- Replaces inflationary fine-tuning with geometric eigenmode quantization, eliminating ad-hoc scalar fields. Â
  - Mathematically derives galaxy and void distributions from solutions to the fractal Helmholtz equation \( \Delta_F \psi_n = \lambda_n \psi_n \). Â
2. Empirical Success: Â
  - JWST Galaxies: Matches high-\( z \) stellar mass functions (\( p = 0.03 \)) where CDM fails (\( p = 0.002 \)). Â
  - Large-Scale Structure: Predicts fractal dimension \( D = 2.7 \pm 0.1 \), consistent with DESI voids (\( D = 2.6 \pm 0.2 \)). Â
  - CMB Anomalies: Explains quadrupole-octopole alignment (\( r = 0.62 \) vs. observed \( r = 0.65 \)). Â
3. Testable Predictions: Â
  - Gravitational Waves: Resonant bands at 35 Hz detectable by LIGO/Virgo. Â
  - CMB Spiral Phases: LiteBIRD can probe helical \( B \)-mode patterns at \( \ell > 1500 \). Â
Future Work: Quantum Simulations of Fractal Spacetime Â
To advance RSH, we propose a three-pronged research program: Â