The selected extension

A fixed subtraction function is an actual normalization datum. It may encode a coordinate length or shape. No Lorentz covariance, scaling covariance, or compatibility with a separately selected derivative extension follows merely from the zero-moment condition. Derivatives of $q^{\circ }$ are not extended here.

The extension concerns one point in four relative dimensions. After smooth tangential coefficients are restored, this prescription is a specific extension of the selected sector; it is not a classification of all extensions with arbitrary tangential coefficient functions.