Exact value of the real Grothendieck constant

Determine the exact value of the real Grothendieck constant K_G, a fundamental constant in functional analysis that governs the maximal quantum-versus-classical advantage in two-player XOR games and the integrality gap of certain semidefinite programs.

Background

The Grothendieck constant K_G is central to functional analysis, quantum information, and theoretical computer science. It characterizes the maximal violation of Bell inequalities for two-player XOR games and the integrality gap of specific semidefinite programs.

Although there are strong numerical bounds and significant advances on both upper and lower bounds (e.g., Krivine’s upper bound and the Davie–Reeds lower bound, with further refinements), the exact value of K_G has not been determined. This paper improves the Davie–Reeds lower bound but the exact constant remains unknown.