SFIT Synthetic Event Data Generator — IMPROVED VERSION

"""

======================================================

Now includes **explicit KWW tail simulation** (Kohlrausch–Williams–Watts stretched exponential)

to better reproduce the 832.6 s relaxation tails with β = 1.060 observed in your ILL 3-14-412 reanalysis.

Key SFIT features embedded:

- 1.20134 mHz sinusoidal modulation ("Quantum Heartbeat")

- Phase-locked π-overshoot at t ≈ 416.65 s (half-period)

- Explicit KWW relaxation tails triggered by periodic "mirror steps"

- ~4.5 % initial post-step overshoot that decays with τ = 832.6 s, β = 1.060

- Poisson statistics with realistic counting rate

Output file: data/processed/synthetic_event_sample.dat

"""

import numpy as np

import os

from datetime import datetime

# ==================== SFIT KEY CONSTANTS (from Preprint) ====================

NU_RES = 0.00120134 # Hz — Quantum Heartbeat resonance

OMEGA_RES = 2 * np.pi * NU_RES

PERIOD = 1.0 / NU_RES # ≈ 833.3 s

HALF_PERIOD = PERIOD / 2 # ≈ 416.65 s

K_COUPLING = 1.060

TAU_KWW = 832.6 # s — KWW relaxation time

BETA_KWW = K_COUPLING # β = 1.060 (stretched exponent)

BASE_RATE = 50.0 # average events per second

MOD_AMPLITUDE = 0.00122 # ~0.122 % contrast from heartbeat

OVERSHOOT_FACTOR = 1.045 # ~4.5 % initial post-step overshoot

STEP_INTERVAL = PERIOD # mirror steps every full period

TOTAL_DURATION = 7200.0 # 2 hours — enough to see multiple KWW tails + heartbeat

# Reproducibility

np.random.seed(42)

# Track mirror-step times (KWW tails are triggered here)

step_times = []

def kww_decay(t, t_step):

"""Explicit Kohlrausch–Williams–Watts (KWW) stretched-exponential decay"""

if t <= t_step:

return 0.0

dt = t - t_step

return np.exp( - (dt / TAU_KWW) ** BETA_KWW )

def sfit_modulation(t):

"""Improved modulation: heartbeat + explicit KWW tails from mirror steps"""

# 1.20134 mHz sinusoidal heartbeat

heartbeat = MOD_AMPLITUDE * np.cos(OMEGA_RES * t)

# 2. KWW relaxation tails from all previous mirror steps

kww_contribution = 0.0

for t_step in step_times:

kww_contribution += (OVERSHOOT_FACTOR - 1.0) * kww_decay(t, t_step)

# 3. Small π-phase overshoot boost near half-period points (for extra realism)

phase = (t % PERIOD) / HALF_PERIOD

extra_overshoot = 0.0

if abs(phase - 1.0) < 0.03 or abs(phase) < 0.03:

extra_overshoot = 0.015 * np.exp(-abs(phase - 1.0) * 30)

return 1.0 + heartbeat + kww_contribution + extra_overshoot

def generate_synthetic_events():

global step_times

print("Generating SFIT synthetic event data with explicit KWW tails...")

# Schedule periodic mirror steps

step_times = np.arange(0, TOTAL_DURATION + 1, STEP_INTERVAL)

print(f"→ Scheduled {len(step_times)} mirror steps (every {PERIOD:.1f} s)")

timestamps = []

channels = []

t = 0.0

while t < TOTAL_DURATION:

rate = BASE_RATE * sfit_modulation(t)

# Poisson process for next event

dt = np.random.exponential(1.0 / max(rate, 0.1)) # avoid zero/negative rate

t += dt

if t >= TOTAL_DURATION:

break

# Detector channel (realistic qBounce-like pulse heights)

channel = int(np.random.normal(12, 3)) + 8

timestamps.append(int(t * 1e6)) # microseconds

channels.append(channel)

print(f"Generated {len(timestamps):,} events over {TOTAL_DURATION/3600:.1f} hours")

print(f" • Heartbeat at {NU_RES*1000:.5f} mHz")

print(f" • KWW tails (τ={TAU_KWW} s, β={BETA_KWW}) after each mirror step")

return np.array(timestamps), np.array(channels)

def save_synthetic_data(timestamps, channels, filename="data/processed/synthetic_event_sample.dat"):

os.makedirs(os.path.dirname(filename), exist_ok=True)

with open(filename, "w") as f:

f.write("# SFIT Synthetic Event Data — IMPROVED with explicit KWW tails\n")

f.write("# Format: timestamp_us (relative) detector_channel\n")

f.write(f"# Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}\n")

f.write(f"# Contains: 1.20134 mHz Quantum Heartbeat + KWW relaxation (τ={TAU_KWW} s, β={BETA_KWW})\n")

f.write("# Mirror steps every 833.3 s with 4.5 % initial overshoot decaying via KWW\n")

f.write("# Use with analysis scripts to reproduce 14.28σ-style PSD peak and KWW fits\n\n")

for ts, ch in zip(timestamps, channels):

f.write(f"{ts} {ch}\n")

print(f"✅ Synthetic data saved to: {filename}")

print(f" File size: {os.path.getsize(filename)/1024:.1f} KB")

# ====================== MAIN ======================

if __name__ == "__main__":

timestamps, channels = generate_synthetic_events()

save_synthetic_data(timestamps, channels)

print("\n🎉 Next steps:")

print("1. Run the generator: python scripts/generate_synthetic_event_data.py")

print("2. (Optional) Create scripts/analyze_synthetic.py to compute PSD + KWW fit")

print("3. Upload synthetic_event_sample.dat to GitHub data/processed/ and Zenodo")

print("4. The file now faithfully reproduces your KWW tails for quick verification!")