Significance without a priority inflation

The useful mathematical feature is the combination of an explicit compact output test, a precise normalization domain, and an equally explicit stopping point. The construction shows how a first background identity can hold exactly in the free quotient while edge and switch defects remain visible outside its algebra.

The source results are credited to Cheung's X-B and X-B-ii XB,XBii. The present contribution is their supported host transfer and audit. No claim of a new physical prediction or a solution of interacting quantum gravity follows from this packaging.