Release and proof boundary

and proof boundary{ Constructed: the named coefficient ${{\Phi }^{(2)}}_{\mathrm{D}}$, its single-entry decomposition, the exact assembled plateau variation, the explicit companion remainder and its support, the Einstein row in metric and auxiliary form, admission of the scalar-only completion, and ordering stability of the enlarged sector.

Corrections to the brief: (1) the admitted insertion enters with coefficient $-1$, forced by the affine slot identity and the gauge-fixed second-order equation; the “$+$” sum is detected as defective; (2) the second slot is determined, so no separate co-transformation row is added; (3) one metric field, no quantized background; (4) X-A's classical on-shell covariance is a premise and is listed as such; (5) “complete” is the scalar-linear sector; the scalar-sourced slot is recorded and admitted, not part of the target.

Not claimed: unqualified invariance of ${{\Phi }^{(2)}}_{\mathrm{D}}$ (the Einstein row is a named remainder), a quantum retarded product of ${\mathcal{J}}_{\mathrm{D}}$, an interacting BRST class, a loop, a state, or an $\epsilon \to 0$ limit.

The XI-G classes remain excluded. The XII-C fixed-input jet remains empty. The inverse coefficient remains $-1$.}