Declarations

and identifier. The requested identifier Oai119-A is used for this development. It does not attribute authorship to N. Cheung or assert registration or endorsement by another series.

scope. The principal result is the printed exact certificate for $n=2,\rho =1/2$, together with its classical information corollary. Supporting scalar and probabilistic results are proved locally. The universal Family 119 assertions are not verified or assumed.

. External manuscript assertions are identified as such. Cheung's supplied manuscripts are cited for their stated comparison interfaces, not imported as proofs of contraction. No exhaustive corpus scan is claimed.

and computational status. No successful Lean execution, execution of the appendix, independent numerical run, successful pdfLaTeX build, referee approval, or journal acceptance is asserted. An unexecuted program is not substituted for the printed integer-square proof.

standing boundaries. For the distinct programmes described in the supplied dossier, this manuscript establishes no result changing their status:

This does not deny the existence of technical continuation manuscripts or their separately scoped interface theorems. No inherited quantum coefficient is admitted here.