Manuscript En07-C@1 · En07-C.tex · section · 3f7e9ebb
The corrected Hawking-to-interface comparison
The corrected Hawking-to-interface comparison · lines 1861–1936
| Semiclassical datum | Finite-interface question | Permissible conclusion |
|---|---|---|
| Thermal occupation factor and absorption probabilities | Does a specified complete accessible channel satisfy a replacement-channel allowance? | Thermal data alone do not prove it. If it is proved, Proposition prop:featureless gives a lower bound, and Corollary cor:compatibility constrains complement allowances. |
| Mass decrease | Is there a complete microscopic prepared dynamics with a justified energy ledger? | An energy ledger is separate from logical recovery. Proposition prop:insufficiency supplies a finite counterexample to their identification. |
| Final disappearance discussed beyond the semiclassical regime | Is there a same-model, access-preserving endpoint map? | Definition def:four states the sufficient obligations; Theorem thm:endpoint is conditional on their construction. |
| Generalized entropy involving horizon area | Does selected entropy determine code recovery? | No: Proposition prop:entropy separates them. The dimension bound in Corollary cor:dimension is not an area law. |
| Particle creation from the incoming vacuum | What is the complete preparation and its purification ledger? | A vacuum emission calculation is not a microscopic logical-channel calculation. Selected residual constancy is insufficient, as Example ex:purifier proves. |
| Semiclassical metric and quantum matter | Has complete gravitational unitary evolution been constructed? | A classical background is an input to the semiclassical comparison. No complete quantum-gravitational dynamics is inferred here. |
| A classical radiation record | Is the record being substituted for a quantum return? | Record-only processing has the obstruction of Theorem thm:classical. A retained quantum output requires its own access declaration. |
The comparison preserves Hawking's calculation as an external semiclassical result. It neither reproduces the Bogoliubov coefficients nor turns a horizon mode decomposition into a physical tensor-factor and receiver theorem.