The Fractal Seed: The Iteration Rule of Reality

A single iteration rule on the five-sphere S⁵ generates all known physics from four inputs: two integers (d=3 spatial dimensions, D=4 spacetime dimensions) and two mathematical constants (π and e). The torsional field evolves by φ → π^B · φ · (1 - e^{-|φ|}), where the structure seed π^B builds angular phase and the process seed (1 - e^{-|φ|}) relaxes the amplitude. Frozen modes are particles; the relaxation fraction ε = 1 - e⁻¹ governs measurement, the Hubble rate, and the cosmological constant through integer powers set by polynomials in d and D. This note establishes the iteration rule and summarizes what follows from it: the complete particle spectrum, coupling constants, mixing matrices, gravity, cosmological parameters, and the identification of the speed of light as the radius of S⁵. There are no free parameters.