Abstract

The proposed XX-F calculation assumes an admitted native Q3 insertion and a quantum Ward operation on its domain. Those objects are not supplied by XX-A–XX-E. An unconditional native breaking term, counterterm cancellation, or interacting identity therefore cannot be released from the attached package.

We nevertheless sharpen the missing interfaces by proving new results on the identical background and free operator. The coupled classical jet transformation has a calculable first-order Leibniz defect on the centrally extended free algebra. A same-operator Cauchy witness proves that its antisymmetric part can be nonzero, excluding a first-order quantum derivation with that leading action on the unfiltered algebra. We then correct the order interpretation: the central-second-jet defect starts at total perturbative order three on a specified weighted regular jet algebra. It is invisible through total order two, while the free-equation quotient obstruction persists at order one.

A weighted Newton theorem replaces unnecessarily strong Schwartz assumptions by explicit decreasing-source bounds, with cutoff-error and output-decay estimates. A finite spatial contact module is reduced to a unique normal form before its Newton image is taken. This prevents presentation-dependent contact counting and illegitimate diagonal readout.

Finally, we derive the exact conditional breaking and repair equations when both the insertion and Ward operation may receive quantum corrections. Linear image membership is separated from nonlinear admissibility restrictions such as positivity. None of these interface theorems verifies the missing native covariance, infrared estimates, quantum operation, or interacting contribution inventory. Native Q3 remains open; Q4 and Q5 remain unentered and unclosed. No universal obstruction to a future native completion is asserted.