Theorem: VII-A-ST local Grade S release

On the supported presentation and finite interface above:

1. the specified action-level switch and unswitched harmonic Cauchy prescription define unique scalar and coordinate coefficients through second order;

2. the first-order plateau cancellation and second-order intertwiner hold under ${\mathcal{G}}_U$, with the full transformation of $k$;

3. the larger compact class retains the exact defect (eq:defect), a negative witness, and the coefficientwise no-higher-repair obstruction;

4. the named plateau coupling jet is stable and has an explicit nonempty sourced subclass;

5. metric and switch dependence obey the truncated-past bound; causal switch agreement gives equality, while a common observation plateau alone does not;

6. the Cauchy-data-preserving classical comparison map is unique and satisfies its cocycle and common-plateau equivariance;

7. the finite evaluation table has a complete destructive instrument, declared dictionaries, a controlled compression limit, and reference-preserving causal transport;

8. no quantum product, quantum Ward identity, radiative coefficient, or counterterm-separation certificate is supplied.

Items (i)–(vii) satisfy Definition def:grade. The repair remains plateau-restricted.

Proof. Propositions prop:scalar and prop:coordinates give (i). Theorem thm:first, Lemma lem:plateaucov, and Theorem thm:second give (ii).

Propositions prop:defect, prop:witness, and Corollary cor:nohigherrepair give (iii). Propositions prop:jetstable and prop:nonempty give (iv).

Propositions prop:support, prop:cutoffequal, and prop:memory prove (v). Proposition prop:classicalcomparison proves (vi). Sections sec:table–sec:transport prove (vii).

Every field-theoretic construction used in these proofs is a classical smooth coefficient construction. The additional quantum objects named in (viii) have not been defined or evaluated here. This is a release limit, not a theorem excluding all future constructions.