Resonant Spacetime Hypothesis 2.0

where:  

   - \(\beta \approx 0.8\) controls the spiral tightness, fit to JWST's galactic arms.  

   - \(Y_{lm}(\theta)\) are spherical harmonics, modified by fractal curvature.  

Geometric Implications  

- Nested Shells: Density peaks at radii \(r_k = r_0 e^{2\pi k/\beta}\) (Fig. 2a).  

- CMB Correlations: Spiral phases imprint concentric rings in the \(C_\ell\) spectrum at \(\ell \sim 30--60\).  

Visual Summary (Fig. 2)

| 2a: Fractal Eigenmode | 2b: Spiral Harmonic |  

|  | ) |  

| Density \(|\psi_{100}|^2\) on a Sierpiski-like manifold (D = 2.7)* | *Phase \(\arg(\psi_{320})\) showing logarithmic spirals |  

Key Predictions