Corrections incorporated into the statement

The following corrections are part of the mathematical formulation, not merely interpretive qualifications.

1. An arbitrary complete isometry preserves the code on $RB$. It does not, by itself, place a recoverable whole code in $B$.

2. A nonconstant residual obstructs exact recovery from $R$. It neither proves residual-only recovery nor proves that both factors fail separately.

3. Accessible readout leaves the unconditioned residual marginal unchanged when its outcomes are ignored. Conditional residual states and joint correlations can change.

4. A residual that never interacts with the accessible factor and returns no outputs cannot emit information across a fixed cut. A transfer or access change must be specified.

5. Terminal Enter on a previously inaccessible residual requires an explicit new permission. It is not an $R$-only decoder instruction.

6. Readout-and-drop cannot improve or further degrade the pre-existing untouched accessible channel: that channel is exactly unchanged.

7. Empty program ownership is not empty physical environment. Measurement and discarded-record stores must be counted in a complete dilation.

8. A record-only obstruction does not prohibit a decoder that also receives surviving quantum information.

9. Thermal occupations are not a complete channel specification. Conversely, the standard equivalence of Stinespring complements is not being denied.

10. Finite termination is a syntactic property, not a physical evaporation endpoint or a proof of permanent absence.