Artem Oktiabrev

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 Polak–Schrijver code has exactly eight private pairs (with the shannon repository, Stages 0–2W)

The lower bound on the Shannon capacity Θ(C7) improved four times between July and August 2026, and every improvement is built on one five-dimensional gadget: the 367-word independent set of Polak and Schrijver (IPL 143 (2019) 37–40) together with eight private pairs — vertices o...