The Arc Law: A Unified Geometric Framework for Transformation

This repository contains the complete documentation, validation data, and interactive visualizers for the Arc Law—a universal mathematical relationship between eigenstructure and observable transformation width: σ = k × |ν|^(-α) The framework unifies transformation dynamics across 40+ orders of magnitude, recovering historical laws as special cases:- Geiger-Nuttall law (1911) at α = 0.5- Sargent's Rule (1933) at α = 5.0 This work assigns geometric structure to imaginary eigenvalue space and shows that long-standing empirical laws are projections of trajectories through that space. Contents: 52 files including core papers, pre-registration documents, validation figures, reproducibility code, and 19 interactive HTML visualizers. Validated across 6 domains: chemistry, quantum physics, nuclear physics, classical mechanics, ecology, and nonlinear dynamics. All results are reproducible using the included code and data.