Question, prerequisite boundary, and release discipline

The question is whether a specified regulated coordinate prescription transforms with the scalar under the same gauge action. A regulator must participate in this calculation. Classical covariance of an unregulated prescription does not establish covariance after convolution, and regularity of coefficient kernels does not establish gauge invariance.

This paper chooses the obstruction branch of that question. The regulator, switch, gauge algebra, and observation test are fixed in Section sec:sheet. The preflight calculation in Section sec:preflight already determines the release. Subsequent sections identify the coefficients and isolate the failed identity; they do not attempt a repair.