Both internal placements of K 5

Put

The complete untested mixed kernel of $B_5$ is

\begin{split}
 K_5^{I,J}(a,b,z)
 =\partial_{b^\mu}\Bigl[
 &f(b)\sigma_\varepsilon(a)
 \partial_{a^\alpha}R(b-a)
 \mathsf A^{\alpha\beta,I}\partial_{a^\beta}L^{\mu,J}(a,z)\\
 +{}&
 f(b)\sigma_\varepsilon(z)
 \partial_{z^\alpha}R(b-z)
 \mathsf A^{\alpha\beta,J}\partial_{z^\beta}L^{\mu,I}(z,a)
 \Bigr].
 \label{eq:K5}

The two underlying products are

They are defined tensor-product pullbacks, including at $a=z$.

Their exact finite differential formulas have total kernel derivative order at most four. On regular separated-cone charts their upper conormal order is one. On comparable-frequency, noncharacteristic internal diagonal charts their upper order is $1/2$.

For the first placement, near a nonzero internal null covector, the diagonal piece and limiting flow-out piece are distinct sixteen-dimensional Lagrangians. They intersect cleanly in dimension fifteen and have tangent sum of dimension seventeen. No single ordinary sixteen-dimensional Lagrangian contains both full local pieces there. The second placement has the corresponding reversed internal separation.

The first missing theorem was a uniform internal amplitude description through this transition:

No common characteristic representation was released XIVH.

The clean intersection is not called non-clean. Its tangent-sum count is not XIV-F's linearized matching count.

analytic boundaries

XIV-G's tested source is a local differential operator of order at most two; its local polynomial symbol is not either response symbol. Smooth residual testing can hide attachment-diagonal wavefront directions. Its balanced-kernel counterexample is not a model of the characteristic singularity of $K_{\mathrm{ret}}$.

The ordinary final product of its two individually defined numerical factors fails the sufficient product criterion at the retained covectors. That audit supplies no full-pair nonvanishing theorem XIVG.

XIV-F's rank-two object is a tangent defect. Its excluded matching has actual dimension fifteen and linearized dimension seventeen. The covector-sum map has rank fourteen, one-dimensional fibers, and an isotropic, non-Lagrangian image in $T^{\ast }W$. Its regular-stage formula is

These are boundaries, not relations used in the present amplitude construction XIVF.