The Spectral Method Computational

A universal computational framework derived from a single mathematical object: a positive trace-one operator K on a 3-dimensional Hilbert space. The commutator K, · generates a U (1) action whose holonomy fixes the spectral contraction factor to r = e^ (-2π), yielding a unique exponential eigenvalue spectrum with no free parameters. The framework provides an algorithmic protocol for analyzing any physical, biological, or social system representable as a three-level hierarchy, outputting all mechanical, electromagnetic, thermodynamic, and decay quantities from three input eigenvalues. Dimensionless physical constants including the fine structure constant (α⁻¹ = 137. 036, matching experiment to 1. 6 ppm), the weak mixing angle, and cosmological density parameters follow without additional fitting. Falsifiable predictions include Δα/α = -1. 25 × 10⁻⁶ at redshift z = 2. 5, testable by ELT/ANDES (2028-2030).