Internal and external quantum uses remain hypotheses

For an external compact probe $g$, a sufficient alternative to XX-D's Schwartz condition is that $\mathcal{C}W(\cdot ,g)$ have the decreasing-source bounds of Theorem thm:weighted, uniformly on bounded probe families. That theorem then defines its original rod. Any Ward-transformed kernel needs the same estimates for its actual transformed entries.

No selected native representative satisfying these conditions is constructed here. The weaker criteria are new usable sufficient conditions, not verification of Q3.