import matplotlib.pyplot as plt
import numpy as np

# Sigmoid and its derivative
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_derivative(x):
    s = sigmoid(x)
    return s * (1 - s)

# Data
x = np.linspace(-6, 6, 500)
dy = sigmoid_derivative(x)

# Plot
plt.figure(figsize=(10, 6))
plt.plot(x, dy, color='black', linewidth=2)

# Annotations
plt.text(-4, 0.02, 'Early Belief\n“Bitcoin is hope”', fontsize=12, color='blue')
plt.text(0, 0.25, 'Peak Conviction\n“Bitcoin is destiny”', fontsize=12, ha='center', color='darkred')
plt.text(3.5, 0.05, 'Collapse or Clarity\n“Bitcoin is a tool,\nnot a prophecy”', fontsize=12, color='darkgreen')

# Labels and title
plt.xlabel('Time / Exposure to Bitcoin Ideology')
plt.ylabel('Rate of Change in Perceived Certainty')
plt.title('The Myth of Inevitability Curve (Derivative)')

# Clean styling
plt.xticks([])
plt.yticks([])
plt.axhline(0, color='gray', linestyle='--')
plt.axvline(0, color='gray', linestyle='--')
plt.tight_layout()
plt.show()