The Collatz Rotation Angle and the Icosahedral Spectrum

Each odd Collatz step rotates the trajectory in log-space by a constant angle α = log₂(3) − 1 ≈ 0.585. The continued fraction of α is [0; 1, 1, 2, 2, 3, 1, 5, 2, 23, ...], with terms 3–7 matching the icosahedral lattice parameters (χ, χ, D, 1, 5). A Monte Carlo test (10⁶ random continued fractions) confirms this is statistically significant (p