Contextuality and Kochen-Specker colorings of integer vectors

Abstract

This note exhibits a new set of 85 three-dimensional integer vectors that has no Kochen-Specker coloring. These vectors represent rank-1 projection matrices with entries in the rational subring $\mathbb{Z}[1/462]$. Consequences are given for (non)contextuality in a purely algebraic sense for partial rings of symmetric matrices over finitely generated rational subrings and $p$-adic integers.Comment: 8 page