Declarations

dependency. Finite matrix and channel facts are used throughout. Stinespring dilation is a standard external structure theorem. The approximate information–disturbance estimate is explicitly imported from KSW; its normalization conversion is proved locally. No Cheung companion is required as a premise for the local finite proofs.

provenance. The unpublished Cheung entries below identify supplied manuscript IDs, versions, and selected labels. No publication venue, DOI, date, or fuller title is invented for those entries. Their complete proofs and corpus-wide relationships have not been independently audited here. The catalogue sheet is cited only as supplied documentary material.

scope. No microscopic gravitational model, collapse-channel construction, coherent asymptotic receiver, thermal implementation optimum, Page curve, firewall resolution, holographic dictionary, or spacetime-emergence theorem is released.

analytic scope. No missing characteristic product is defined. No ${R_1}^{(1)}$ is admitted, and no Ward differential is applied to an absent coefficient. The admission-dependent XV-B exit is not opened. XVI-N is not discharged. O.1 remains NOT_CLOSED.

and submission. The source is written as one standalone pdfLaTeX file with an internal bibliography and no external figures or data files. No successful pdfLaTeX execution, proof-assistant verification, numerical execution, independent referee review, or journal acceptance is asserted. Before submission, the author should confirm metadata, archive the cited unpublished versions, run the build to convergence, check all references and equation links, and obtain independent checking of the mathematical arguments. These administrative and verification requirements do not replace any missing physical theorem.