Declarations

. The mathematical claims are the stated analytical arguments. Successful compilation, executed numerical optimization, proof-assistant verification, independent technical review, and journal acceptance are not asserted.

status. Published external results are identified by ordinary bibliographic records. Cheung companion manuscripts and OpenAI family descriptions are identified as supplied unpublished records or excerpts. The latter are not represented as independently verified published articles. Responsible authorship and archival accessibility of the unpublished records should be confirmed before submission.

. No novelty claim is made for exact correction, no-hiding, Stinespring dilation, entanglement-breaking channels, or the information–disturbance theorem. Documentary continuation, comparison, and separation relations do not automatically make one manuscript a premise of another.