Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research

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The Vandermonde determinant squared serves as the mathematical kernel that unifies the eigenvalue density of Gaussian Unitary Ensemble (GUE) random matrices and the statistical distribution of Riemann zeta zeros, a connection bridged by the Weyl chamber volume of the A_{N-1} root system. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22732676

September 13, 2026Open Access

Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research

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Key Points

To establish the structural identity connecting Gaussian Unitary Ensemble eigenvalue distributions and the statistical spacing of Riemann zeta zeros through the geometry of Weyl chambers.
Analyzed the mathematical formulation of the squared Vandermonde determinant within Gaussian Unitary Ensemble (GUE) joint eigenvalue probability densities.
Evaluated integration boundaries across the fundamental Weyl chamber of the A_{N-1} root system defining ordered eigenvalue spaces.
Mapped spectral statistics to the Montgomery–Odlyzko law governing pair correlations of nontrivial Riemann zeta zeros.
Identified the squared Vandermonde determinant as the universal kernel linking GUE spectral density directly to the distribution of Riemann zeta zeros.
Demonstrated that the Weyl chamber volume of the A_{N-1} root system serves as the explicit geometric bridge mediating eigenvalue repulsion and zeta zero spacing.

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Implication

Theoretical analysis reveals structural equivalence between Gaussian Unitary Ensemble eigenvalues and Riemann zeta zeros via Weyl chambers, highlighting deep algebraic symmetry in number theory.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b41e0926e14a848b39a8 https://doi.org/10.5281/zenodo.22732676

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Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research

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Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research

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