Resonant Spacetime Hypothesis 2.0

2. Large-Scale Structure (LSS)

- Filament Detection: Apply the DisPerSE algorithm to simulated density fields, extract skeletons, and cross-correlate with SDSS/BOSS filaments using:  

  \[\xi(r) = \frac{\langle \delta_{\text{sim}}(\mathbf{x}) \delta_{\text{obs}}(\mathbf{x} + \mathbf{r}) \rangle}{\sigma_{\text{sim}} \sigma_{\text{obs}}}.\]  

- Void Statistics: Compare the void probability function (VPF) to DESI data.  

- Key Findings:  

- RSH vs. CDM: 15% higher filament correlation at r 50 Mpc/h (p < 0.01).  

- Fractal Dimension: Simulated VPF yields D = 2.68 0.05 vs. DESI's D = 2.71 0.07.  

Visual Summary (Fig. 4)

| 4a: C Comparison | 4b: Filament Cross-Correlation |  

|  |  |  

| Planck TT (black) vs. RSH (red); shaded: 1 errors* | *Correlation (r) for SDSS (blue) and RSH (orange) |