Asymptotic behavior of tolerated error for disjoint unions

Determine whether the tolerated error per context \(\varepsilon\) for disjoint unions of contextuality configurations tends to a limiting value or tends to 1 as the number of copies increases.

Background

The paper observes that disjoint unions of anticommutation graphs produce contextual configurations whose number of contexts grows multiplicatively while the number of observables grows additively. In particular, three copies of the Petersen graph, corresponding to three Mermin pentagrams, achieve ε=0.707\varepsilon=0.707, the largest confirmed value in the study.

The authors identify the asymptotic behavior of this construction as unresolved: it is not known whether repeated disjoint unions approach a value strictly below 1 or become arbitrarily robust, with tolerated error per context approaching 1.

References

Three copies of the Petersen graph, i.e. three Mermin pentagrams, thus attain \varepsilon = 0.707$, ahead of 3 $ L(K_{3,3})$ at $0.637$ and 2 $ L(K_6)$ at $0.612$ -- stacking copies of the smallest classical examples beats every connected configuration we found, and whether $\varepsilon$ tends to a limit or to 1 as the number of copies grows is open.

— Automated search for highly contextual Kochen-Specker proofs  (2609.19862 - Muller et al., 17 Sep 2026) in Section Discussion and Outlooks