A documentary audit, not a universal impossibility theorem

A complete certificate for the observable studied here needs:

1. a named background and normalized time;

2. a named quantum field;

3. a specified state with an admissible two-point distribution;

4. a defined number or detector observable;

5. a scattering or propagation identification;

6. an evaluated expectation and any required regulator or late-time limit.

The supplied record does not exhibit this certificate in any of the pre-existing landmarks discussed below. This is a restricted documentary conclusion. It does not assert that no future construction, or no unexamined manuscript, can provide it.

{}1.14 {@{}p{0.23}p{0.70}@{}} Landmark or cluster & Supplied result and the non-transfer boundary
Landmark or cluster & Supplied result and the non-transfer boundary

I–V; I thm:main & The excerpts specify finite Born semantics and distinct representation or instrument problems. They do not construct the Schwarzschild wave equation, the affine horizon state, or its number expectation. A measurement rule consumes an observable and channel; it does not select the field state.

VI–VIII; VII-F prop:spacelike; VIII-B thm:dictionary; VIII-C thm:C5 & The supplied theorems concern relational descent, a specified conical family, spacelike slices, and support for prescribed block channels. The cited constructions select neither the black-hole horizon nor the state used in this paper. A backward channel-support set is not identified with a spacetime causal past or an island.

IX–X & According to the supplied summary, these are sharp-product and ramp-convolution models. Their remainder coefficients are not identified with an asymptotic scalar number covariance.

XI-A lem:compatibility & The excerpt proves the classical necessary condition $({\partial }_{\mu }{g}_{\mathrm{XI}}){T_0}^{\mu \nu }=0$. Here $g_{\mathrm{XI}}$ denotes the inherited source coefficient, not the metric $\mathrm{g}$ of (eq:metric). The condition is not a state, a Bogoliubov calculation, or a stress-tensor expectation.

XII–XV; XIV-I, XIV-J; XV-B & The excerpts distinguish defined internal kernels, partial off-characteristic references, and the unresolved full characteristic map. XIV-J stops at J2 without quantum admission. XV-B exists as a technical interface manuscript but does not supply the inherited full map or its admission. None of these statements constructs (eq:numberdensity).

XVI-N; XVI-O & The supplied obstruction in XVI-N is conditional on its declared prepared-source class. XVI-O constructs a kernel subsector under a specified prescription while retaining bulk and insertion limits. A constructed kernel Ward subsector is not bulk symmetry restoration, and a counterterm is not the present emission observable. O.1 remains NOT_CLOSED in the supplied record.