Smallest Kochen-Specker vector set in three dimensions
In plain words
The Kochen-Specker theorem uses a finite set of directions in 3D space to prove that quantum outcomes cannot all be fixed in advance. The smallest such set has between 24 and 31 directions, and the exact number is unknown.
Precise statement
A Kochen-Specker set in $R^3$ is a finite set of vectors admitting no $0/1$ assignment in which every orthogonal triple has exactly one 1 and no two orthogonal vectors are both 1. Determine the minimum size $n_{\min}$; known $24 \le n_{\min} \le 31$ (lower bound by SAT solving with computer algebra, Li, Bright and Ganesh, arXiv:2306.13319, and independently by Kirchweger, Peitl and Szeider, 2023; upper bound from the 31-vector Conway-Kochen set).
What would settle it
An exhaustive, computer-certified search of orthogonality graphs with 24 to 30 vertices, or an explicit smaller set.
Status in the literature
Unverified note
Lean-checked certificates for the geometric half of the 24-vector bound appeared in July 2026 (arXiv:2607.26413); the bound itself is unchanged.