Resonant Spacetime Hypothesis 2.0

```  

Step 3: Add Instrumental Noise  

Simulate LiteBIRD-like noise (2 K-arcmin):  

```python  

def add_noise(map_Q, map_U, N_side, sigma=2e-6):  

    noise_Q = np.random.normal(0, sigma, 12 * N_side2)  

    noise_U = np.random.normal(0, sigma, 12 * N_side2)  

    return map_Q + noise_Q, map_U + noise_U  

```  

3. Analysis: Spiral-Phase Detection

Step 4: Phase Gradient Statistic