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April 21, 20260 citationsOpen Access

Three-Dimensional Spectral Scaling and GUE-Type Level Statistics in a Deterministic VE55 Lattice with U131 Wilson Phases

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KTKen TakadaEEnumiaze

Key Points

  • This research aims to explore the spectral behaviors and statistical characteristics of a VE55 lattice model with Wilson phases.
  • Conducted a numerical analysis on a deterministic VE55 lattice model with U131 Wilson phases.
  • Calculated a three-dimensional spectral window using a positive-mode heat-kernel.
  • Investigated the statistical transition from GOE to GUE through complex perturbation methods.
  • Identified a strongly attractive RG fixed-point reformulation of the α-1 equation.
  • Detected a three-dimensional spectral window at the largest tested scale.
  • Observed a statistical transition from GOE to GUE after applying complex Hermitian perturbation.

Abstract

This paper presents a claim-bounded numerical study of a deterministic VE55 lattice model with U131 Wilson phases. It records three finite outputs: a strongly attractive RG fixed-point reformulation of the self-consistent α-1 equation, a three-dimensional spectral window in the positive-mode heat-kernel diagnostic at the largest tested scale, and a GOE-to-GUE statistical transition after deterministic complexification followed by complex Hermitian perturbation. The paper is explicit that these are finite numerical results, not analytic proofs of an infinite-scale continuum limit, a perturbation-free deterministic GUE realization, or a theorem about the zeta zeros.

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Cite This Study

Takada et al. (2026) studied this question.

synapsesocial.com/papers/69e7143fcb99343efc98dae4https://doi.org/10.5281/zenodo.19647789
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