The complete-sum calculation protocol

1: keep the full inventory. Retain

with both crossed terms. The row definitions are printed in Appendix app:kernels.

2: cover all sectors meeting the patch. Besides the rescaled core, account for the supported response incidence, the $b-z$ cone in $K_{47}$, the $a-z$ and $z-a$ cone tips in the two $K_5$ placements, and the complementary sectors on each compact joint support. A core or annular calculation is not a complete estimate.

3: standardize conventions. Use one tensor pairing, derivative placement, density, relative-slot sign, and coefficient-distribution representation. For example,

does not mean differentiation of the whole incidence product.

4: calculate and collect before deciding. Produce exact local representations, extract candidate orders, transpose to one common test-jet convention, and sum all row–vertex contributions at each order. A nonzero branch coefficient is not a complete obstruction.

5: certify the complete remainder. State one finite derivative order on each fixed compact support. Include the tails and any partition derivatives. A leading algebraic zero without a vanishing complete remainder does not prove convergence.