The gravitational branch remains separate

The supplied XII-A–F chain has the following scope:

1. XII-A constructs a free-shell carrier and ordering transport.

2. XII-B distinguishes density weighting from source weighting.

3. XII-C selects the cubic-only density modification and proves its actual Euler source.

4. XII-D constructs a smooth classical retarded response and an admitted completed insertion.

5. XII-E assembles the second metric slot with the sign ${{\Phi }_{\mathrm{D}}}^{(2)}={{\mathcal{A}}_2}^{\mathrm{sc}}-{\mathcal{C}}_{3,\mathrm{D}}$.

6. XII-F evaluates a nonzero auxiliary remainder even when the propagated companion vanishes.

These are distinct claims CheungXIIA,CheungXIIB,CheungXIIC, CheungXIID,CheungXIIE,CheungXIIF.

In particular, the supplied XII-F witness has the signed value

It is a classical variation of a named off-shell lift tested on an initial free-shell configuration. It is not the response (eq:kubo), not a normalization difference, and not a quantum Ward identity.

The affine second-slot identity already determines the minus sign. An admission theorem alone does not prove a kernel nonzero, and a second co-transformation row must not be added to a slot whose variation already contains that transformation.