Journal of Liberated Mathematics

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Published May 13, 2025 | Version v10
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Spectral Coherence and Geometric Reformulation of the Riemann Hypothesis via Torsion-Free Vector Waves

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  • 1. Independent researcher

Description

We introduce a geometric and spectral reformulation of the Riemann Hypothesis based on the analysis of a complex vector-valued function, the Function of Residual Oscillation (FOR(N)), defined by a regularized spectral sum over the nontrivial zeros of the Riemann zeta function. This function reveals a torsion structure in the complex plane that is minimized under the critical-line condition Re(ρ) = 1/2. By analyzing the directional stability of the associated vectors, we demonstrate that the Riemann Hypothesis is equivalent to the global vanishing of the spectral torsion function τ(N). The approach combines geodesic vector dynamics, coherence cancellation, and asymptotic convergence, providing a new structural perspective on one of the most fundamental problems in mathematics.

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References

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