Quantum Phase-Space Regulator: Planck's Constant and the Raw Density Correlation of Riemann Zeta Zeros

We analyse raw (unscaled) spacings between non-trivial zeros of the Riemann zeta function on the critical line. The main analytic result is an identity from the Riemann–von Mangoldt formula: the mean action scale ΔS = ΔT·log(T/2π) equals 2πℏ for the mean local spacing. Planck's constant ℏ appears as the phase-space quantisation scale in the Berry–Keating model H=xp, not as a fixed spacing on the imaginary axis. Unfolding to dimensionless GUE statistics is reinterpreted as the change of variables s = ΔS/(2πℏ). This work does NOT prove the Riemann Hypothesis. The upload includes the full manuscript (English ), illustrative spacing figures, and supplementary numerical analysis code for reproducibility. AI disclosure: manuscript preparation and numerical checks were assisted by Cursor Agent; the author retains responsibility for the content.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-24
DOI
https://doi.org/10.5281/zenodo.20831450
Primary Topic
Theoretical and Computational Physics
Type
preprint
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preprint

Quantum Phase-Space Regulator: Planck's Constant and the Raw Density Correlation of Riemann Zeta Zeros

Jaroslaw Pelwecki
Zenodo (CERN European Organization for Nuclear Research)
Theoretical and Computational Physics
preprint

Quantum Phase-Space Regulator: Planck's Constant and the Raw Density Correlation of Riemann Zeta Zeros

Jaroslaw Pelwecki
preprint en

Abstract

We analyse raw (unscaled) spacings between non-trivial zeros of the Riemann zeta function on the critical line. The main analytic result is an identity from the Riemann–von Mangoldt formula: the mean action scale ΔS = ΔT·log(T/2π) equals 2πℏ for the mean local spacing. Planck's constant ℏ appears as the phase-space quantisation scale in the Berry–Keating model H=xp, not as a fixed spacing on the imaginary axis. Unfolding to dimensionless GUE statistics is reinterpreted as the change of variables s = ΔS/(2πℏ). This work does NOT prove the Riemann Hypothesis. The upload includes the full manuscript (English ), illustrative spacing figures, and supplementary numerical analysis code for reproducibility. AI disclosure: manuscript preparation and numerical checks were assisted by Cursor Agent; the author retains responsibility for the content.

Zenodo (CERN European Organization for Nuclear Research)
Oldham Council (GB)
Theoretical and Computational Physics
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