No finite-code identification

A type-$\mathrm{III}$ algebra is not replaced by a finite tensor factor with a global density matrix. A proposed bridge to the finite channel module must specify:

1. the logical algebra and its actual inclusion or encoding;

2. normal preparation, access, and recovery maps;

3. the complete dilation or a separately justified complement;

4. a reference-stable error topology and comparison allowances;

5. the relation of the modular defect $T$ to the chosen task.

No such bridge is supplied merely by Theorem thm:bounded. The separate existence results for ergodic states on type-${\mathrm{III}}_1$ factors retain their own hypotheses MarrakchiVaes.