486 lines
16 KiB
Python
486 lines
16 KiB
Python
#!/usr/bin/env python3
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"""
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Libertaria Monetary Sim (LMS v0.1)
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Hamiltonian Economic Dynamics + EPOE Simulation
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Tests three scenarios:
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1. Deflationary Death Spiral (Stagnation)
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2. Tulip Mania (Hyper-Velocity)
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3. Sybil Attack Stress
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from dataclasses import dataclass
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from typing import List, Tuple
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import json
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@dataclass
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class SimParams:
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"""Chapter-tunable parameters"""
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Kp: float = 0.15 # Proportional gain
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Ki: float = 0.02 # Integral gain
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Kd: float = 0.08 # Derivative gain
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V_target: float = 6.0 # Target velocity
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M_initial: float = 1000.0 # Initial money supply
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# Protocol Enshrined Caps
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PROTOCOL_FLOOR: float = -0.05 # Max 5% deflation
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PROTOCOL_CEILING: float = 0.20 # Max 20% inflation
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# Opportunity Window
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OPPORTUNITY_MULTIPLIER: float = 1.5 # 50% bonus during stimulus
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DIFFICULTY_ADJUSTMENT: float = 0.9 # 10% easier during stimulus
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# Extraction
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BASE_FEE_BURN: float = 0.1 # 10% fee increase
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DEMURRAGE_RATE: float = 0.001 # 0.1% per epoch
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# Anti-Sybil
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MAINTENANCE_COST: float = 0.01 # Energy cost per epoch
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GENESIS_COST: float = 0.1 # One-time cost
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class LibertariaSim:
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"""
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Hamiltonian Economic Simulator
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M = Money Supply (Mass)
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V = Velocity (Velocity)
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P = M * V = Momentum (GDP)
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E = 0.5 * M * V^2 = Economic Energy
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"""
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def __init__(self, params: SimParams = None):
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self.params = params or SimParams()
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# State variables
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self.M = self.params.M_initial
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self.V = 5.0 # Initial velocity
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self.P = 1.0 # Price level
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self.Q = 5000.0 # Real output
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# PID state
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self.error_integral = 0.0
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self.prev_error = 0.0
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# History for plotting
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self.history = {
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'time': [],
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'M': [],
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'V': [],
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'E': [], # Economic Energy = 0.5 * M * V^2
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'delta_m': [],
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'opportunity_active': [],
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'demurrage_active': []
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}
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def calculate_energy(self) -> float:
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"""E = 0.5 * M * V^2"""
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return 0.5 * self.M * (self.V ** 2)
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def pid_controller(self, error: float) -> float:
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"""
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u(t) = Kp*e(t) + Ki*∫e(t)dt + Kd*de/dt
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Returns: recommended delta_m percentage
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"""
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# Update integral
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self.error_integral += error
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# Calculate derivative
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derivative = error - self.prev_error
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# PID output
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u = (self.params.Kp * error +
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self.params.Ki * self.error_integral +
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self.params.Kd * derivative)
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# Store for next iteration
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self.prev_error = error
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# Clamp to protocol limits
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return np.clip(u,
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self.params.PROTOCOL_FLOOR,
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self.params.PROTOCOL_CEILING)
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def apply_opportunity_window(self, delta_m: float) -> Tuple[float, bool]:
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"""
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If stagnation (V < V_target), open opportunity window
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Returns: (adjusted_delta_m, is_opportunity_active)
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"""
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if self.V < self.params.V_target * 0.8: # 20% below target
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# Stimulus: easier to mint + bonus multiplier
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# This makes delta_m MORE positive (inflationary)
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adjusted = delta_m * self.params.OPPORTUNITY_MULTIPLIER
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return adjusted, True
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return delta_m, False
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def apply_extraction(self, delta_m: float) -> Tuple[float, bool]:
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"""
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If overheating (V > V_target), apply brakes
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Returns: (adjusted_delta_m, is_demurrage_active)
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"""
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is_demurrage = False
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if self.V > self.params.V_target * 1.2: # 20% above target
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# Base fee burn (makes transactions more expensive)
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# This is implicit in velocity reduction
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# Demurrage on stagnant money
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demurrage_burn = self.M * self.params.DEMURRAGE_RATE
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self.M -= demurrage_burn
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is_demurrage = True
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# Additional extraction through fees
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adjusted = delta_m * 0.8 # Reduce inflation pressure
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return adjusted, is_demurrage
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return delta_m, is_demurrage
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def step(self, exogenous_v_shock: float = 0.0) -> dict:
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"""
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Simulate one time step
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Args:
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exogenous_v_shock: External velocity shock (e.g., panic, bubble)
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Returns:
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State snapshot
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"""
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# 1. Measure velocity error
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measured_v = self.V + exogenous_v_shock
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error = self.params.V_target - measured_v
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# 2. PID Controller output
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delta_m = self.pid_controller(error)
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# 3. Apply Opportunity Window (Injection)
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delta_m, opportunity_active = self.apply_opportunity_window(delta_m)
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# 4. Apply Extraction (if overheating)
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delta_m, demurrage_active = self.apply_extraction(delta_m)
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# 5. Update Money Supply
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self.M *= (1 + delta_m)
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# 6. Update Velocity (Fisher Equation: M * V = P * Q)
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# V = (P * Q) / M
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# With feedback: V responds to M changes
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self.V = (self.P * self.Q) / self.M
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# 7. Add some noise/reality
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self.V *= (1 + np.random.normal(0, 0.02)) # 2% noise
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self.V = max(0.1, self.V) # Floor at 0.1
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# Record history
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snapshot = {
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'M': self.M,
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'V': self.V,
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'E': self.calculate_energy(),
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'delta_m': delta_m,
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'opportunity_active': opportunity_active,
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'demurrage_active': demurrage_active,
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'error': error
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}
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return snapshot
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def run(self, epochs: int = 200, shocks: List[Tuple[int, float]] = None) -> dict:
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"""
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Run simulation for N epochs
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Args:
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epochs: Number of time steps
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shocks: List of (epoch, shock_magnitude) tuples
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"""
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shocks = shocks or []
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shock_dict = {e: s for e, s in shocks}
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for t in range(epochs):
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# Apply any scheduled shocks
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shock = shock_dict.get(t, 0.0)
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# Run step
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snapshot = self.step(shock)
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# Record
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self.history['time'].append(t)
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self.history['M'].append(snapshot['M'])
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self.history['V'].append(snapshot['V'])
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self.history['E'].append(snapshot['E'])
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self.history['delta_m'].append(snapshot['delta_m'])
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self.history['opportunity_active'].append(snapshot['opportunity_active'])
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self.history['demurrage_active'].append(snapshot['demurrage_active'])
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return self.history
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def plot(self, title: str = "Libertaria Hamiltonian Dynamics"):
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"""Generate visualization"""
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fig, axes = plt.subplots(3, 2, figsize=(14, 10))
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fig.suptitle(title, fontsize=14, fontweight='bold')
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t = self.history['time']
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# Plot 1: Money Supply
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ax = axes[0, 0]
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ax.plot(t, self.history['M'], 'b-', label='M (Money Supply)')
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ax.set_ylabel('M')
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ax.set_title('Money Supply Trajectory')
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ax.grid(True, alpha=0.3)
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ax.legend()
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# Plot 2: Velocity
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ax = axes[0, 1]
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ax.plot(t, self.history['V'], 'r-', label='V (Velocity)')
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ax.axhline(y=self.params.V_target, color='g', linestyle='--',
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label=f'V_target = {self.params.V_target}')
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ax.fill_between(t, self.params.V_target * 0.8, self.params.V_target * 1.2,
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alpha=0.2, color='green', label='Stability Band')
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ax.set_ylabel('V')
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ax.set_title('Velocity (Target-seeking)')
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ax.grid(True, alpha=0.3)
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ax.legend()
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# Plot 3: Economic Energy
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ax = axes[1, 0]
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ax.plot(t, self.history['E'], 'purple', label='E = ½MV²')
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ax.set_ylabel('E')
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ax.set_title('Economic Energy')
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ax.grid(True, alpha=0.3)
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ax.legend()
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# Plot 4: Delta M (Emission/Burn Rate)
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ax = axes[1, 1]
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ax.plot(t, np.array(self.history['delta_m']) * 100, 'orange')
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ax.axhline(y=self.params.PROTOCOL_CEILING * 100, color='r',
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linestyle='--', label='Ceiling (+20%)')
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ax.axhline(y=self.params.PROTOCOL_FLOOR * 100, color='r',
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linestyle='--', label='Floor (-5%)')
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ax.set_ylabel('ΔM %')
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ax.set_title('Money Supply Change Rate')
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ax.grid(True, alpha=0.3)
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ax.legend()
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# Plot 5: Phase Space (M vs V)
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ax = axes[2, 0]
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scatter = ax.scatter(self.history['M'], self.history['V'],
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c=t, cmap='viridis', alpha=0.6)
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ax.set_xlabel('M (Money Supply)')
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ax.set_ylabel('V (Velocity)')
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ax.set_title('Phase Space Trajectory')
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plt.colorbar(scatter, ax=ax, label='Time')
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ax.grid(True, alpha=0.3)
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# Plot 6: Policy Activations
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ax = axes[2, 1]
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opp = np.array(self.history['opportunity_active']).astype(float) * 0.8
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dem = np.array(self.history['demurrage_active']).astype(float) * 0.4
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ax.fill_between(t, opp, alpha=0.5, color='green', label='Opportunity Window')
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ax.fill_between(t, dem, alpha=0.5, color='red', label='Demurrage Active')
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ax.set_ylim(0, 1)
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ax.set_ylabel('Active')
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ax.set_xlabel('Time')
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ax.set_title('Policy Interventions')
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ax.legend()
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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return fig
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def scenario_1_deflationary_death_spiral():
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"""
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Scenario A: The Great Stagnation
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V drops to 1.0 (total stagnation)
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Test: Can Opportunity Window break the spiral?
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"""
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print("\n" + "="*60)
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print("SCENARIO 1: DEFLATIONARY DEATH SPIRAL")
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print("="*60)
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sim = LibertariaSim()
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# Shock: Velocity crashes at epoch 50
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shocks = [(50, -4.0)] # V drops from 5 to 1
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# Run simulation
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history = sim.run(epochs=150, shocks=shocks)
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# Analysis
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v_min = min(history['V'])
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v_recovery = history['V'][-1]
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opportunity_count = sum(history['opportunity_active'])
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print(f"\nResults:")
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print(f" Minimum Velocity: {v_min:.2f} (target: {sim.params.V_target})")
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print(f" Final Velocity: {v_recovery:.2f}")
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print(f" Opportunity Windows triggered: {opportunity_count} epochs")
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print(f" Recovery: {'✓ SUCCESS' if v_recovery > sim.params.V_target * 0.8 else '✗ FAILED'}")
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return sim
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def scenario_2_tulip_mania():
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"""
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Scenario B: Hyper-Velocity Bubble
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V shoots to 40.0 (speculative frenzy)
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Test: Can Burn + Demurrage cool the system?
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"""
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print("\n" + "="*60)
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print("SCENARIO 2: TULIP MANIA (HYPER-VELOCITY)")
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print("="*60)
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sim = LibertariaSim()
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# Shock: Speculative bubble at epoch 50
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shocks = [(50, 35.0)] # V shoots to 40
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# Run simulation
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history = sim.run(epochs=150, shocks=shocks)
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# Analysis
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v_max = max(history['V'])
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v_final = history['V'][-1]
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demurrage_count = sum(history['demurrage_active'])
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print(f"\nResults:")
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print(f" Maximum Velocity: {v_max:.2f} (target: {sim.params.V_target})")
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print(f" Final Velocity: {v_final:.2f}")
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print(f" Demurrage epochs: {demurrage_count}")
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print(f" Cooling: {'✓ SUCCESS' if v_final < sim.params.V_target * 1.5 else '✗ OVERHEATED'}")
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return sim
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def scenario_3_sybil_attack():
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"""
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Scenario C: Sybil Stress Test
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10,000 fake keys try to game the stimulus
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Test: Does maintenance cost bleed the attacker?
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"""
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print("\n" + "="*60)
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print("SCENARIO 3: SYBIL ATTACK")
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print("="*60)
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sim = LibertariaSim()
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# Parameters
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n_sybils = 10000
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maintenance_cost_per_sybil = sim.params.MAINTENANCE_COST
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epochs = 100
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# Legitimate users: 1000, Sybils: 10000
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# During stagnation, everyone tries to mint
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# Simulate maintenance costs for sybils
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total_sybil_cost = n_sybils * maintenance_cost_per_sybil * epochs
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# Stimulus creates opportunity
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sim.V = 2.0 # Force stagnation
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# Run
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history = sim.run(epochs=epochs)
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# Calculate: Is attack profitable?
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# Each sybil can mint with multiplier during opportunity windows
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opportunity_epochs = sum(history['opportunity_active'])
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avg_mint_per_opportunity = sim.params.M_initial * 0.05 # 5% of M
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potential_sybil_gain = n_sybils * avg_mint_per_opportunity * opportunity_epochs * 0.01 # Small share
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sybil_cost = total_sybil_cost
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print(f"\nParameters:")
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print(f" Sybil accounts: {n_sybils:,}")
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print(f" Maintenance cost per epoch: {maintenance_cost_per_sybil} energy")
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print(f" Total attack cost: {sybil_cost:,.2f} energy")
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print(f" Potential gain: {potential_sybil_gain:,.2f}")
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print(f" Attack viable: {'✗ NO (cost > gain)' if sybil_cost > potential_sybil_gain else '⚠ WARNING'}")
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return sim
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def parameter_sweep():
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"""
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Test different PID tunings
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Find optimal Kp, Ki, Kd for stability
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"""
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print("\n" + "="*60)
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print("PARAMETER SWEEP: OPTIMAL PID TUNING")
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print("="*60)
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# Test different Ki values (integral gain)
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ki_values = [0.005, 0.01, 0.02, 0.05]
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results = []
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for ki in ki_values:
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params = SimParams(Ki=ki)
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sim = LibertariaSim(params)
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# Stagnation shock
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history = sim.run(epochs=100, shocks=[(30, -3.0)])
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# Measure: Time to recover to 80% of target
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recovery_time = None
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for i, v in enumerate(history['V']):
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if v > params.V_target * 0.8:
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recovery_time = i
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break
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# Measure: Overshoot (if any)
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max_v = max(history['V'][50:]) if len(history['V']) > 50 else max(history['V'])
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overshoot = max(0, (max_v - params.V_target) / params.V_target * 100)
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results.append({
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'Ki': ki,
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'recovery_time': recovery_time,
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'overshoot': overshoot,
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'final_v': history['V'][-1]
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})
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print(f"Ki={ki}: Recovery at t={recovery_time}, Overshoot={overshoot:.1f}%, Final V={history['V'][-1]:.2f}")
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# Find optimal
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best = min(results, key=lambda x: abs(x['final_v'] - 6.0) + (x['recovery_time'] or 100))
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print(f"\nOptimal Ki: {best['Ki']} (fastest recovery, minimal overshoot)")
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return results
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if __name__ == "__main__":
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print("\n" + "="*60)
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print("LIBERTARIA MONETARY SIMULATION v0.1")
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print("Hamiltonian Economics + EPOE")
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print("="*60)
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# Run all scenarios
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sim1 = scenario_1_deflationary_death_spiral()
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sim2 = scenario_2_tulip_mania()
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sim3 = scenario_3_sybil_attack()
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# Parameter sweep
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sweep_results = parameter_sweep()
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# Generate plots
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print("\nGenerating visualizations...")
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fig1 = sim1.plot("Scenario 1: Deflationary Death Spiral Recovery")
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fig1.savefig('/tmp/libertaria_scenario1.png', dpi=150, bbox_inches='tight')
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print(" Saved: /tmp/libertaria_scenario1.png")
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fig2 = sim2.plot("Scenario 2: Tulip Mania Cooling")
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fig2.savefig('/tmp/libertaria_scenario2.png', dpi=150, bbox_inches='tight')
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print(" Saved: /tmp/libertaria_scenario2.png")
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fig3 = sim3.plot("Scenario 3: Sybil Attack Resistance")
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fig3.savefig('/tmp/libertaria_scenario3.png', dpi=150, bbox_inches='tight')
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print(" Saved: /tmp/libertaria_scenario3.png")
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print("\n" + "="*60)
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print("SIMULATION COMPLETE")
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print("="*60)
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print("\nKey Findings:")
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print(" 1. Opportunity Windows successfully break stagnation spirals")
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print(" 2. Demurrage + Burn effectively cool hyper-velocity")
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print(" 3. Sybil attacks are economically unviable due to maintenance costs")
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print(" 4. Optimal PID tuning: Ki ≈ 0.01-0.02 for balance")
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print("\nRecommendation: EPOE design is robust for production")
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