Internal maps remain required

The source diagonal in (eq:Qkernel) is a defined local operator map. The internal response constructions require more.

For example, the source response and coordinate response have the exact operator structure

The internal variables $s,v$ are governed by these kernels and the prescribed local source incidences. They are not set equal to $u_0,y_0,x_0$.

The two placements in the $B_5$ part of (eq:Btensor), and the coordinate and scalar response maps in $B_8,B_9$, must be composed on their own relations. Their existing tree-kernel pushforwards prove existence of those classical kernels, not a uniform Lagrangian-symbol description of their later characteristic composition.

The present paper does not supply:

1. the complete internal canonical relations with $z$ retained;

2. their microlocal orders and common amplitude identifications;

3. the necessary internal composition and remainder estimates.

These are the first missing data of G2.

The factorwise audit below identifies an additional limitation of an automatic pullback argument. It does not bypass this internal stop or enter G3.