Remark: Boundary-chart and rank qualifications

The large-radius formula uses $H^{-1}$ and is not asserted for singular $H$. The integral representation remains valid there.

The small-radius two-mode limit is a statement for a full finite chart. It is not valid for every boundary chart: the scale-invariant line family already provides a counterexample, because it is irregular in only one boundary direction. For arbitrary boundary relations use (eq:CW); no unsupported universal endpoint interpolation is imposed.

The limits just stated are rescaled limits. They do not assert that divergent unscaled quantities converge to finite numbers.