Manuscript En07-B@1 · En07-B.tex · section · 45dff4a1

Conclusion

Release theorem and solution criterion › Conclusion · lines 1988–2031

The repaired endpoint statement is

complete isometry + justified outgoing access + access-preserving endpoint + constant complete complement ⟹ deterministic outgoing quantum recovery, δ_{full} (V_{\infty}) \leq ζ ⟹ ε_{rec} (N_{\infty}) \leq min {1, 2 ζ} .

By contrast,

d_{⋄} (N, T_{ω}) \leq η ⟹ ε_{rec} (N) \geq max {0, 1 - d^{- 2} - η} .

The two boxes concern different channels. Destructive Enter is neither box's decoder. Operational readout-and-drop is partial trace, not a physical annihilation theorem and not a Landauer-cost formula.

The black-hole information problem has therefore not been closed by this release. What has been completed is the finite mathematical certificate and the corrected same-model exit contract. A future physical argument must earn that contract without changing the meaning of recovery, residual, or access.

Displayed formulas in this passage

unlabeled · line 1991
$complete isometry + justified outgoing access + access-preserving endpoint + constant complete complement ⟹ deterministic outgoing quantum recovery, δ_{full} (V_{\infty}) \leq ζ ⟹ ε_{rec} (N_{\infty}) \leq min {1, 2 ζ} .$
unlabeled · line 2009
$d_{⋄} (N, T_{ω}) \leq η ⟹ ε_{rec} (N) \geq max {0, 1 - d^{- 2} - η} .$