Resonant Spacetime Hypothesis 2.0

Prediction

The fundamental eigenfrequency of a Poincar dodecahedral space with radius \( R \) is:  

\[f_1 = \frac{c \sqrt{\lambda_1}}{2\pi} \approx 35 \pm 2 \, \text{Hz},\]  

where \( \lambda_1 \approx 20.0/R^2 \) is the first eigenvalue (see Section 3), and \( R \approx 0.9 \, \text{Gpc} \) from CMB constraints.  

Observational Strategy

1.Matched Filtering

   - Construct template waveforms for resonant modes:  

     \[h(t) = h_0 \sin(2\pi f_1 t) e^{-t/\tau},\]  

     where \( \tau \sim 1 \, \text{ms} \) is the damping timescale (set by spacetime curvature).  

   - Cross-correlate with LIGO/Virgo/KAGRA O4 strain data (20--200 Hz band) using:  

     \[\text{SNR} = \frac{\langle h | d \rangle}{\sqrt{\langle h | h \rangle}},\]