A necessary correction to product-order bookkeeping

Thus the two-endpoint obligation is not required for every product described merely as a “second-order lapse product.” Its exact grading must be declared. It remains required whenever the actual announced operation contains two noncompact rod legs.

The native two-rod canonical tail retained from XX-C is

Its nonzero inverse-distance coefficient must be preserved by a two-rod covariance domain. It cannot be removed by demanding inverse-square decay of both ordered terms.

No two-rod quantum product is evaluated in this manuscript. Equation (eq:twoRod) is an unchanged canonical constraint, not a calculation of a lapse anomaly.

Finally, one free contraction of a quadratic insertion is not a complete interacting one-loop coefficient. A complete claim requires the interactions, ghost and auxiliary contributions, retarded normalization, and all terms at the stated coupling order.