The Python Verification Script

import numpy as np

import matplotlib.pyplot as plt

from scipy.fft import fft, fftfreq

# --- 1. SET THE SFIT PARAMETERS ---

nu_echo = 0.0012 # The 1.2 mHz Predicted Heartbeat

T_period = 1 / nu_echo # ~833 seconds

duration = 5000 # Total observation time (seconds)

fs = 0.1 # Sampling rate (10 samples per second)

alpha = 0.05 # Modulation depth from k constant

# --- 2. GENERATE TIME-SERIES DATA ---

t = np.arange(0, duration, 1/fs)

# Standard Rabi Oscillation (Simulating a 10mHz transition)

rabi_freq = 0.01

standard_p = 0.5 * (1 + np.sin(2 * np.pi * rabi_freq * t))

# Apply the Stevenson-Flux Modulation (The 1.2 mHz Echo)

sfit_p = standard_p * (1 + alpha * np.cos(2 * np.pi * nu_echo * t))

# Add Gaussian Noise (Simulating detector background)

noise = np.random.normal(0, 0.02, len(t))

raw_data = sfit_p + noise

# --- 3. FOURIER ANALYSIS (The "Hunt" for 1.2 mHz) ---

# We subtract the mean to focus on the oscillations (residuals)

residuals = raw_data - np.mean(raw_data)

yf = fft(residuals)

xf = fftfreq(len(t), 1/fs)

# --- 4. VISUALIZATION ---

plt.figure(figsize=(12, 6))

# Plotting the Power Spectral Density

plt.plot(xf, np.abs(yf))

plt.xlim(0, 0.005) # Zooming in on the sub-mHz window

plt.axvline(x=nu_echo, color='r', linestyle='--', label='SFIT Prediction (1.2 mHz)')

plt.title("Power Spectral Density: Hunting for the Stevenson Resonance")

plt.xlabel("Frequency (Hz)")

plt.ylabel("Magnitude")

plt.legend()

plt.grid()

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