Declarations

review. The author field is intentionally empty. Authorized author, affiliation, and contribution metadata are required for a signed submission. Attribution of documentary records to N. Cheung or OpenAI does not assign authorship of this adaptation.

and bibliographic status. Registered manuscripts are identified by their supplied version rather than an invented publication date. Their statements are not independent verification of other programmes. The journal citation to Cheung's Enter article follows the bibliographic record supplied with the question; no unverified update of its publication status is asserted here.

and implementation. The document is one conventional pdfLaTeX source with an internal bibliography. No successful pdfLaTeX execution, numerical run, symbolic-computation execution, hardware compilation, experiment, proof-assistant check, independent referee certification, or journal acceptance of this adaptation is asserted. The mathematical release consists of the stated definitions and proofs.