Optimal CHSH Violation at 45° Tied to Crystallographic Rotation Restrictions — E8 Intelligence Research

August 1, 2026Open Access

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Key Points

The study investigates the conditions under which the CHSH inequality is optimally violated and its relationship with crystallographic symmetries.
Analyzed CHSH inequality and optimal violation conditions at specific angles.
Examined crystallographic restrictions and their relation to quantum violations.
Explored geometric harmony constants linked to the optimal measurement angle.
Optimal violation of the CHSH inequality occurs at 45° angle with a quantum value of S ≈ 2.828 (2√2).
Connected the 45° angle to 8-fold symmetry associated with non-crystallographic rotations.
Established a relationship between quantum nonlocality and crystallographic symmetry restrictions.

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Finding optimal CHSH violation at 45° angle demonstrates ties to crystallographic restriction, suggesting implications for quantum geometry.

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Andrew Stewart Caldin (2026) studied this question.

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