Universal Barrier Ratio π/√2 from Spectral Geometry of the Bernoulli Manifold

Key Points

• This research aims to derive a universal barrier ratio related to spectral geometry and confirm its applicability across multiple physical systems.
• Derivation of the barrier ratio using spectral geometry principles
• Application of Čencov uniqueness, Fourier-Parseval, and Fisher-variance identity
• Verification across 17 systems in 8 independent physical domains
• Confirmed the barrier ratio with a high correlation (R²=0.999)
• Zero free parameters were found in the derivation
• Validated across diverse domains including magnetism and biology

Abstract