Proved dependencies

The main theorem uses only:

1. the explicit switched density (eq:Lg) and auxiliary density (eq:Aeps), with the explicit ramp (eq:chi);

2. coefficientwise Cauchy existence, uniqueness, finite propagation, and continuity on the slab (Lemma lem:cauchy);

3. the support conditions $\overline{U}\subset P_g$ and $\overline{U}\subset \{\epsilon <t<T\}$;

4. naturality of metric densities and of divergence-form scalar density operators under genuine diffeomorphisms, transferred to the formal group by Taylor expansion (Lemmas lem:group and lem:natural);

5. formal inversion of a map with leading term the identity;

6. the complete second-order metric pullback (eq:metricpull).

No quantum product, counterterm classification, earlier-series theorem, or finite response matrix is used. The companion manuscripts are quoted in Section sec:prereq for comparison and non-transfer only; none of their theorems is a premise.