Resonant Spacetime Hypothesis 2.0

1. Gravitational Waves 

   - Resonant modes generate discrete frequencies \(f_n \sim \sqrt{\lambda_n} \approx 35 \times n \, \text{Hz}\).  

   - Detectable by LIGO/Virgo via matched filtering of stochastic backgrounds.  

2.CMB Anomalies

   - Spiral harmonics induce non-Gaussian \(B\)-mode patterns at \(\ell > 1000\).  

   - Testable with LiteBIRD or CMB-S4.  

3. Large-Scale Structure

   - Void hierarchy: Fractal modes predict voids at scales \( \sim 50\, \text{Mpc} \times e^{k\pi/2\beta} \).  

Transition to Numerical Methods  

Section 3 solves \(\Delta_F \psi_n = \lambda_n \psi_n\) numerically on a 3-torus lattice, while Section 4 compares the resulting \(P(k)\) to Planck and DESI data.  

References