Golden Ratio Geometry in Rotating Spacetime: A Unified Framework for Quantum Spin, Fractal Scaling, and Cosmological Structure

This work proposes a geometric framework linking the golden ratio (φ), universal rotation, and physical structures across scales. Under frame-dragging in rotating spacetime, stable trajectories form helical paths that follow φ-proportional geometry. We show that: (1) Spin-1/2 and 720° rotation emerge from golden-angle phase sampling; (2) Wave–particle duality arises as a projection effect of 3D helices onto a 2D boundary; (3) Biological scaling (3/4 law) is derived from φ-based fractal dimensional equilibrium; (4) Cosmological rotation parameter a ≈ 1/φ² ≈ 0.382 predicts CMB anisotropy and galaxy spin asymmetry. This establishes the golden ratio as a universal geometric invariant governing stability under rotational dynamics.