Assumption: VII-D parent, in the IX-B placement

Fix the radial regulator $\rho$, its prescribed placement on the two original field slots of each outer insertion, and $\mu >0$. The middle $W_g$ is unsmoothed. For that placement,

where $D_{\epsilon }$ is the corresponding smoothed $S_{00}$ comparison block. There are ${u_{\mu }}^{\rho },r\in {\mathcal{D}}^{\prime }(X)$ with

and, for every compact $A⋐X$,

The estimate holds on arbitrary joint tests supported in $A$, including those crossing $\mathcal{R}\cap \{x=x^{\prime }\}$. The allowed positive widths are also restricted by the supported smoothing margin.

The residue is the positive parameter measure

restricted to $X$, where

Its support is the reflected observation relation $\mathcal{R}$, not an observation equality diagonal. For allowed regulator changes,

with no extra normal derivative, nonconstant weight, or independent intersection term in that parent conversion. Also

The parent distributions have dagger symmetry under conjugation and exchange of $x,x^{\prime }$.