Corrections to tempting but invalid shortcuts

The following repairs are part of the mathematical formulation:

1. Negative conditional entropy of a selected late packet is stated separately; it is not inferred from global unitarity alone.

2. The structural logical space is distinguished from the fixed-pair message slice. Full partner operators are not claimed to act invariantly on that slice.

3. Partner reconstruction is one linear prescription on the whole declared structural space, not unrelated state-by-state rules.

4. A reconstructed partner is not treated as an additional commuting quantum copy.

5. Complete complements retain joint residual outputs and fixed preparation purifications.

6. Entropy, spectrum, record, Choi, and diamond-norm certificates are not identified.

7. The distilled-purifier calculation uses the original proxy before considering a transported observable assignment.

8. Geometry, state regularity, detector realization, and backreaction remain independent physical obligations.