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math.GM2025
The Resonance Bias Framework: Resonance, Structure, and Arithmetic in Quadrature Error
William Cook
We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or s…
math.GM2025
A Recursive Block Pillar Structure in the Kolakoski Sequence K(1,3)
William Cook
The Kolakoski sequence K(1,3) over {1, 3} is known to be structured, unlike K(1,2), with symbol frequency d approx. 0.397 linked to the Pisot number alpha (real root of x^3 - 2x^2…