Paper T21: Triadic Coherence and Modified Bell Inequalities: A Real-Valued Framework for Deterministic Quantum Correlations

In standard quantum mechanics, Bell inequality violations are interpreted as evi-dence against local realism. The CHSH inequality, violated up to Tsirelson’s bound of2√2,[3] appears to preclude deterministic hidden-variable theories. However, within theframework of Holosphere Theory, quantum correlations are reinterpreted as emergingfrom angular coherence propagation in a discrete, triadic lattice of spinning Planck-scale spheres. This geometric substrate enables deterministic, local mechanisms toreplicate and exceed standard quantum correlations. In this paper, we derive a real-valued, triadic Bell inequality with a maximal violation of 2√3, arising from coherencevectors in a 3D angular strain space. We show that this bound naturally emerges fromthe eigenstructure of triadic rotation operators and propose concrete experimental testsusing photonic orbital angular momentum modes and strain-aligned NV centers in di-amond. [7] These results suggest that quantum entanglement may be a manifestationof deterministic angular strain coherence rather than nonlocal probability collapse.