Manuscript En07-C@1 · En07-C.tex · section · 3f7e9ebb

Conclusion

Mathematical release and the same-model exit contract › Conclusion · lines 2228–2257

The corrected finite-interface statement is

complete isometry ⟹ joint restoration, constant complete complement ⟺ exact outgoing quantum recovery, d_{⋄} (E, T_{σ}) \leq ζ ⟹ ε_{rec} \leq min {q_{d}, 2 ζ}, d_{⋄} (N, T_{ω}) \leq η ⟹ ε_{rec} \geq max {0, q_{d} - η}, Drop_{Z} Enter_{B} = Tr_{B}, energy \neq = erasure cost \neq = residual leakage, gravitational endpoint implication: conditional .

Hawking's thermal emission result remains a semiclassical result. The finite interface supplies precise questions and certificates for outgoing quantum recovery. It does not answer those questions for gravity by changing the meaning of radiation, residual, observation, or endpoint.

Displayed formulas in this passage

unlabeled · line 2231
$complete isometry ⟹ joint restoration, constant complete complement ⟺ exact outgoing quantum recovery, d_{⋄} (E, T_{σ}) \leq ζ ⟹ ε_{rec} \leq min {q_{d}, 2 ζ}, d_{⋄} (N, T_{ω}) \leq η ⟹ ε_{rec} \geq max {0, q_{d} - η}, Drop_{Z} Enter_{B} = Tr_{B}, energy \neq = erasure cost \neq = residual leakage, gravitational endpoint implication: conditional .$