Theorem: Oai280-A separation and finite certification

For an independently declared finite sector record, the finite operational contracts in this paper establish:

1. exact schedule support containment for the specified complete finite network;

2. tensor-free snapshot determination exactly under the UCP factorization conditions of Theorem thm:comparison;

3. full-code exact recovery exactly under the constant complete-complement condition of Theorem thm:exact;

4. a simultaneous finite-confidence half-diamond certificate for the declared label-tagged qubit channels in Theorem thm:main;

5. explicit nonidentification of recovery and entropy histories from fixed sector, fusion, and extension records;

6. separation of conformal energy estimates from an absent dimensionful gravitational identification.

These conclusions neither verify Family 280 nor instantiate Family 290-02, a gravitational endpoint, an island, or a Page curve. They do not construct the inherited full characteristic map or admit its quantum coefficient.

Proof. Items one through four are Proposition prop:schedule, Theorem thm:comparison, Theorem thm:exact, and Theorem thm:main. Item five follows from Propositions prop:goodbad–prop:histories, Proposition prop:fusion, and Theorem thm:extensionseparation. Item six follows from the energy estimates and Proposition prop:energyscale.

The remaining targets require data of different types that do not occur in the hypotheses or constructions of those proofs. In particular, the universal VOA correspondence appears only in a source-record environment, and no modular or characteristic distributional operation is performed.