Theorem: Oai282-A finite release

For the independently declared contracts in this paper:

1. a supplied scalar trace potential yields the exact flat-space improvement identities of Theorem thm:improvement;

2. conformal-Killing current conservation follows from symmetry, conservation, and zero trace;

3. affine local Ward actions are unchanged under the spacelike-collar contract of Proposition prop:affine-ward;

4. the named finite Ward identities have the exact defect decomposition and quantitative certificate of Theorem thm:ward;

5. finite admissible correction feasibility is decided by Proposition prop:finitefit, while extension beyond the tested family requires a coverage argument;

6. the optional bounded-score contract gives the simultaneous finite tolerance certificate of Theorem thm:statistics;

7. fixed Ward, modular, or scaling records do not determine the independently appended code recovery or entropy histories of Definition def:completion.

These results do not prove the existence or physical admission of a new $L$ under the Family 282 hypotheses. They do not construct a global conformal action on the entire bounded net, Einstein dynamics, an ultraviolet matching theorem, a gravitational endpoint, or the inherited characteristic quantum coefficient.

Proof. Items one through six are the cited local calculations and finite-interface theorems. Item seven is Propositions prop:recovery-separation and prop:history.

The additional conclusions would require mathematical objects not constructed by those arguments: scalar reconstruction and all mixed-product admission, generator integration and net covariance, a gravitational action and identification, an ultraviolet-to-low-energy matching map, or the separately named characteristic graph construction. The Family 282 statement appears only as Record record:main.