Debugging summary and final theorem

The following corrections are necessary for a coherent release:

1. The interaction bound must apply to one aggregated term per support, or be replaced by an explicit interaction-density bound.

2. $Z_A$ must include both crossing-edge endpoint sets for the stated factor $2$.

3. A universal area law is a documentary record here, not an assumption disguised as a definition.

4. Reading a proof architecture is not verifying the proof. The accessible supplied passages do not certify every stage.

5. The explicit constant is not the only unverified object; the earlier analytic estimates must also be checked.

6. A positive spectral constraint is not a graph-local constraint system.

7. Replica moment identities do not supply quantitative conditional-information transport.

8. Polynomial PEPS bond dimension does not by itself give efficient tensors, contraction, preparation, or a uniform constant-area bound by the elementary cut argument.

9. Dropping uniqueness unrestrictedly is not merely an open generalization: it permits the volume-law counterexample above.

10. A full-system gap does not imply a uniform restricted gap.

11. The Rényi exclusion must distinguish $\alpha >1$ from $0<\alpha <1$, and complementary mutual information already equals twice the entropy.

12. The dimer spectrum is $({\cos }^2\theta ,{\sin }^2\theta )$, with maximum entropy $\log 2$.

13. An instantaneous ground-state path is not evolution generated by its parent Hamiltonian.

14. A forty-shot limitation must name the confidence procedure; it is not a universal information-theoretic sample lower bound.

15. Zero simulated bias is not a physical calibration certificate.

16. The existence of the technical manuscript XV-B is distinct from opening its downstream coefficient-admission exit.