Manuscript Hawk01-B@1 · Hawk01-B.tex · section · cfa976f1
Small corrections: the changed assumption
Small corrections: the changed assumption · lines 1422–1470
Hawk01-B@1#tab:paircomparison
This proposition states explicit entropy hypotheses. Its parameter is not identified with Mathur's pair-amplitude correction parameter. Mathur's small-corrections theorem establishes positive entropy growth from a more specific near-Hawking pair assumption Mathur2009,MathurPlumberg2011. Thermal-looking outgoing marginals alone do not provide those hypotheses.
four distinct comparisons for the constructed process.
| Comparison | Result or explicit boundary |
|---|---|
| Outgoing number statistics | Vacuum/one-particle probabilities are calculated exactly. Selected thermal comparisons have (eq:fullthermaldeviation), not an assumed zero error. |
| Outgoing one-block marginal | Every key or attempt block is exactly message-independent. This does not make their joint state independent. |
| Near-horizon pair state | No near-horizon pair identification or norm-closeness theorem is supplied. The logical-transfer map replaces a fresh-pair production rule. |
| Local semiclassical evolution | No local curved-spacetime interaction deriving (eq:attemptmap) is supplied. Its coupling of residual logical state to an outgoing sector is a phenomenological transfer assumption. |
| Endpoint | The residual is transferred by a separate completion. It is not evolved through the terminal regime using the fixed-background source law. |
The model therefore does not evade the small-corrections theorem while retaining its assumptions. It changes the emission rule and does not assert small corrections to the full Hawking pair structure. At an entropy-decreasing endpoint, the positive-growth hypotheses of Proposition prop:pairentropy cannot all hold.