Theorem: X-A-ST local Grade S release

For the prescribed conical host, supported completion presentation, fixed switch and ramp, fixed Cauchy data, and plateau algebra specified before the calculation:

1. the coordinate and scalar coefficient problems are uniquely constructed through ${\kappa }^2$;

2. preflight is exact on the frozen algebra, while the excluded edge class has the explicit defect (eq:edge) and the coefficientwise obstruction of Corollary cor:edgeorder;

3. the full coordinate intertwiner and off-shell relational covariance hold through ${\kappa }^2$; the switched scalar solution intertwines with unchanged free input;

4. the varied-action identity displays all terms proportional to $1-g$ or $\partial g$, and its auxiliary coordinate counterpart displays the corresponding ramp terms;

5. the mandatory pure-gauge, sourced, and zero-switch diagnostics have the stated exact values and scopes;

6. the coefficients satisfy the retained-past support bound and fixed-$\epsilon$ continuity; their first derivative kernels at a smooth configuration have the specified smooth compact representatives;

7. the finite encoding has a complete destructive-clock instrument, scheduled locality, a target-adapted reference-preserving regular route, and a finite resource/error ledger.

These statements form local Grade S, not Grade E.

No intrinsic conical Green operator, time-ordered product ${\mathsf{T}}_2$, normalized retarded product $R_1$, quantum Ward identity, boundary algebra, or sharp-regulator limit is constructed.

Proof. The host and completion are fixed in Section sec:host. Propositions prop:coordeq and prop:scalarconstruction prove (i). Section sec:preflight proves (ii). Theorem thm:main proves (iii). Section sec:routeII proves (iv). Section sec:diagnostics proves (v). Proposition prop:continuity, Lemma lem:patch, Lemma lem:kernel, and Proposition prop:kernels prove (vi). The finite channel and transport sections prove (vii), including every clause of Definition def:grade.

All field-theoretic operations used are classical smooth coefficient constructions on the completion. The excluded quantum objects have not been defined by any of those operations.