Scope, contributions, and dependency policy

The five-qubit perfect code is established quantum error-correction theory Laflamme,KnillLaflamme. Perfect tensors furnish the building blocks of the holographic tensor-network codes of Pastawski, Yoshida, Harlow, and Preskill HaPPY. Experimental five-qubit encoding and decoding are also established Gong. We claim neither a new code nor a first implementation.

The contribution here is a connected operational construction:

The finite statistical certificate concerns the resulting end-to-end logical channel, not a region name or a sector tag.

Cheung's supplied En02-B record already identifies the ideal five-qubit access threshold and distinguishes resource-limited execution from information-theoretic recovery CheungEn02B. Oai280-A supplies the simultaneous three-correlation certificate Oai280A; Oai265-B and Oai290-A supply related finite-confidence and decision architectures CheungOai265B,CheungOai290A. The results needed below are proved locally with their actual finite hypotheses. No supplied companion manuscript is a theorem premise.