{"id":"palomar/PALOMAR-2026-10-28-000030","url":"https://github.com/stalex444/tsirelson-contractions/tree/ef7bd3b81c4cda7030329bc1057df7b00e9efb9b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000030-v1.json","repo":"https://github.com/stalex444/tsirelson-contractions","tags":["quant-ph","math-ph","math.OA","msc:81P40","msc:81P15","msc:47A20","msc:46L05"],"score":0,"title":"CHSH bounds for contractions by dilation: Tsirelson's bound, the classical bound under a commuting party, and the necessity of noncommutativity","trust":"high","domain":"quant-ph","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"quant-ph","summary":"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…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Quantum generalizations of Bell's inequality","identifier":"Letters in Mathematical Physics 4 (1980) 93-100","relationship":"formalizes"}]}