependent terms and their master identity must be supplied separately.

The same issue applies more strongly to the observable-dependent tree $\mathcal{T}(f,g)$. It is an output associated with an observation test. It is not automatically an interaction Hamiltonian defining one universal differential.

Consequently no assertion of interacting nilpotence is made. The gauge-fixed bosonic action's breaking, the auxiliary–ghost completion, and the invariant action's Noether identity remain distinct. Omitting the Einstein cubic vertex is still a scope restriction, not a proof that the missing terms of a master identity vanish.

The next section only tests a necessary leading coefficient of the proposed closure equation. It does not bypass these gates.