WWDC26：2026 年 6 月 8 日至 12 日 (太平洋时间)

A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this contradiction requires only 13 vectors, a remarkably low number for 8 dimensions.

The design spectrum of a simple graph $G$ is the set of positive integers $n$ such that there exists an edgewise decomposition of the complete graph $K_n$ into $n(n - 1)/(2 |E(G)|)$ copies of $G$. We compute the design spectra for 7788 6-regular graphs with 12 vertices.