Debugging the proposed identifications

The following corrections are part of the release.

1. A stationary exterior is not a collapse geometry. The main theorem fixes Schwarzschild and a particular horizon boundary state. It does not replace the collapse initial-value problem by a metric name. The conditional local transfer theorem states its peeling hypotheses separately.

2. Hadamard is a regularity condition, not a complete state specification. The selected state is the affine-horizon/Killing-infinity product state. Bulk Hadamard regularity is supplied by the declared external theorem. An arbitrary Hadamard state is not automatically this state.

3. An apparent horizon is not by itself sufficient thermal data. A nonstationary foliation does not automatically provide the normalized Killing generator, affine-frequency state, and propagation estimates used here. A Vaidya extension needs its own precise hypotheses.

4. Horizon detailed balance is not global Unruh KMS equilibrium. The incoming infinity channel is in its vacuum. Greybody scattering produces the occupation ${\Gamma }_{\ell }{n}_{\mathrm{H}}$, not a generally KMS outgoing state.

5. A continuum mode is not a finite number observable. The distribution (eq:numberdensity), the packet observable (eq:packet), and the mode-window counting convention (eq:windowcount) are different objects with their normalizations made explicit.

6. A number observable does not require a bulk stress-tensor calculation. The number covariance has been evaluated directly. The boundary subtraction is not represented as a four-dimensional $⟨T_{ab}{⟩}_{\mathrm{ren}}$ calculation. No bulk stress tensor is evaluated in this paper.

7. A sufficient product criterion failing is not universal nonexistence. The supplied XIV–XV unresolved gates are retained as unresolved, not promoted to proofs that every characteristic construction is impossible.

8. The XVI obstruction is not automatically transported to another background. Changing the metric neither proves a completion of the old prepared insertion nor proves that the old conditional obstruction applies unchanged to a new insertion. Either transfer requires a hypothesis-by-hypothesis identification.

9. A restored kernel subsector is not restored bulk symmetry. The supplied XVI-O record distinguishes its constructed subsector, bulk matched set, and inherited insertion. Those verdicts are not collapsed.

10. A rate does not determine a microscopic channel. Even after (eq:rate), a finite consumer must specify time scheduling, multiple-emission rules, energy cutoffs, coherent amplitudes, and dilation data. Decoder performance and an entropy curve do not provide those choices.

11. Package checks are not proofs. No numerical test, archive manifest, compilation flag, or machine-checking certificate is used as a premise here. The manuscript provides mathematical arguments; it does not claim formal verification.