Theorem: X-L-ST mathematical release

For the data and domains explicitly fixed in this paper:

1. the free field differential, gauge fermion, auxiliary–ghost Green matrix, and graded causal carrier have the retained normalization;

2. the nonlinear field rules define an off-shell nilpotent classical derivation;

3. the classical master residual gives the exact restricted nilpotent domain ${\mathcal{B}}_{{\mathcal{R}}_{\mathrm{cl}}}$;

4. unchanged unrestricted free-shell descent is obstructed by the explicit compactly tested witness (eq:witness);

5. quotient correction requires both ideal preservation and square-zero, and quantum free-fiber recovery requires the additional presentation data of Definition def:quantuminput;

6. the odd master residual and even reciprocity pairing remain distinct, with restricted obstruction tests and qualified finite feasibility certificates;

7. identical installed X-H-ST report interfaces are recovered exactly, with full residual and reference outputs;

8. finite adaptive composition, regular transport, fit checks, and complete-channel error budgets retain their precise stated scope.

The constructed release is local and classical/operational. The nontrivial interacting quantum presentation remains uninstantiated.

XV-B is not opened as a downstream quantum-admission exit. XVI-N and Route B are not discharged. O.1 stays _CLOSED outside its independently earned scopes. No inherited characteristic quantum coefficient is admitted.

Proof. Propositions prop:gfnorm and prop:Ghb, with Theorem thm:freeBRST, prove (i). Theorem thm:kinematic proves (ii). Proposition prop:masterresidual and Theorem thm:restricted prove (iii). Theorem thm:nondescent proves (iv). Theorems thm:conditionalquotient and thm:conditionalquantum prove (v). Section sec:separation proves (vi). Theorems thm:instrument and thm:reportrecovery prove (vii). Section sec:composition proves (viii).

The standing analytical exits require constructions not present among these results, as recorded in Section sec:boundaries.