The sharp-domain obstruction is not removed by notation

The supplied IX-A statement gives a continuous coordinate separating the unchanged regular approximants from the proposed sharp insertion. The supplied IX-B statement distinguishes a ternary numerical finite part from a second sharp binary product CheungIXA,CheungIXB. The VII-C obstruction concerns its stated extension and continuity hypotheses CheungVIIC.

None of those problems is used in the benchmark. Conversely, the benchmark's explicit distribution does not construct the missing sharp insertion, change its admission topology, or contradict those results.