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Explores how non-abelian holonomy impacts local fixed points and spectral statistics in modular settings, suggesting new insights.
We study a modular pole lattice built from PSL(2,ℤ) generators and show how non-abelian holonomy produces two distinct structures.At the local level, square holonomies admit fixed points characterized by the golden ratio.At the global level, the collective effect of holonomy interactions induces channel mixing and curvature, leading to a transition between Poisson and GUE-type spectral statistics.This framework separates local geometric invariants from global statistical behavior within a unified modular setting.
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Jeong Min Yeon (2026) studied this question.
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