The Last Law: A Complete Scientific Work

Description: A unified body of scientific work comprising 34 papers establishing, testing, and applying the Universal Cascade Law — a universal law of geometric organization in nonlinear systems. The law states that nonlinear coupled systems with unbounded extreme-range behavior exhibit geometric organization in the form of fractal architecture, with basin boundaries spaced by the Feigenbaum constant. The work derives from first principles: the Feigenbaum constant, the inflationary parameters, the origin of dark energy (as a clock error in the time emergence function), and the origin of dark matter (as a ruler error in the spatial metric of bound systems). None of these derivations have been falsified. The collection spans mathematics, physics, cosmology, astrophysics, genomics, medicine, and psychology — demonstrating that a single geometric law governs nonlinear coupled systems at every scale from the Planck length to the Schwarzschild radius and beyond. Contains 34 individually published papers (each with independent DOIs), 90 figures, 18 tables, a preface, foreword, and methodological note. All computational code is publicly available at github.com/lucian-png/resonance-theory-code. Keywords: Universal Cascade Law, fractal geometry, Feigenbaum constant, nonlinear dynamics, dark matter, dark energy, time emergence, cosmology, universal law, geometric organization, bifurcation theory, solution space geometry