Theorem: Oai069-A finite recovery and consistency release

For the explicitly defined benchmark:

1. the finite-monodromy local systems on $E$ have the constructive dagger equivalence of Theorem thm:category;

2. the Fourier matrix realizes its regular-representation character comparison and the finite identities (eq:finite-weyl);

3. the receiver-only programme (eq:decoder) exactly returns the named local-system label and qubit multiplicity subsystem, uniformly over references and gauge correlations;

4. removal of coefficient legs has the sharp all-decoder errors and exact named-effect recovery of Theorem thm:loss;

5. every predeclared complete implemented task has the matrix-unit coverage and simultaneous finite-confidence certificate of Section sec:certification;

6. the independently supplied free scalar has the unique normalized traceless stress in the declared homogeneous conserved class, with two-probe coverage and the finite Ward-defect comparison of Section sec:free.

No item uses the truth of Record record:069. No item identifies the finite abelian functor or the free scalar with a specialization of its connected-simple quantum Langlands equivalence.

Proof. Items one and two are Theorem thm:category and Proposition prop:fourier. Items three and four are Theorems thm:exact and thm:loss. Item five combines Proposition prop:channelcoverage, Lemma lem:choi, and Theorem thm:simultaneous. Item six is Proposition prop:improvement, Theorem thm:stresscoverage, and Proposition prop:ward. Their assumptions and proofs are independent of the source equivalence.