No nonlinear singular geometry is manufactured

The conical metric in the chosen smooth coordinates is

It has no direction-independent value at $x=0$ when $\alpha \ne 1$. Products such as $g_{ij}{\partial }_k{\delta }_{\mathcal{W}}$, a distributional Einstein tensor built from unspecified products, or a singular-connection divergence of arbitrary contacts are not defined by the finite parts above.

Our mixed tensors are ordinary tensor distributions on the auxiliary smooth completion. Their regular restrictions are the physical mixed tensors, and their extended Ward identities are those fixed in Definition def:Ward. A core regularization or nonlinear generalized-function framework would require a separate construction and comparison GerochTraschen. No such comparison is asserted.