A draft for rapid modeling using a non-iterative function of the GUE, Riemann, GOE spectral distributions and the Wigner semicircle

In this short paper, we present a draft approach for modeling spectral distributions using a non-iterative function. With a simple change of constants, this function can reproduce multiple distributions with a precision of up to 10⁻¹⁷ in the computation of normalized standard deviation, when using 10⁷ samples and a computation time under one second, without any optimization or parallelization. The computation was performed on an HP Z workstation. This function successfully models the GUE, GOE distributions, the spacing distribution of the non-trivial zeros of the Riemann zeta function, and the Wigner semicircle. All cases were validated using the Kolmogorov-Smirnov test. Unlike traditional methods based on random matrices or integrable equations, this approach starts from a highly precise empirical result, without reference to any theoretical model, suggesting the existence of an as-yet unknown underlying structure. This function belongs to a family of non-iterative functions that have already been used for other achievements such as: Synthesizing shapes from the simplest (circle, square, etc.) to much more complex structures. Modeling a long series of known and unknown distributions. Modeling dynamic phenomena (bifurcations, hysteresis, R. May's logistic equation for r=4). The point cloud modeling Shaw’s dripping faucet experiment. Heavy-tailed distributions and other types.