The sheet's three symbols, and the double count

The production sheet asked for ${\delta }_{\mathrm{split}}+{\delta }_0{\mathcal{C}}_3+{\delta }_{\mathrm{gf}}$, with XI-E's values. In the ledger above these are:

Their literal sum is $0+I+0=I$. That number is not an obstruction. The “by-hand $+I$” inside ${\delta }_{\mathrm{split}}$ is the shift $\gamma \mapsto \gamma +\kappa {\mathcal{L}}_{\xi }\gamma$ restored by XI-E in a parametrization with an external second coefficient $k$ and an independent field $\gamma$; L3 is the shift ${\mathcal{L}}_{\xi }\gamma$ generated by the cubic response once $k=u_3[\gamma ]$. They are one term in two notations. XI-E's theorem is correct in its own parametrization, and XI-E's ${\delta }_0{\mathcal{C}}_3=I$ is correct; what is incorrect is the sheet's instruction to add them. Removing the duplicate gives (eq:ledger). Nothing is dropped: ${\mathcal{C}}_3$ is retained, and so is its $I$. The sheet's expectation ${\delta }_{\mathrm{gf}}=-I$ is replaced by the computed value ${\delta }_{\mathrm{gf}}=0$.