Manuscript Oai272-A@1 · Oai272-A.tex · section · a40828a0
Hypothesis ledger
Stage 4: hypothesis changes and named-model tests › Hypothesis ledger · lines 1858–1910
| Proposed change | Correct implication | Disposition |
|---|---|---|
| Proposed change | Correct implication | Disposition |
| Bound communication or impose one-way discussion | These are subclasses of the frozen protocol model. | The same zero upper bound is inherited; no game-repetition theorem is needed. |
| Allow extra shared private resources | The initial product-resource rule is removed. | A supplied private bit already changes the task. The theorem does not cover it. |
| Replace represented class by all PPT states | PPT is weaker than the representing-map hypotheses. | Not justified; positive-key PPT examples prevent a universal zero-key conclusion. |
| Allow non-PPT inputs | The state class is enlarged. | No result about a non-PPT zero-key state is proved here. |
| Remove product-free range | The sufficient entanglement certificate is lost. | Zero-key theorem may still apply through ; entanglement needs another proof. |
| Reduce dimensions or | The external construction is changed. | No minimality or dimension reduction is established. |
| Replace two different maps by one repeated channel | Trace preservation and map equality are additional requirements. | Use the completion theorem; do not identify the original dimension-ten maps as channels. |
| Infer failure of every later iterate | A second-iterate statement gives no such implication. | Blocked by logic, Proposition prop:cube, and the separately stated eventual-breaking literature. |
| Compare Families 265, 273, 276, or 277 | Spatial entropy, bosonic entropy, classical capacity, and game repetition have different operational inputs. | No key-rate or protocol-model transfer is made. |
The numbered-family descriptions are documentary comparisons from the supplied plan, not independently proved theorems used in this manuscript ComparisonDossier.