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Published June 24, 2025 | Version v1

The Riemann Hypothesis as a Harmonic Collapse Theorem in a Logarithmic Resonance Field

Description

We present a proof of the Riemann Hypothesis based on harmonic resonance collapse dynamics within a complex logarithmic frequency field. By reinterpreting the Riemann zeta function ζ(s) as a superposition of rotating phasors with amplitudes n−σ and frequencies logn, we demonstrate that full destructive interference, required for a zero, can only occur when σ = 1/2. This establishes the critical line as the exclusive collapse corridor for nontrivial zeros. The model aligns with the functional equation of ζ(s) and supports the Hilbert–P´ olya conjecture via spectral resonance behavior

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Available
2025-06-24