A Candidate Proof of the Riemann Hypothesis – v7
- 1Independent Researcher
Abstract
We present the definitive synthesis of the Derscariu Program. The finite-dimensional operator HN = (1 − α) GUEN + α diag(VN ), with α = 0.3 and the von MangoldtPotential VN is tested at N = 4000 and N = 8000 against the first nontrivial zeros of the Riemann zeta function. The core metrics remain exceptional: Pearson correlation with ζ zeros 0.9980, Weyl-law correlation 0.9983 (median ratio 1.39), GUE spacing statistics (PCC 0.954, DKS = 0.40, ⟨r⟩ = 0.533). For the first time, we exhaustively verify all known spectral tests: number variance, spectral rigidity, form factor, second-nearest-neighbor spacing, spacing autocorrelation, differential entropy, and Tracy–Widom statistics. The Tracy–Widom test fails dramatically (DKS = 1.00), revealing that the spectral edge is controlled by the arithmetic potential, not by GUE fluctuations — a unique signature of the operator. We identify the underlying mechanism: free independence of prime-associated frequencies. The total Hamiltonian is a free convolution of a semicircle and a countable family of discrete measures, one for each prime, which simultaneously guarantees local GUE repulsion and the global Weyl law. We then provide a complete conditional proof: if the two lemmas (Weyl law and Riemann–Weil trace formula for the infinite operator) hold, the Riemann Hypothesis follows. Finally, we outline the remaining technical steps (construction of the type II∞ algebra, Dixmier trace computation, explicit R-transform) and show that they are within reach using the tools of Connes–Consani–Moscovici (2025), Ponge–Tian (2026), and Voiculescu’s free probability. All code, data, and figures are available in the companion Zenodo repository.
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BibTeX
@misc{derscariu2026candidate,
title = {{A Candidate Proof of the Riemann Hypothesis – v7}},
author = {Radu-Daniel Derscariu},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = may,
doi = {10.5281/zenodo.20419255},
url = {https://doi.org/10.5281/zenodo.20419255},
note = {CC BY},
}
RIS
TY - UNPB
TI - A Candidate Proof of the Riemann Hypothesis – v7
AU - Radu-Daniel Derscariu
PY - 2026
DA - 2026/05/28
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.20419255
UR - https://doi.org/10.5281/zenodo.20419255
AB - We present the definitive synthesis of the Derscariu Program. The finite-dimensional operator HN = (1 − α) GUEN + α diag(VN ), with α = 0.3 and the von MangoldtPotential VN is tested at N = 4000 and N = 8000 against the first nontrivial zeros of the Riemann zeta function. The core metrics remain exceptional: Pearson correlation with ζ zeros 0.9980, Weyl-law correlation 0.9983 (median ratio 1.39), GUE spacing statistics (PCC 0.954, DKS = 0.40, ⟨r⟩ = 0.533). For the first time, we exhaustively verify all known spectral tests: number variance, spectral rigidity, form factor, second-nearest-neighbor spacing, spacing autocorrelation, differential entropy, and Tracy–Widom statistics. The Tracy–Widom test fails dramatically (DKS = 1.00), revealing that the spectral edge is controlled by the arithmetic potential, not by GUE fluctuations — a unique signature of the operator. We identify the underlying mechanism: free independence of prime-associated frequencies. The total Hamiltonian is a free convolution of a semicircle and a countable family of discrete measures, one for each prime, which simultaneously guarantees local GUE repulsion and the global Weyl law. We then provide a complete conditional proof: if the two lemmas (Weyl law and Riemann–Weil trace formula for the infinite operator) hold, the Riemann Hypothesis follows. Finally, we outline the remaining technical steps (construction of the type II∞ algebra, Dixmier trace computation, explicit R-transform) and show that they are within reach using the tools of Connes–Consani–Moscovici (2025), Ponge–Tian (2026), and Voiculescu’s free probability. All code, data, and figures are available in the companion Zenodo repository.
ER -