Remark: Stretch: explicit nonzero scaling residue

Massless homogeneity of $S$ (XVI-K, Lemma lem:homog) and $\mathrm{sd}(S^2)=4$ (XVI-K, Lemma lem:nonzero) give the contact form $A_{\mu }(S^2)=r_{\mu }(S^2)\delta$ for the scale-variation coefficient $r_{\mu }(S^2)$, but do not by themselves evaluate it or prove $r_{\mu }(S^2)\ne 0$: a nonzero homogeneous distribution of degree $-4$ may still have vanishing spherical average against the radial derivative of ${\varpi }_{\mu }$. An explicit nonzero scaling residue in the reserved anomaly sense $(E+4+N)R(u)$ would require either the angular integral of $S^2$ on the unit sphere (or an equivalent Hadamard coefficient) or an independent computation of $⟨{\mathfrak{R}}_{\mathrm{L}}(S^2),\mu {\partial }_{\mu }{\varpi }_{\mu }⟩$. Neither is imported from XVI-K/XVI-J in a form that yields a numerical nonvanishing here. Unresolved: whether $r_{\mu }(S^2)\ne 0$ for the present $\varpi$, and whether a nonzero scaling residue (anomaly form) occurs.