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

Key Points

• To derive and confirm a universal strong-coupling barrier ratio based on spectral geometry.
• Theorem derived from spectral geometry of the Bernoulli manifold.
• Analyses conducted across 17 systems in 8 different physical domains.
• Utilized Čencov uniqueness, Fourier-Parseval, and Fisher-variance identity.
• Confirmed across N=17 systems in 8 independent physical domains.
• Achieved R²=0.999 with zero free parameters.