Theorem: Operator-route verdict

For the route fixed in Definition def:route:

1. the common ambient space and test locus are named: $W$ and $N={\tilde{\mathcal{N}}}_{\mathrm{att}}$;

2. the copied positive relation supplies diagnostic input covectors, not a common symbol relation;

3. the complete tested local source has a valid differential operator symbol;

4. smooth residual testing alone does not preserve the attachment wavefront information needed by joint composition;

5. the ordinary factorwise pullback shortcut fails on the specified retained numerical incidence;

6. the complete internal symbol relations and the common relation and bundle for (eq:target) have not been constructed.

The first unresolved gate is G2, within the inherited F2/E1/D2/J2 stop.

Proof. The choice (eq:chosenN) gives (i). Proposition prop:zerosum gives (ii). Proposition prop:sourceoperator gives (iii). Proposition prop:testing gives (iv). Theorem thm:pullbackfailure and Corollary cor:shortcut give (v).

The source polynomial and the individual factor symbols supply none of the missing internal composition and uniform common-kernel symbol theorems listed in Section sec:G2. No alternative representation or characteristic prescription has been constructed. This is exactly (vi), and it prevents entry into G3.