Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

Corrections required by the proposed plan

Background, terminology, and debugging › Corrections required by the proposed plan · lines 170–278

Hawk07-A@1#tab:debug

{}1.12

used throughout Hawk07-A.
Proposed statement	Correct statement
Proposed statement	Correct statement
A large, nonconstant complement implies high leakage and a nearly constant accessible channel.	Residual dimension alone proves neither assertion. Nonconstancy obstructs exact full-code recovery, but can be arbitrarily small. An accessible replacement comparison needs its own estimate.
Leakage and recovery error peak at the Page cut.	For the nested release used here, both optimal recovery error and complete leakage are nonincreasing. An intermediate entropy maximum cannot be identified with their maximum.
The dimension of the accumulated record defines the neck.	A classical outcome alphabet is not coherent quantum storage. The entropy comparison uses the dimensions of the unmeasured factors.
The receiver is late radiation $R$ , while the recovery theorem uses late radiation and early memory.	We write late radiation as $P_{k}$ , early memory as $E$ , and the entire accessible interface as $R_{k} = P_{k} E$ . There is no hidden grant of $E$ .
An early reference entangled with the diary is accessible.	The diary's untouched test reference is $Q$ , never accessible to the decoder. Accessible $E$ purifies an independent old-vault register $H$ .
The pure Page–Sen mean applies to the early-entangled preparation.	After tracing $E$ , the vault is a random rank- $h$ projector divided by $h$ , not generally a Haar pure state.
Enter on late radiation permanently blocks recovery even if $E$ remains quantum.	The permanent entanglement-breaking bound concerns a purely classical returned interface. A classical record plus surviving quantum $E$ can recover, as teleportation demonstrates.
There is no second commuting representation of the logical matrix algebra anywhere on the joint space.	Independent matrix algebras may commute. What is excluded is two commuting, code-preserving representations that both implement the same unknown logical input.
A half-diamond bound is a full-diamond bound.	We use $d_{⋄} = \frac{1}{2} ∥ \cdot ∥_{⋄}$ . The full-diamond error is twice the half-diamond error.
Readout and $dropBit$ remove the physical complete complement.	They remove returned names. A complete realization retains unreturned record stores and measurement environments.
Fixed residual constancy reconstructs every independently variable residual state.	Constancy removes logical input dependence. Recovery of a new, independently variable $B (B)$ is a different task.
A successful postselected branch is a deterministic decoder.	Its success probability and failure branch must be retained. An input-dependent normalized branch is not a linear CPTP channel.

These are mathematical corrections, not changes in physical interpretation alone.