Dual Coxeter Number Governs Random Matrix Universality Classes — E8 Intelligence Research

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Random matrix universality classes are governed by the dual Coxeter number of the underlying symmetry group, and this universality extends to Riemann zeta zeros and supersymmetric formulations. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22324460

September 5, 2026Open Access

Dual Coxeter Number Governs Random Matrix Universality Classes — E8 Intelligence Research

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Key Points

Identify how the dual Coxeter number connects Lie group symmetries to universality classes across random matrix ensembles, supersymmetric formulations, and Riemann zeta zeros.
Evaluated level repulsion exponents across Gaussian Orthogonal (β = 1), Unitary (β = 2), and Symplectic (β = 4) ensembles.
Calculated spectral form factor dynamics and formulated graded supermatrix structures using the Hubbard-Stratonovich transformation.
Demonstrated that the dual Coxeter number governs spectral statistics across symmetry groups, matching h∨ = N for SU(N) and h∨ = N − 2 for SO(N).
Confirmed that Gaussian Unitary Ensemble level repulsion (β = 2) matches the distribution of non-trivial Riemann zeta zeros.

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Implication

Theoretical analysis reveals dual Coxeter numbers govern universality classes in random matrix ensembles, highlighting deep symmetry links to Riemann zeta zeros and supersymmetry.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9e8576c3034f961570dae5 https://doi.org/10.5281/zenodo.22324460

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Dual Coxeter Number Governs Random Matrix Universality Classes — E8 Intelligence Research

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Dual Coxeter Number Governs Random Matrix Universality Classes — E8 Intelligence Research

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