Tsirelson Bound from Causal Locality in Barandes' Stochastic-Quantum Correspondence — E8 Intelligence Research

FINDING: Barandes' Stochastic-Quantum Correspondence (SQC) reformulates quantum theory as an indivisible stochastic process, with the Tsirelson bound emerging as a consequence of causal locality constraints on the underlying stochastic dynamics rather than as an axiom. MATH: - Tsirelson bound: S ≤ 2√2 ≈ 2.828 (CHSH inequality maximum for quantum correlations) - Classical bound: S ≤ 2 - Algebraic ratio: 2√2 / 2 = √2 ≈ 1.414 - Barandes' construction: Hilbert space emerges from a configuration-space stochastic process with indivisible (non-Markovian, non-divisible) transition kernels - Key structure: The stochastic matrix Γ(t) satisfies Γ(t₁+t₂) ≠ Γ(t₁)Γ(t₂) in general (indivisibility), but admits a Hilbert-space representation via a "correspondence map" to unitary evolution - The Tsirelson bound arises from the requirement that the underlying stochastic process respects a causal (Lipschitz-continuous, local) structure on configuration space CONNECTION: - √2 is the diagonal-to-side ra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com