Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8

Understand

The 240 root vectors of the Lie algebra E8 lead to a system of 120 rays in a real 8-dimensional Hilbert space that contains a large number of parity proofs of the Kochen-Specker theorem.

• After introducing the rays in a triacontagonal representation due to Coxeter, we present their Kochen-Specker diagram in the form of a "basis table" showing all 2025 bases (i.e., sets of eight mutually orthogonal rays) formed by the rays.
• Only a few of the bases are actually listed, but simple rules are given, based on the symmetries of E8, for obtaining all the other bases from the ones shown.
• The basis table is an object of great interest because all the parity proofs of E8 can be exhibited as subsets of it.