Analytical exploration of Riemann zeta zeros reveals connections with Planck's constant, indicating phase-space quantization.
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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Jaroslaw Pelwecki (2026) studied this question.
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