The Arc Theorem: A Geometric Theory of Transformation Rates

The Arc Theorem: A Geometric Theory of Transformation Rates This repository contains the complete formal derivation, validation record, and supporting evidence for the Arc Theorem — a theorem establishing that observed scaling exponents in rate laws are geometric invariants arising from traversal through imaginary space. The theorem states: α=dT+dC×ϕ2π\alpha = d_T + d_C \times \frac{\phi}{2\pi}α=dT+dC×2πϕ where: α\alphaα is the observed scaling exponent dTd_TdT is the terminal (mode-counting) dimension dCd_CdC is the cycling dimension ϕ\phiϕ is the traversal angle in imaginary space The Arc Theorem demonstrates that historically empirical laws across physics, chemistry, biology, and dynamical systems are projections of trajectories through structured imaginary space. This release (v4) establishes theorem status through: Independent derivations from Wigner threshold theory Instanton and Euclidean action formalism Classical evanescent wave analysis (Maxwell-only) Cross-domain validation and preregistered tests The repository includes formal proofs, derivation manuscripts, empirical validation figures, preregistration documents, reproducibility code, and interactive visualizers. All results are fully reproducible using included data and scripts. This is an archival scientific release. No files are reorganized or rewritten. See README_V4.md and CHANGELOG.md for full version details. Title changed to match theorem status