Behavioral Biometrics Engine
Deterministic motor control analysis powered by 12 peer-reviewed techniques that identify bots by how users interact — not what they click. Detrended Fluctuation Analysis (DFA) extracts persistent fBm scaling exponents, Recurrence Quantification Analysis (RQA) maps trajectory determinism, FFT isolates the 8–12 Hz physiological micro-tremor band, and Approximate Entropy quantifies timing regularity — forming a multi-modal behavioral identity that no automation framework can replicate in real time.
All behavioral entropy is collected passively through non-blocking event listeners. Analysis runs transparently at the signal-processing layer — no CAPTCHAs, no challenges, no friction introduced into the user experience. The biomechanics of human motor control become your invisible authentication layer.
Behavioral Motion Analysis
Real-time biometric physics engine
Click "Start Tracking" and move your mouse
Behavioral Signal Taxonomy
Each signal modality captures a biomechanically distinct axis of human motor behavior. The thresholds below reflect empirically calibrated detection boundaries — human ranges are derived from verified legitimate traffic distributions using kernel density estimation across millions of sessions.
Nonlinear Dynamics & Complexity
Detrended Fluctuation Analysis (DFA, Peng et al. 1994) extracts the scaling exponent α of integrated, detrended trajectory residuals — humans exhibit persistent fractional Brownian motion (α ≈ 0.6–0.8), while bots produce random-walk α ≈ 0.5. Recurrence Quantification Analysis (RQA, Marwan et al. 2007) builds binary recurrence matrices and computes determinism (diagonal lines), laminarity (vertical lines), and trapping time. Approximate Entropy (ApEn, Pincus 1991) quantifies sequence regularity: low ApEn → deterministic automation, moderate ApEn → stochastic human motor planning.
| Metric | Human Range | Bot Signature |
|---|---|---|
| DFA Scaling Exponent α Long-range correlation in mouse trajectories | α ≈ 0.6–0.8 (persistent fBm) | α ≈ 0.5 (random walk) |
| RQA Determinism Diagonal line ratio in recurrence matrix | DET ≈ 0.3–0.7 | DET > 0.95 or < 0.05 |
| RQA Laminarity Vertical line ratio in recurrence matrix | LAM ≈ 0.2–0.6 | LAM > 0.9 (stuck states) |
| Approximate Entropy Template-match regularity measure (m=2, r=0.2σ) | ApEn ≈ 0.3–0.8 | ApEn < 0.1 (deterministic) |
Spectral & Frequency Domain
A Cooley-Tukey radix-2 FFT isolates the 8–12 Hz physiological micro-tremor band endemic to all human hand movements (Hallett 1998, Deuschl et al. 2001). Spectral entropy H_s = −Σ p_k log₂ p_k across the full power spectrum quantifies spectral flatness — humans exhibit moderate spectral entropy reflecting diverse frequency components, while bots produce near-zero (single dominant frequency) or maximum (uniform white noise) spectral entropy.
| Metric | Human Range | Bot Signature |
|---|---|---|
| Micro-Tremor Power (8–12 Hz) Band-pass FFT spectral power density | Present, 0.2–1.5px amplitude | Absent (0 amplitude) |
| Spectral Entropy Normalized Shannon entropy of power spectrum | H_s ≈ 0.4–0.8 (diverse) | H_s < 0.1 or > 0.95 |
| Peak Frequency Dominant frequency in motion spectrum | 2–8 Hz dominant | Flat or single spike |
Kinematic & Curvature Analysis
Bézier curvature deviation measures departure from ideal cubic interpolation — automation tools generate geometrically perfect curves with near-zero residuals. The jerk profile (Flash & Hogan 1985, minimum-jerk model) evaluates the third positional derivative: human reaching movements produce smooth bell-shaped speed profiles reflecting biomechanical constraints (tendon elasticity, muscle fiber recruitment, joint moment-of-inertia coupling), while bots exhibit step-function or zero jerk.
| Metric | Human Range | Bot Signature |
|---|---|---|
| Bézier Curvature κ κ = |x′y″−y′x″|/(x′²+y′²)^1.5 | Moderate deviation | Near-zero (perfect curves) |
| Jerk Profile (d³x/dt³) Third positional derivative (Flash & Hogan 1985) | Smooth, bell-shaped | Step functions or zero |
| Speed Profile Shape Velocity peak position along trajectory | Asymmetric bell curve | Constant or linear ramp |
Temporal Typing & Session Analysis
Digraph latency models (Monrose & Rubin 2000) learn per-bigram transition time distributions (μ, σ) and z-score new observations against them. Keystroke burstiness (Goh & Barabási 2008) quantifies B = (σ_τ − μ_τ) / (σ_τ + μ_τ) — values near 0 indicate Poisson-like human cadence, while B near ±1 reveals deterministic automation or adversarial randomization. Form-fill timing models field completion durations against a Gamma distribution to detect paste-injection. Honeypot fields catch bots that interact with invisible DOM elements.
| Metric | Human Range | Bot Signature |
|---|---|---|
| Digraph Latency Z-Score Per-bigram (th, er, in) timing deviation | |z| < 2.0 (learned pairs) | |z| > 3.0 (uniform timing) |
| Burstiness B (σ−μ)/(σ+μ) inter-event time coefficient | B ≈ −0.2 to 0.3 | B < −0.8 or > 0.8 |
| Form Fill Timing Field completion time vs. Gamma CDF | Gamma-distributed | Instant (<50ms) paste |
| Honeypot Interaction Invisible CSS-hidden form field trap | No interaction (0) | Fills hidden fields (1) |
Signal Processing Pipeline
Raw input events flow through four deterministic processing stages before producing the composite humanLikelihood score that feeds into the Bayesian risk fusion core as weighted behavioral evidence.
Signal Acquisition
Raw input events (mousemove, keydown, keyup, touchstart, devicemotion) are captured via passive event listeners with microsecond-resolution timestamps from performance.now(). Events are buffered in a ring buffer with configurable window size, ensuring constant memory overhead regardless of session duration.
Feature Extraction
Time-series data undergoes feature transformation: Cooley-Tukey radix-2 FFT for spectral decomposition and micro-tremor band isolation, DFA for scaling exponent extraction, RQA for recurrence matrix construction, ApEn for regularity quantification, and Bézier curvature + jerk computation for kinematic profiling. Each feature vector is dimensionally independent.
Anomaly Scoring
Each extracted feature is evaluated against learned reference distributions of verified human behavior. Deviations are quantified using information-theoretic divergence measures — KL divergence for distributional shift, Jensen-Shannon for symmetric distance, and Fisher information for parameter sensitivity — producing per-signal anomaly scores with calibrated confidence.
Behavioral Evidence Fusion
Individual behavioral anomaly scores are fused into a composite humanLikelihood value (0–1) using weighted evidence accumulation with signal-specific reliability priors. This behavioral evidence feeds directly into the Bayesian risk fusion core alongside device, network, velocity, and temporal signals.
Theoretical Foundations
The behavioral engine is grounded in peer-reviewed computational neuroscience, motor control theory, and information-theoretic signal processing research. Every detection threshold traces to a citable scientific basis — no opaque neural networks, no unexplainable predictions.
DFA — Detrended Fluctuation Analysis (Peng et al. 1994)
DFA extracts the scaling exponent α by integrating the detrended time series, dividing into non-overlapping windows, fitting least-squares trend lines, computing the fluctuation function F(n), and deriving α from the log-log regression slope. Human mouse trajectories exhibit persistent fractional Brownian motion (α ≈ 0.6–0.8), indicating smooth, biomechanically purposeful reaching. Pure random-walk behavior (α ≈ 0.5) betrays scripted paths, while α > 0.9 indicates mechanistically regular automation.
RQA — Recurrence Quantification Analysis (Marwan et al. 2007)
RQA constructs a binary recurrence matrix R(i,j) = Θ(ε − ‖x_i − x_j‖) from phase-space embedded trajectories. Diagonal lines in the matrix indicate deterministic dynamics (determinism ratio DET), vertical lines indicate laminar states (laminarity LAM), and trapping time TT measures average laminar episode length. Human movements produce moderate DET (0.3–0.7) and LAM (0.2–0.6); bots exhibit extreme values — DET > 0.95 (perfectly repeating paths) or DET < 0.05 (random noise injection).
FFT Micro-Tremor & Spectral Entropy
Human hands exhibit involuntary oscillation at 8–12 Hz driven by the spinal stretch reflex loop (Hallett 1998, Deuschl et al. 2001). A Cooley-Tukey radix-2 FFT extracts spectral power density in this physiological band. Spectral entropy H_s = −Σ p_k log₂ p_k quantifies spectral flatness — humans exhibit moderate H_s reflecting diverse frequency components, bots produce near-zero (single spike) or maximum (uniform noise). The jerk profile (Flash & Hogan 1985) evaluates the third positional derivative, distinguishing bell-shaped biomechanical speed profiles from step-function automation.
ApEn, Digraph Latency & Bayesian Fusion
Approximate Entropy (Pincus 1991) counts template matches within tolerance r for embedding dimensions m and m+1, quantifying regularity: low ApEn → deterministic automation, moderate ApEn → stochastic human motor planning. Digraph latency models (Monrose & Rubin 2000) learn per-bigram (μ, σ) distributions and z-score new observations. Keystroke burstiness B = (σ−μ)/(σ+μ) (Goh & Barabási 2008) separates Poisson-like human cadence from automated patterns. All 11 sub-scores fuse via adaptive Bayesian weighted combination into a single humanLikelihood output.
Why Behavioral Signals Are Computationally Unforgeable
Device fingerprints can be spoofed. IP addresses can be rotated through proxy infrastructure. But the biomechanics of human motor control — governed by neuromuscular physiology and decades of motor learning — cannot be faithfully simulated in real time by any known computational system.
Physiological Origin
Micro-tremors arise from the spinal cord stretch reflex loop — an involuntary neuromuscular feedback mechanism operating at 8–12 Hz. No software can inject realistic oscillation into cursor coordinates at the correct amplitude, phase relationship, and frequency distribution simultaneously. The signal is inherent to biological motor control.
Temporal Complexity
Keystroke di-graph timing reflects years of motor learning embedded in procedural memory. Each typist develops a unique temporal signature for common character pairs (th, er, in, an) that evolves slowly over months — the timing distributions are shaped by neuromuscular adaptation, not algorithmic processes. Automation cannot replicate this learned temporal structure.
Multi-Modal Correlation
Genuine users exhibit cross-modal behavioral consistency: typing rhythm correlates with mouse movement style, scroll velocity, and touch pressure patterns. These correlations arise from shared neuromuscular substrate. Automation tools inject each modality independently, breaking the natural inter-modal covariance structure that characterizes human interaction.
Invisible Authentication Through Motor Control
Behavioral biometrics run passively from SDK initialization. No user interaction required — no CAPTCHAs, no cognitive challenges, no degraded experience. The biomechanics of human motor control become your frictionless authentication layer.