Theorem: II-B Grade S release

For the frozen action, external domain, and contact class of Sections sec:algebra–sec:certificate, the prescribed background (eq:metric), and the declared finite experiment:

1. the complete three-row contact certificate is unchanged:

   $$m_S=(0,16/3,16/3{)}^T,\mathrm{rank}{N}_S=\mathrm{rank}[N_S\mid m_S]=2,$$

   with original minor $64$, fit coefficients $2/3,2/3$, and left kernel $\mathrm{span}\{(1,0,0)\}$;

2. destructive Enter supplies the complete four-code instrument (eq:instrument), consuming both clock names;

3. the dictionary supplies history-event labels and the external labels of II, and its pullback preserves the finite fit and complete response image;

4. the finite table-probe instruments realize that response space as centered binary instruments, with exact correctness on every referenced input;

5. the target-adapted route transports the surviving payload by the identity logical channel, with the resource ledger (eq:peak);

6. complete scheduled influence is contained in the prescribed metric causal relation.

Thus the construction satisfies Definition def:grade. Its contact status remains $\mathrm{SEP}$-finite.

Proof. Item (i) is Theorem thm:frozen. Theorem thm:instrument proves (ii). Definitions def:calibration, (eq:delta), Proposition prop:agreement, and Theorem thm:pullback prove (iii). Theorem thm:operational-embedding proves (iv). Theorem thm:transport and (eq:composed) prove (v). Theorem thm:locality proves (vi).

All names, settings, locations, gates, records, and route resources have been specified. These are precisely the five clauses of the Grade S contract. No additional global contact argument has been supplied.