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This research aims to derive a universal barrier ratio related to spectral geometry and confirm its applicability across multiple physical systems.

March 30, 2026Open Access

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

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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

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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