Remark: Why this does not repair joint admission

The compact test $q_{f,h}$ is obtained {after fixing $h$}. It does not establish joint microcausal admission of the original metric–scalar kernel. In particular, the metric dependence through the zero-Cauchy map $w[h]$ can retain the initial-surface structure which is central to VII-B's obstruction CheungVIIB. A smooth scalar test with a classical parameter is a different typed object from a distributional kernel with a quantized metric slot.