Bias Reduction
99.9%
Mean bias collapse from naive random-direction sampling to persistent renormalized tracking.
AURAL Validation
Licensing-ready black-box validation
AURAL — Renormalized Black-Box FTLE Validation
Spectral growth rate γ(x) is estimable from trajectory observations alone. This simulated Lorenz benchmark shows persistent renormalization collapsing directional bias, recovering the dominant local instability rate, and supporting a black-box-compatible governance claim.
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Trajectory-only estimation — no structural or white-box access required.
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Persistent renormalization keeps the perturbation in the linear regime and aligns with the dominant Lyapunov direction.
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Licensing signal — black-box compatibility removes the key adoption barrier for external governance layers.
Headline claim
Static dashboard backed by reproducible simulation output.
Loading result JSON…
Claim 1
Spectral growth rate γ(x) is measurable from trajectory observations alone.
Claim 2
Renormalization suppresses contracting-direction bias and keeps the perturbation vector calibrated.
Claim 3
The measured rate is accurate enough to support adaptive, energy-bounded governance logic.
RMS Improvement
42.08%
Error dispersion drops materially once the estimator is kept in the linear regime.
Mean Accuracy
0.07%
Absolute percent gap between the renormalized mean estimate and Benettin ground truth.
Primary results table
Loaded from AURAL_FTLE_results.json when available, with licensing-safe fallbacks.
| Metric | True (Benettin) | Raw Estimator | Renormalized Estimator |
|---|---|---|---|
| Largest Lyapunov λ₁ | 0.903099 | — | — |
| Mean Estimate | — | −4.075180 | 0.902442 |
| Mean Bias | — | −5.255000 | −0.000657 |
| RMS Error | — | 7.337471 | 4.249555 |
Proof chain is complete
The licensing narrative depends on the full chain, not a single statistic.
Step 1
Renormalization keeps ‖δ‖ = ε, so the estimator remains inside the local linear regime.
Step 2
Linear-regime tracking suppresses curvature contamination and converges toward the dominant growth direction.
Step 3
Accurate γ̂ is suitable for downstream adaptive law inputs and energy-bounded governance control.
Step 4
All measurements arise from outputs only, establishing black-box compatibility for licensing.
Why this matters for licensing
Prospective licensees need evidence that governance does not depend on privileged model access.
Barrier removed
Black-box AI systems are the hardest governance target because the controller cannot inspect weights, architecture, or internal state. AURAL demonstrates a viable trajectory-only path.
Mechanism validated
The raw estimator fails for the predicted reason: random perturbation directions are dominated by the strongly contracting exponent. Persistent renormalization fixes the failure mode structurally.
Commercial relevance
This is the difference between a white-box laboratory result and a licensing-ready external governance claim suitable for partner diligence.
Simulation scope
Reproducible, fixed-seed Lorenz benchmark.
System
Lorenz attractor with σ = 10, ρ = 28, β = 8/3.
Numerics
RK4 integration for nominal, perturbed, and tangent trajectories.
Estimator variants
Raw finite-difference vs. persistent renormalized black-box FTLE estimator.
Artifacts
JSON-backed metrics and publication-ready figures generated by the Python simulation.
Generated figures
These images are produced by the simulation script and embedded directly in this deployable static page.
