Resonant Spacetime Hypothesis 2.0

- Concentric rings** in \( C_\ell^{BB} \) at \( \ell \sim 1000--3000 \).  

- Parity-violating \( TB \) correlations** with phase \( \exp(i \beta \ln \ell) \).  

Observational Strategy

1. LiteBIRD High-\( \ell \) Analysis

   - Apply wavelet decomposition (e.g., steerable pyramids) to isolate spiral modes.  

   - Compute phase-gradient statistics:  

     \[\mathcal{P}(\ell) = \left\langle \left| \frac{\partial \arg(B_\ell^m)}{\partial m} \right| \right\rangle,\]  

     where \( \mathcal{P} \approx \beta \) for RSH (vs. random phases in CDM).  

2. Discriminatory Power

   - Signal-to-Noise: LiteBIRD's \( \Delta T \sim 2 \, \mu\text{K-arcmin} \) can detect \( \beta > 0.1 \) at \( \ell = 2000 \) (5).  

Validation