Theorem: IV-B interface release

Fix the conical geometry (eq:metric), the developing patch, the flat-completion prescription, and the three independently defined represented models above. Then:

1. each model has the complete Ramsey–Enter channel (eq:composed), with a consumed finite clock context, a classical record, surviving rods and matter, and arbitrary untouched references;

2. the three positive-contrast conclusions hold in their stated, separate regulator regimes, together with their exact interpolation-off controls;

3. Model 1 admits the stated edge removal with pointwise complete trace-norm convergence; Model 2 admits complete diamond-norm spectral convergence at each fixed finite $M$; Model 3 retains its selected finite $\Lambda ,M$;

4. compact coefficient and curvature pairings agree with their conical-patch readings under the declared completion;

5. finite carrier/control networks with causal block certificates obey the schedule-past bound, and the target-adapted route implements exact complete null transport of a finite payload;

6. the records do not uniquely determine the geometric dictionary, and neither a quantum return of the consumed clock nor a finite canonical commutator follows.

Thus a Grade-S interface adaptation is constructed. An intrinsic-cone field adaptation and a compact causal implementation of the global apparatuses are not established. Grade E is not constructed.

Proof. The operator and record assertions are Proposition prop:A1, Theorems thm:model1, thm:spectral-channel, thm:model2, and thm:model3. Proposition prop:edge identifies the precise unbounded-model topology. Lemma lem:patch proves the geometric pairing statement. Theorems thm:instrument and thm:composition prove the complete clock attachment.

Theorems thm:locality and thm:transport give the finite causal-wire and transport assertions on their explicitly certified interfaces. Propositions prop:three-separations, prop:event, and prop:nonunique establish the remaining separations. Proposition prop:no-global-transfer explains why the stronger field and implementation assertions are not deductions from these results.