What question did this study set out to answer?

To derive and confirm a universal strong-coupling barrier ratio based on spectral geometry.

March 30, 2026Open Access

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.

Abstract

Derives the universal strong-coupling barrier ratio barrier = d × π/√2 as a theorem from spectral geometry of the Bernoulli manifold (Čencov uniqueness, Fourier-Parseval, Fisher-variance identity). Confirmed across N=17 systems in 8 independent physical domains (R²=0.999, zero free parameters). Domains: magnetism, CDW, electromagnetism, kagome metals, atmospheric physics, astrophysics, nuclear physics, biology.

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Anthony W. Eckert

Damghan University

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

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Abstract

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