Mathematical and physical corrections incorporated

The following corrections are part of the manuscript's definitions and proofs, not outstanding claims.

1. Normalized hypotheses. The states ${\tau }_{b\mid j}$ in (eq:taudef) contain a factor $1/2$; the optimal-score prefactor is consequently $1/8$.

2. Correct null hierarchy. Message independence gives $1/2$. A complete trusted-qubit measure-before-query channel gives $3/4$. A general semiclassical null gives its certified supremum (eq:physicalnull). These bounds are not interchanged.

3. Complete attempts. The primary score retains failed capture and apparatus branches. Input-dependent flags are included in the state rather than treated as harmless heralds.

4. Exact versus quasistatic geometry. An instantaneous Schwarzschild sequence is not an exact evaporating spacetime. The adiabatic indicator does not supply its own channel-error theorem.

5. Energy eigenmodes versus packets. Exact energy-shell conservation is proved in the declared energy-eigenmode regulator. Finite-time packet transfer requires an additional approximation certificate.

6. Finite source energy. An unbounded thermal occupation tail is not emitted from a finite mass in the exact completion. The finite $L$ obeys (eq:energycut); the thermal discrepancy and number moments are displayed separately.

7. Full covariance. Packet orthogonality does not justify dropping the off-diagonal matrix elements of $K$.

8. Quantum versus classical cutoff errors. A commuting Gaussian cutoff has exact trace-distance tail ${\delta }_L$. A general joint quantum state uses the gentle-projection allowance (eq:cutofferror).

9. Spectra versus channels. The completions are given by isometries and complete partial traces, not arbitrary additive density-matrix corrections. Conservation, positivity, and normalization are proved.

10. Recovery certificate on all operators. Constant complement must hold on every matrix unit, including the ${\sigma }_y$ direction, not only on the four square preparations.

11. Access and resource pricing. The early key and coherent radiation are declared resources. Destructive number records have their own strictly smaller optimum in (eq:numberoptimum).

12. Statistical unit. The sample size counts complete independent attempts. A simulated source and an actual astronomical source are not identified.

13. Unresolved dependencies. Partial source records and quotient criteria are not substituted for missing microscopic dynamics or missing characteristic distributional constructions.