Code decoding is not a quantum-return decoder

The map $\mathrm{Dec}$ in Theorem C6 interprets canonical classical code words as geometric descriptions and ignores retained histories. It is not a CPTP decoder from an independently justified restricted quantum output. The complete reversible permutation can be inverted when all its registers are retained; this does not certify recovery from the current code block after histories are discarded.

For example, the completion

retains input distinctions in the second register when $f$ merges two inputs. Ignoring that register loses those distinctions. Even a coherent basis-history copy is not a destructive measurement performed by the scheduling word.

The following standard finite statements make the distinction precise. They are independent comparison results, not premises of C1–C6.