FINDING: Tsirelson's bound is the algebraic maximum quantum correlation \ (22\) for the CHSH inequality, proven via operator norm constraints on anticommuting observables. | MATH: CHSH inequality classical bound = 2; quantum maximum = \ (22 2. 828\) ; Tsirelson's bound emerges from \ (\|A₁B₁ + A₁B₂ + A₂B₁ - A₂B₂\| 22\) for self-adjoint operators \ (Aᵢ, Bⱼ\) with \ (\|Aᵢ\|, \|Bⱼ\| 1\) and \ (Aᵢ, Bⱼ = 0\). The proof uses the algebraic identity \ ( (A₁ + A₂) B₁ + (A₁ - A₂) B₂\) and the C*-algebra norm inequality \ (\|X + Y\|² + \|X - Y\|² 2 (\|X\|² + \|Y\|²) \). | CONNECTION: \ (22\) is not a golden ratio constant, but the ratio \ (22 / 2 = 2 1. 414\) appears in crystallographic root systems (e. g. , \ (Bₙ\) lattice spacing) and in the diagonal of a unit square. The bound's algebraic structure involves anticommutation relations reminiscent of Clifford algebras, which underlie spinor representations and certain Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Mon,) studied this question.