Declarations

review. The author field is intentionally empty. Authorized author, affiliation, contribution, and submission metadata must be supplied for a signed submission. Citing N. Cheung's articles and documentary manuscript records does not assign authorship of this adaptation.

and attribution status. The bibliography distinguishes the journal article, standard mathematical literature, and internal manuscript records. Internal sheets are cited by the supplied versions or identifiers without invented publication dates or DOIs. The OpenAI catalogue is a separate source collection attributed to OpenAI OpenAIRecord; no theorem from it is a premise, and no family is independently verified here.

scope. The constructions are local, classical, off shell, and polynomial. The finite operational package acts on supplied encodings and matrices. It is not an instrument on an unknown continuum configuration, a quantum-field representation theorem, or a gravitational evolution law.

. This is one conventional pdfLaTeX source with an internal bibliography and no external figures or bibliography files. No successful pdfLaTeX execution, independently executed symbolic or numerical calculation, hardware compilation, experiment, proof-assistant verification, independent referee certification, or journal acceptance is asserted. The mathematical release consists of the explicit statements and proofs above.