Number Theory

    

A Rigorous Proof of the Riemann Hypothesis via Geometric Characterization of the Dirichlet Eta Function: Half-Angle Residual Dynamics and Invariant Level-Crossing Barriers ```[span_0](start_span)[span_0](end_span)

Authors: Ali Rıza Şahin

This paper establishes a rigorous real-analytic and geometric framework governing the distribution of the non-trivial zeros of the Dirichlet eta function $eta(s)$ across the critical strip $mathcal{S}={sinmathbb{C}:00$ simultaneously across dual orthogonal projections with an exact $pi/4$ phase shift. We establish that this simultaneous locking condition enforces an overdetermined phase alignment and a structural polarization disparity between the dual channels, providing an absolute real-variable obstruction that strictly confines all non-trivial zeros to the critical line $mathbb{R}(s)=1/2$. By demonstrating that this geometric barrier is mathematically insurmountable, this work establishes a rigorous and definitive proof of the Riemann Hypothesis.

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[v1] 2026-10-06 00:35:46

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