Batch A: D02, D12, D14a–c

All five graphs are vanishing under the declared prescription: there is no UV pole, the finite part is $0$, and no p14r counterterm is needed. Every scaleless member is a pure power divergence ($\omega =2,4$), so the zero is not a $1/{ϵ}_{\mathrm{UV}}-1/{ϵ}_{\mathrm{IR}}$ cancellation.

• IR-regulator mass (analysis only). With a mass the poles are proportional to ${\kappa }^2{m}^{4}hh$ and ${\kappa }^2{m}^2{p}^{2}hh$, which are order-0/2 contacts excluded by N4, or to $\kappa m^{4}h$, for which the ${\kappa }^1$ basis is empty. All of them vanish as $m\to 0$.

• Analytic regulator. It does not separate the UV from the IR here.

• Cross-check. Two routes agree: the frozen dred lift with S0, and an independent symmetric tensor integration.

• D12. D12 (${\kappa }^{2}hh$) is kept separate from the order-$\kappa$ one-point slot (D14a–c). D12_status moves from Missing to vanishing_under_declared_prescription. This is derived under P's own prescription; XVI-O's value is not imported.