Resonant Spacetime Hypothesis 2.0

- Simulated Maps: Inject spiral harmonics into Gaussian random fields (Fig. 5b).  

- Systematics Check: Rotate phases by \( \pi/2 \) to test instrument artifacts.  

Visual Summary (Fig. 5)

5a: GW Resonance Band | 5b: CMB Spiral Modes |  

|  |  |  

| Predicted excess power at 35 Hz (red)* | *Phase \( \arg(B_\ell^m) \) for \( \ell = 1500--2500 \)|  

Key Equations

1. GW Strain Amplitude

   \[h_0 \sim \frac{G \rho_{\text{res}} {c^4} \lambda_1^{-1/2} \approx 10^{-24} \, \text{for} \, \rho_{\text{res}} \sim 10^{-17} \, \text{kg/m}^3.\]  

2. Phase-Gradient Statistic

   \[\mathcal{P}(\ell) = \frac{1}{2\ell + 1} \sum_{m=-\ell}^\ell \left| \frac{\partial \arg(B_\ell^m)}{\partial m} \right|.\]