The analytical and operational halves

The principal analytical source is N. Cheung's X-A-conv, version 1, here called X-A–Convolution XConv. It fixes a spacetime convolution of switched metric arguments and proves that its coordinate prescription fails covariance on the gauge algebra declared before the calculation.

The principal operational comparison is Cheung's X-Enter, version 1 XEnter. Its proposed supported companion, X-Enter-ST, is the source supplied in the preceding development XEnterST. That source already separates the coefficient orbit, the complete readout, and the supplied-report instrument.

The present manuscript supplies the analytical half of this supported comparison. In particular, it states the actual mollifier and witness, proves the Cauchy and preflight identities, derives strict positivity, and retains the second-order defects. It does not infer these facts from an unspecified smoothing operator.

The ramp construction of X-A and X-A-ST is a separate prescription XA,XAST. No ramp identity is an input to the convolution obstruction.