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Quantitative Refinements of Arithmetic Holonomy Bounds: Mixed Source Metrics and Joint Moment Determinants

This preprint develops quantitative refinements of the arithmetic holonomy framework of Calegari–Dimitrov–Tang. Using unequal row degrees, mixed source metrics, and joint moment determinants, it establishes the following upper bounds for the irrationality exponent μ: μ(π) ≤ 6.70μ...