Geometric Proof of Kochen-Specker Theorem via Fano Plane and PSL(2,7) — E8 Intelligence Research

FINDING: The Kochen-Specker theorem is proven geometrically using a finite set of rays in 3D real space, directly linked to the Fano plane and the group PSL(2,7), which also underlies the octonion multiplication table and contextuality in quantum mechanics. | MATH: The proof uses 33 rays in R^3 (or 117 in a simpler variant) forming a configuration that admits no 2-coloring (0/1 assignment) consistent with orthogonality constraints. The Fano plane is the projective plane of order 2, with 7 points and 7 lines, each line containing 3 points. PSL(2,7) is the simple group of order 168, isomorphic to GL(3,2) and the automorphism group of the Fano plane. Octonion multiplication is encoded by the Fano plane: each line corresponds to a triple of imaginary units (e₁, e₂, e₃) satisfying e₁e₂ = e₃, with cyclic permutations. The Kochen-Specker configuration is a 3D real realization of this combinatorial structure. | CONNECTION: The Fano plane is a finite projective plane of order 2, whose symmetry Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com