Theorem: En05-C release

On the domains specified in this manuscript:

1. snapshot determinacy for all global states, UCP local factorization, and Heisenberg regional containment are equivalent;

2. the factorization is unique and stable under independent matrix references;

3. center probabilities are part of the affine snapshot, and restricted preparation tests have the exact annihilator criterion;

4. the normal von Neumann comparison holds for all normal states;

5. the finite ${\mathbb{Z}}_2$ net, its centerful regional algebras, complete instruments, and successful and failed locality tests are explicitly constructed;

6. specified internal Kraus devices give one-layer containment, ancestral factorization, matched replacement invariance, metric upper bounds, and exterior-fixing no-signalling;

7. regional channel restrictions alone do not specify complete devices, and shared central data obstruct unrestricted independent regional changes;

8. a product-preserving bounded-sequence observable limit and an exact finite-mode spatial gauge refinement limit are constructed;

9. continuum domain of dependence transfers under the displayed matched spacetime-realization assumptions.

No general relativistic gauge-field scaling limit or physical frame-covariance conclusion is part of this release.

Proof. Items (i)–(ii) are Theorem thm:comparison and Corollary cor:reference. Item (iii) is Proposition prop:centers and Proposition prop:relative. Item (iv) is Theorem thm:normal. Item (v) is Proposition prop:gaugenet, Theorem thm:thetaalgebras, and the explicit examples. Item (vi) is Theorems thm:onelayer, thm:ancestry, thm:matched, thm:nosignalling, and Corollary cor:metric. Item (vii) is Propositions prop:extensiongap and prop:sharedcenter. Item (viii) is Theorems thm:sequence, thm:refinementnet, and thm:operationalrefinement. Item (ix) is Theorem thm:continuum.