Theorem: IX-B-ST local Grade S release

Retain the host contract and Assumptions ass:carrier, ass:tensor, and ass:VIID. Under the finite operational permissions, IX-B-ST establishes:

1. a supported local placement of the source-locked IX-B comparison on the regular part of the prescribed cone, without changing the host or supplying a global conical inverse;

2. the eight unlabelled connected skeletons and the unique fully contracted selected triangle, with factor $2$;

3. a positive reflected-relation residue, its exact local density, and a separated-support observation-diagonal limitation;

4. the derivative–spectator finite part and complete parent-conversion transfer, with order loss $64\to 64+d$ and explicit smooth bounds;

5. an infinite observation-derivative orbit, distinct from the one-parameter parent conversion and from an unrestricted weighted class;

6. equality of the two regularized numerical parenthesizations and the admitted first-stage output (eq:Qpartial), with sign $-2$;

7. finite enclosure propagation, one destructive clock, complete fixed-table channels, and the exact fixed-table channel-distance formula;

8. residual-record and source separations, scheduled locality, exact deterministic no-signalling, and separately certified causal containment;

9. a nonempty regular buffered protocol transporting an unknown quantum payload and its classical calibration history, with arbitrary untouched references and a finite resource ledger.

These statements form local Grade S. They neither remove the VII-C obstruction under its original requirements nor construct either sharp second multiplication. The quantum certificate remains -open.

Proof. Sections sec:host–sec:inputs fix the supported input and prove its geometric distinctions. Theorem thm:skeletons and Proposition prop:unique give (ii). Section sec:geometry gives (iii). Section sec:descendants gives (iv), and Section sec:orbits gives (v). Section sec:association gives (vi). Section sec:finite gives (vii). Sections sec:residual–sec:transport give (viii)–(ix), including the complete error bridge. Theorem thm:transfer completes (i).

Proposition prop:obstruction retains the specified normal-topology incompatibility. Proposition prop:missing identifies the absent binary maps. None of the finite channel results defines them.