PHL Protocol Prototype

This is a conceptual prototype of the Perfect Harmony Ledger consensus mechanism. Lyapunov stability, SNARK proofs, and adaptive optimization are simulated for demonstration.

Perfect Harmony Ledger

Next-generation blockchain consensus with global invariants, Lyapunov stability, recursive SNARKs, and adaptive optimization for perfect harmony.

Global Invariant
1000.0
Perfect harmony
Network Harmony
96%
Optimal convergence
Energy Efficiency
87%
Ultra-efficient
Active Nodes
3
Distributed consensus

Node States & Lyapunov Energy

node-001

3 neighbors
0.120
Energy
94%
Convergence
State Vector:
0.85
0.92
0.78
0.95

node-002

3 neighbors
0.080
Energy
97%
Convergence
State Vector:
0.88
0.89
0.81
0.93

node-003

3 neighbors
0.150
Energy
92%
Convergence
State Vector:
0.87
0.91
0.79
0.94

Consensus Metrics

Lyapunov Function0.230
Convergence Speed94%
Proof Aggregation91%
Network Harmony96%

Adaptive Control

Step Size0.150
Convergence Threshold0.0010
Energy Optimization89%
Quantum-InspiredActive
Evolutionary ActiveActive
Topological MonitoringActive

Recent Blocks

#1234560s ago
Invariant: 1000.0
Energy Reduction: 85%
Nodes: 156
#1234630s ago
Invariant: 1000.0
Energy Reduction: 87%
Nodes: 158
#1234710s ago
Invariant: 1000.0
Energy Reduction: 89%
Nodes: 160

PHL Architecture Overview

Local Operational Layer

  • • State Representation: Each node holds state vector xᵢ ∈ ℝᵈ
  • • Local Update Rule: Gradient descent on Lyapunov function
  • • Discrete Averaging: Continuous disagreement minimization
  • • Contraction Mapping: Guaranteed convergence to unique fixed point

Aggregation & Proof Layer

  • • Global Invariant: F(x) = Σwᵢxᵢ = C (constant)
  • • SNARK Circuits: Cryptographic proof of harmony
  • • Recursive Composition: Constant-time verification
  • • Proof Aggregation: Compact chain validation

Adaptive Optimization

  • • Model Predictive Control: Real-time parameter tuning
  • • Quantum-Inspired: Annealing for local minima escape
  • • Evolutionary Algorithms: Genetic optimization
  • • Topological Monitoring: Persistent homology analysis

Mathematical Foundation

Lyapunov Stability

Lyapunov Function:
V(x) = ½ Σᵢ Σⱼ∈N(i) aᵢⱼ||xᵢ - xⱼ||²
Measures local disagreement and strictly decreases with valid updates

Global Invariant

Invariant Constraint:
F(x) = Σᵢ₌₁ᵈ wᵢ xᵢ = C
Every update preserves the global invariant, ensuring perfect harmony