Resonant Spacetime Hypothesis 2.0

- Finite-Difference Time Domain (FDTD): For wave propagation in fractal boundary conditions.  

- Adaptive Mesh Refinement (AMR): Resolves high-density regions (e.g., galaxy clusters) down to 10 kpc/h.  

- GPU Acceleration: CUDA kernels for solving the fractal Helmholtz equation.  

2. Simulation Parameters:  

| Parameter           | Value               | Physical Meaning                  |  

| Box size            | 500 Mpc/h           | Comoving volume side length       |  

| Resolution          | 1024 grid cells    | Cell size: **0.5 Mpc/h**          |  

| Initial conditions  | 20 lowest eigenmodes | Gaussian (CDM-like) vs. log-periodic (RSH) |  

| Time steps          | 10 (t = 1 Myr)    | From z = 20 to z = 0              |  

Initial Conditions 

- Gaussian: Amplitude distribution \( A_n \sim \mathcal{N}(0, P(k_n)) \), where \( P(k) \) is the Planck 2018 power spectrum.