[Contribution] Tutorial notebook: algebraic GW150914 waveform vs PyCBC templates

[matshaba]

Hi,

The PyCBC tutorials teach GW data analysis using NR-calibrated templates. I'd like
to propose a contributed notebook showing an algebraic baseline for comparison.

Notebook concept: "Tutorial X: Alternative waveform models — algebraic vs template"

# Cell 1: Standard PyCBC template
from pycbc.waveform import get_td_waveform

hp_pycbc, hc_pycbc = get_td_waveform(
    approximant='IMRPhenomD',
    mass1=36.2, mass2=29.1,
    delta_t=1.0/4096, f_lower=20
)

# Cell 2: QGD algebraic waveform (no NR calibration)
def qgd_algebraic(M1, M2, t_array):
    G, c, M_sun = 6.674e-11, 3e8, 1.989e30
    Mf = (M1 + M2) * 0.95 * M_sun
    f_peak = 0.747 * c**3 / (2*np.pi * G * Mf)
    tau = G * Mf / (0.178 * c**3)
    t_merger_idx = np.argmax(np.abs(t_array))
    h = np.zeros_like(t_array)
    post = t_array > t_merger_idx
    h[post] = np.exp(-t_array[post]/tau) * np.cos(2*np.pi*f_peak*t_array[post])
    return h

# Cell 3: Overlap comparison
from pycbc.filter import match
m, _ = match(hp_pycbc, hp_qgd, psd=None, low_frequency_cutoff=20.0)
print(f"Overlap (QGD vs IMRPhenomD): {m:.3f}")

Educational value: Shows students that the fundamental QNM frequency can be
derived algebraically from M_final, making NR calibration transparent.

Preprint: https://doi.org/10.5281/zenodo.18605058
Code: https://github.com/matshaba/Quantum-Gravity-Dynamics

Quick References:
https://github.com/matshaba/Quantum-Gravity-Dynamics/blob/main/docs/summary.md