The shape of a private pair redistributes its cost: private pairs as a property of the code (with the shannon repository, Stages 2-2W-2)

A companion note (doi:10.5281/zenodo.22979509) proves that the Polak–Schrijver 367-word code in C7⊠5 admits exactly eight private pairs. This note explains why the number of private pairs is not, by itself, a lever for the gadget recursions behind the recent lower bounds on Θ(C7). The forbidden and the penalised regions a pair creates are the intersection and the union of two closed neighbourhoods, so their sizes add up to 2·3d (inclusion–exclusion): the shape of a pair moves cost between the two regions but cannot lower it. We list the five shapes in C7⊠5 with their costs and the largest independent set found carrying each; show that every 367-word code we can reach carries only the two-coordinate shape; that up to automorphism every nine-pair code we can reach has the same sixteen forbidden regions; and that against all of them the best auxiliary set found has 366 words, one short — 3-opt optimal, and not proved maximum. The record contains the note (PDF) and the archive of the repository at tag v1.2.0: sets, verifier, scripts, preregistrations, and the machine reconciliation of every number in the note.