Resonant Spacetime Hypothesis 2.0

1. Void Radius Definition:  

   \[R_v = \left( \frac{3V}{4\pi} \right)^{1/3}, \quad V = \text{void volume}.\]  

2. Fractal Dimension 

   \[N(R_v) \propto R_v^{-D} \quad \Rightarrow \quad D = -\frac{d\log N}{d\log R_v}.\]  

5. Results from RSH Simulations 

Sample       | Fractal Dimension (D) | Void Count (R > 30 Mpc/h) |  

| RSH (Simulated)  | 2.72 0.08           | 112 9                   |  

| DESI (Observed)  | 2.63 0.15           | 105 12                  |  

| CDM (Millennium)| 3.01 0.05           | 87 7                    |  

Interpretation  

- RSH's D 2.7 matches DESI, supporting fractal eigenmode structure.