Contact defects of differentiation

These formulas compare extensions of punctured products with derivatives of already extended distributions. They do not establish a Leibniz rule for the prescription. Any rewriting using derivatives must retain the displayed defects.

The domain of ${\mathfrak{R}}_{\mathrm{K}}$ is the finite span $\mathcal{V}$, not all distributions. In particular, no multiplicative renormalization map on individual edge factors is defined. Derivative compatibility is only meaningful here when both the input and the corresponding punctured derivative belong to the stated span.

No Lorentz covariance follows from an arbitrary $\varpi$. No covariance or derivative normalization is imposed in addition to (eq:moments). Trace reversal remains in the finite fiber coefficients; it does not act on the scalar extension problem.