CHSH bounds for contractions by dilation: Tsirelson's bound, the classical bound under a commuting party, and the necessity of noncommutativity
Kernel-checked transfer of the exact CHSH constants for self-adjoint involutions (Mathlib's IsCHSHTuple in a C*-normed ring: the norm of the CHSH operator T = A0 B0 + A0 B1 + A1 B0 - A1 B1 is at most 2*sqrt(2), equals 2 under a commuting party (the equality in a nontrivial real C*-normed algebra; the A (x) Z + sqrt(1 - A^2) (x) X (Halmos 1950), applied with ONE ANCILLA PER OBSERVABLE: the four dilations form a Mathlib IsCHSHTuple on n (x) (C^2)^(x)4, every commutation relation among the four observables transfers to the dilations, the dilated CHSH operator compresses to T, and compression…
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