Kuramoto Pentagonal : Spin-Locking Protection

Architecture de Correction d'Erreur Quantique Passive

"Error is not a bug. It is a loss of synchronization."

Kuramoto Pentagonal is the quantum error correction layer of the Lichen architecture. Instead of costly active error correction (measuring and flipping bits), it uses passive synchronization (Kuramoto coupling) in a pentagonal topology to prevent errors from occurring in the first place.

🛡️ Core Principles

1. Passive Synchronization: Spontaneous phase-locking via the Kuramoto Hamiltonian prevents decoherence.
2. Pentagonal Topology: The $C_5$ symmetry creates a "frustrated" ground state that is robust against local perturbations.
3. CRAID Integration: Provides 60% fault tolerance (data survives the loss of 2/5 qubits).

📂 Contents

• docs/theory_spin_locking.md: The full physics manifesto explaining the Hamiltonian and topological protection.
• poc/pentagonal_sim.py: A Python/QuTiP simulation script demonstrating the auto-correction mechanism.
• FORMULAS.md: The immutable mathematical reference (Hamiltonians).

🧪 Key Validations

• Self-Healing: Simulation shows spins realigning after noise injection.
• Fault Tolerance: Information persists with 2 dead qubits.

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