Normalization and debugging audit

The following safeguards are incorporated into the statements and proofs.

1. Half-diamond constants. KSW uses a raw stabilized norm. The substitution ${\Vert \mathcal{C}-\mathcal{T}\Vert }_{\diamond }=2{\delta }_{\mathrm{leak}}$ and the output half-norm give $\sqrt{2{\delta }_{\mathrm{leak}}}$, not an unjustified different square-root coefficient.

2. Complete complement. Key purifiers, pending code, excluded radiation, and detector environments are included. Visible-source mass alone does not characterize $F_t$.

3. Internal resource generation. The first isometry creates the key correlation from a fixed preparation. No early-radiation assistance is silently supplied.

4. Sequential consistency. Every $V_t$ acts on the actual previous residual. Previously completed branches emit vacuum; pending branches retain their state when transfer fails.

5. Energy and dimensions. Energy conservation is branchwise. The degeneracy and source-dimension ledger are stated explicitly. They are not inferred from an astrophysical entropy formula.

6. Endpoint accounting. The main endpoint emits all residual basis information. The retaining counterexample explicitly keeps a logical memory and therefore has a different endpoint condition.

7. Entropy-input distinction. Pure-input radiation entropy histories can coincide while the channels differ. Reference and mixed-input data distinguish the examples.

8. Marginal compatibility. One transfer excitation across the attempt sequence imposes ${\sum }_j{w}_j\le 1$. Arbitrary independent exact thermal weights are not promised.

9. Thermal versus near-horizon state. The local trace-distance calibration is not a proof of near-Hawking pair creation or local semiclassical coupling.

10. Coherent versus destructive access. Reading the key or the occupied-sector flag need not measure the logical basis. Reading every occupation rail does, and has a different exact optimum.

11. Single input versus worst case. Approximate Bell fidelity and mutual information use explicit dimension-dependent conversions before any diamond claim.

12. Regulator completeness. Overflow is flagged, not postselected. A general quantum cutoff uses its referenced projection allowance.

13. Reproducibility. The small example is specified by exact matrix entries and rational parameters. No unperformed numerical solver or compilation run is claimed.

14. Scope. Neither the sequential model nor the entropy counterexample disproves island reconstruction or solves realistic evaporation.