Corrections to the proposed reading

The number $1/5$ is an unhalved trace-norm gap; the conventional trace-distance gap is $1/10$.

The dimension-ten maps are not silently trace-preserving channels. Normalize their Choi state by $\mathrm{Tr}Z$.

The represented-class hypothesis is stronger than merely being PPT. Some PPT states have positive distillable key.

Common local transcript factors are required simultaneously for all four bit branches. Separate branchwise factorizations without shared local pairs are insufficient.

A complete public record cannot be replaced by a selected bit, a finite prefix without a justified limit, or a transcript with inconvenient messages removed.

Completion on the actual input is not completion on the probe input. The positive-filter argument explicitly removes auxiliary defaults.

Unrestricted joint local processing of copies is retained: tensor closure applies to arbitrary effects on all of each party's copies, not merely product effects across copies.

Restricting communication preserves an already universal impossibility statement. It does not require a new entangled-game theorem.

Product-free range certifies entanglement, not the key gap by itself, and it is not necessary for general entanglement.

The full channel Choi matrix contains product vectors from its absorbing flag. Its entangled corner, not its entire range, certifies non-entanglement-breaking square.

A Bell-overlap test for recovery cannot witness PPT entanglement. The required separating observable must be specified independently.

An entanglement witness is not a separable decomposition. The witness algorithm's input promises and non-polynomial cost exposure must be retained.

The supplementary combinatorial integer checks and the dimension-ten arithmetic certificate are distinct proof components.

The inspected Comparator statements contain sorry. Their scope note is not evidence of completed formal proofs, and neither statement formalizes $K_D(\rho )=0$.

Finite statistical coverage and universal mathematical certification are different evidence types. No finite sample enumerates all copy numbers and protocols.

A second-iterate counterexample is compatible with later entanglement breaking and supplies no gravitational conclusion.