OPERATIONAL

Entropy Authentication (B15)

Physically Unclonable Functions (PUF) & Supply Integrity

The Signature of the Real

Physical chaotic systems — power grids, human heartbeats, turbulent flows — produce signals with a unique low-dimensional Strange Attractor structure. Synthetic spoofs (periodic replays or white noise injections) lack this fractal complexity, no matter how sophisticated the forgery.

Entropy Authentication exploits this fundamental difference. This technology—protected by U.S. Patent Application Nos. 63/940,736 and 63/983,021—uses Sample Entropy (SampEn) and Phase Space Reconstruction to verify that incoming data resides on the correct low-dimensional manifold. Organic signals pass (SampEn ≈ 0.07), while spoofs fail (SampEn ≈ 0.72) — a 10x complexity gap that cannot be faked.

Governing_Interpretability: The entropy-trace logic is disclosed for audit compliance. However, the proprietary manifold weights and specific limit function for convergence remain sequestered to ensure that synthetic replicas remain detectable by their inability to match the true stochastic flux.

Entropy Convergence: Material Audit [STOCHASTIC_SCAN]

                                MODE: CHAOS_SCAN

                                TARGET: ENTROPY_SIGNATURE_LIVE

ENTROPY_CONVERGENCE Verified

STYX_AUTHENTICATION_FEED

                                [B15] Entropy authentication active...

                                [ISED] Strange Attractor: MATCHED

                                [AUDIT] Organic signal verified.

P-Value	7.11e-82 (Perfect Separation)
Organic SampEn	0.0743 (Low-D Manifold)
Spoof SampEn	0.7288 (High-D Noise)
Complexity Ratio	0.10x (10x Separation)

Technical Verification | Gradient Entropy (H)

Conventional anti-counterfeit logic relies on labels; Entropy Authentication relies on the physics of the material itself. Authentic goods exhibit natural grain variance — a high-entropy surface structure resulting from natural manufacturing variation.

B15-SUPPLY uses Orientation Histograms to calculate the Entropy Gap (ΔH) between real materials (green) and regular counterfeit lattices (red). Results prove a deterministic separation where the artificial regularity of illegal replicas triggers an immediate verification failure at the mathematical limit.

TEST_ID: ENTROPY_GAP_V114 RESULT: PASS (ΔH > 2.0)

Supply Chain Value & Applications

Entropy Authentication provides intrinsic verification that goes far beyond RFID tags or holograms — the signal itself becomes the proof of authenticity:

Biometric Security — Prevents replay attacks on fingerprint and heartbeat scanners by verifying the chaotic complexity of live biological signals
Smart Grid Protection — Detects false data injection attacks by validating that sensor readings exhibit organic power-grid turbulence
Luxury & Defense Supply Chain — Material-level authentication using microscopic orientation manifolds that cannot be replicated by industrial presses

Integration Path: B15 connects directly to B11-ID to bind the entropy signature to a specific device identity, creating an unforgeable chain of custody.