Zero-Count Deviation Identity: S(T) as Accumulated Gap Fluctuation

Numerical identity: S(γ_n) ≈ Σ_{k<n}(1 − gap_k/ρ(t_k)), ρ(t) = 2π/log(t/2π), verified over 298,190 zeros (t ≤ 200,000) with r = 0.999958. The ρ-choice is uniquely pinned: fixed/halved/ doubled alternatives give r ≈ −0.38/0.94/−0.94. Residual error converges (0.48 → 0.11). This is a numerical identity, NOT a proof. Pure Python, fully reproducible.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-14
DOI
https://doi.org/10.5281/zenodo.21931143
Primary Topic
Theoretical and Computational Physics
Type
article
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article

Zero-Count Deviation Identity: S(T) as Accumulated Gap Fluctuation

TE J
Zenodo (CERN European Organization for Nuclear Research)
Theoretical and Computational Physics
article

Zero-Count Deviation Identity: S(T) as Accumulated Gap Fluctuation

TE J
article en

Abstract

Numerical identity: S(γ_n) ≈ Σ_{k<n}(1 − gap_k/ρ(t_k)), ρ(t) = 2π/log(t/2π), verified over 298,190 zeros (t ≤ 200,000) with r = 0.999958. The ρ-choice is uniquely pinned: fixed/halved/ doubled alternatives give r ≈ −0.38/0.94/−0.94. Residual error converges (0.48 → 0.11). This is a numerical identity, NOT a proof. Pure Python, fully reproducible.

Zenodo (CERN European Organization for Nuclear Research)
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Theoretical and Computational Physics
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Zero-Count Deviation Identity: S(T) as Accumulated Gap Fluctuation — TE J · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS