Analytical corrections and submission checks

The construction incorporates the following corrections to the motivating proposal:

1. The transfer family is stated independently of its continuum realization. Full transfer is not falsely reported as a finite-time continuum result.

2. The specified decoder's zero-transfer error is one, whereas the optimal deterministic error is $3/4$.

3. The Bell-input spectra and mutual-information values are labeled as input-specific.

4. The complete noisy complement includes the dephasing register $F$.

5. At full transfer, complete dephasing has optimal recovery error $1/2$, proved for all deterministic decoders.

6. Reference concurrence is calculated using the spin-flip spectrum, not identified with a bath-mode entanglement measure.

7. The extraction parameter is not assumed monotone along a physical time trajectory.

8. The Knill–Laflamme journal citation uses the publisher's Physical Review A article, rather than the conflicting journal metadata displayed on the supplied arXiv landing page.

Before claiming an executed verification package, independently:

• compile until all references stabilize and inspect the PDF;

• construct the isometry matrices directly and check ${V_{\eta }}^{†}{V}_{\eta }=I$;

• trace the full referenced states independently of the displayed marginal formulas;

• compare spin-flip and partial-transpose spectra with the analytical expressions, including $\eta =0,1$;

• verify the noisy isometry with all $EF$ registers retained;

• retain input data, package versions, tolerances, raw outputs, and failures for every executed numerical test.

These are proposed checks, not execution claims. Floating-point agreement is not a rigorous certificate.