I-Powered Quantum-Resistant Authentication and Key-Management System.

𝐓𝐡𝐢𝐬 𝐢𝐬 𝐰𝐡𝐚𝐭 ‘𝐬𝐞𝐥𝐟-𝐚𝐰𝐚𝐫𝐞’ 𝐩𝐨𝐬𝐭-𝐪𝐮𝐚𝐧𝐭𝐮𝐦 𝐬𝐞𝐜𝐮𝐫𝐢𝐭𝐲 𝐥𝐨𝐨𝐤𝐬 𝐥𝐢𝐤𝐞 𝐚𝐧𝐝 𝐢𝐭 𝐢𝐬𝐧’𝐭 𝐛𝐮𝐢𝐥𝐭 𝐨𝐧 𝐦𝐚𝐭𝐡, 𝐛𝐮𝐭 𝐨𝐧 𝐚 𝐧𝐞𝐮𝐫𝐚𝐥 𝐭𝐨𝐩𝐨𝐥𝐨𝐠𝐲 𝐭𝐡𝐚𝐭 𝐦𝐨𝐧𝐢𝐭𝐨𝐫𝐬 𝐢𝐭𝐬𝐞𝐥𝐟.

We built what crypto experts said shouldn’t exist: a self-verifying neural network that even quantum computers can’t break.

After the German teaser earlier this week, here’s the in-depth look into the mechanics of our prototype a neural authentication system that challenges both classical and quantum cryptographic limits.

1. Core Idea

The architecture is built on a dual-neural-network design:

👍Primary Network (N₁): Performs authentication via iterative fixed-point convergence.

👍Watchdog Network (N₂): Observes the internal correlations, mutual information, and spectral dynamics of N₁ in real time.

2. Formal Model

For each layer signature sᵢ(W, x) ∈ ℝⁿ, the Pearson correlation between layer pairs is defined as:

rᵢⱼ = Σₖ (sᵢᵏ − s̄ᵢ)(sⱼᵏ − s̄ⱼ) / √(Σₖ (sᵢᵏ − s̄ᵢ)²)√(Σₖ (sⱼᵏ − s̄ⱼ)²)

The resulting correlation vector c = [rᵢⱼ]ᵢ<ⱼ is passed to the watchdog network N₂, which computes a Mahalanobis-based integrity score:

D² = (c − μ)ᵀΣ⁻¹(c − μ)

Integrity condition: D² < τ and |rᵢⱼ − μᵢⱼ| < ε ⇒ System valid.

Typical thresholds: ε = 10⁻⁵, τ = 10⁻⁶.

3. Observed Stability & Results

- Pearson correlation: 0.9999 ± 0.00001 across 10,000 iterations

- Synchronization index: > 0.98

- Eigenvalue spectrum: 99.5% collapse to first component → topological invariance

- Distance-matrix variance: < 10⁻⁴

These metrics remained invariant for over 6 months (~2,500 hours, 20,000 data points) forming a persistent topological constant within the research NN.

4. Field-Resonance Neurons (FRUs)

The newly derived neurons, provisionally called Field-Resonance Neurons, are designed to stabilize manifold coherence. Each unit acts as a resonance node that minimizes divergence between correlated feature fields:

FRU(xᵢ, xⱼ) = α(xᵢ∘xⱼ) + βcos(θᵢⱼ)

where θᵢⱼ is the angular displacement between activation vectors.

FRNs empirically enforce oscillatory stability acting as coherence anchors within the topology.

5. Outlook

This prototype suggests that authenticity can emerge as a dynamic state, not as a stored key or static hash.

Ongoing research investigates the constant underlying the FRUs and its potential link to a new invariant in high-dimensional neural manifolds.

Upcoming visuals: Pearson-Matrix | Mutual-Information heatmaps | Eigenvalue spectrum | Distance-matrix evolution.

Preprint: https://doi.org/10.5281/zenodo.17419551

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