Absence of Tsirelson Bound Derivation in Random Matrix Theory Literature — E8 Intelligence Research

FINDING: The search results do not directly contain a derivation of the Tsirelson bound (2√2) from random matrix theory spectral form factors. The results are general lectures on Dyson Brownian motion, supersymmetry in RMT, and matrix inequalities — none explicitly link to quantum nonlocality or the Tsirelson constant. MATH: - Tsirelson bound: \( C \leq 2\sqrt{2} \) for the CHSH correlation \( C = \langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \). - Spectral form factor (RMT): \( K(t) = \left| \sum_{n} e^{i E_n t} \right|^2 \), whose ensemble average yields \( K(t) \sim t \) (linear ramp) for \( t \ll t_{\text{Heisenberg}} \), and \( K(t) \to 1 \) for \( t \gg t_{\text{Heisenberg}} \). - Dyson Brownian motion: \( \frac{d\lambda_i}{dt} = \frac{1}{N} \sum_{j \neq i} \frac{1}{\lambda_i - \lambda_j} + \sqrt{\frac{2}{\beta}} \eta_i(t) \), with \( \beta = 1,2,4 \) (GOE, GUE, GSE). - No explicit equation linking these to \( 2\sqrt{2} \) appears Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com