PAXV Science: From 1989 to Quantum-Electrical Events
The math, physics, and engineering that power Watcher/ PAXV—organized chronologically and operationally. We begin in 1989 and progress to today’s 52 GS/s acquisition, FPGA/AI fusion, and fractal storage that preserves voltage–current waveforms for forensics at practical cost.
Chronological Science Timeline (1989 → 2025)
What We Control
Impedance, rise-time, jitter, attenuation, equalization, thermal budgets, bus throughput, RAID reliability. This is the deterministic layer that ensures the signal we capture is physically valid and time-aligned.
- Transmission line math: \(Z_0, \Gamma, \mathrm{VSWR}, t_r \approx 0.35/B\)
- ADC math: \(\Delta, P_q, \mathrm{SNR}_\text{ideal}, \mathrm{ENOB}\)
- Clock/jitter: \(\mathrm{SNR}_\text{jitter}, \sigma_t \leftrightarrow \mathcal{L}(f)\)
- Links: eye budgets, RJ/DJ, BER bathtubs
- Thermal & power: \(P=VI\), \(I^2R\), \(\Delta T = P\theta_{JA}\)
Why It Matters
Leading-edge fidelity is bounded by bandwidth, noise, and timing—so the backbone preserves edge truth. Without it, anomalies are indistinguishable from artifacts.
What We Discover
Sub-picosecond differences and variance patterns in 19 ps snapshots that depart from expectation. We model distributional drift and retain anomaly information through compression.
- Time–bandwidth product; matched filters; Cramér–Rao bounds
- Variance, KL, Mahalanobis, CUSUM for anomaly persistence
- Fractal IFS + wavelets with anomaly-first distortion budgets
- Mutual information retention and reconstruction PSNR
Why It Matters
We preserve the “quantum-electrical event” signatures through math, not myth—so post-capture forensics can reconstitute the true analog state behind the digital traffic.
Explanations by Depth (6th Grade → PhD)
6th Grade
Electricity makes waves. We take super-fast pictures of those waves so we can see tiny changes others miss.
High School
Sampling faster than the signal’s bandwidth lets us reconstruct it. Edges need bandwidth; noise and jitter blur edges.
Undergraduate
Nyquist/Shannon, rise-time vs BW, impedance & reflections, ADC quantization & ENOB, jitter-limited SNR, BER.
Graduate
Group delay, phase noise integration, eye budgets, STFT/ wavelets, Wiener/Kalman filters, rate–distortion.
PhD
Fractal IFS coding with collage bounds, anomaly-preserving thresholds, MI retention, compressed sensing guarantees.
End-to-End Logic Flow (Capture → Classify → Store → Reconstruct)
Blue path = primary ingest & compression; gold path = dual-layer anomaly-first compression; lower branch = real-time classification → reconstruction → forensic playback.