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.
Authors
- Jaroslaw Pelwecki
Institutions
- Oldham Council (GB)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-24
- DOI
- https://doi.org/10.5281/zenodo.20831451
- Primary Topic
- Theoretical and Computational Physics
- Type
- preprint