Lemma

On the open set $U$, the generated tensor is $T=\mathcal{K}u$ in ${\mathcal{D}}^{\prime }(U)$, with

The coefficients are derived from the generated $T$. All $256$ symbolic components are the primary check. Invariant structures are documented and are not an independent basis claim. The operators $P_{\mathrm{tr}}$ are not the corpus trace-reversal operator $\mathcal{P}$. Then ${T^R}_{\mathrm{tr}}=\mathcal{K}{u_{\mu }}^R$ and

with $\mathrm{sd}(\mathcal{K}{u_{\mu }}^R)\le 8$. A missing scaling degree stays Unresolved and is never defaulted to $8$. Wavefront existence is not equality of distributions.