Declarations

scope. The proofs concern explicit finite interfaces, complete finite-dimensional channels, prescribed local kinematics, and non-determination witnesses. The illustrative reset-channel limits do not constitute the native incidence continuum limit.

scope. Unpublished manuscripts are cited by supplied version and filename. Their descriptive titles are not expanded where a verified full title was not supplied. Native geometric certificates and unprinted predecessor proofs are not theorem premises.

and static debugging. The source uses standard pdfLaTeX packages, an internal bibliography, and no external figures or input files. Its notation, theorem references, and finite/continuum quantifiers have been organized to avoid the identified interface confusions. No successful pdfLaTeX execution, proof-assistant verification, independent symbolic or numerical execution, referee approval, or journal acceptance is asserted.

. Equation (eq:classical-channel) is a finite semantic channel definition, not an executed program or a verified native Enter-calculus compilation. Hardware realization, qubit occupancy, gate synthesis, and implementation error require separate certificates.

. The manuscript is anonymous. Citation of N. Cheung does not establish authorship of this manuscript. A signed submission must supply the responsible author's authorized metadata.

. A signed submission should provide stable copies or archival locations for the cited unpublished versions. The mathematical proofs here do not require their unprinted arguments.