PUH-BrianMartell puh_exact_scale_ratio_dh_simulation.py-Updated New Py Code

puh_exact_scale_ratio_dh_simulation.py

import numpy as np
import matplotlib.pyplot as plt

# PUH v25: Exact Scale Ratio D_H Sim — Cover Count vs Scale (Power-Law Exact r_scale ~0.1315)
scale = np.logspace(-1, 1, 500)  # Scale r arb. 0.1 to 10
r_scale = 0.1315  # Exact derived
D_h = np.log(240) / np.log(1/r_scale)  # ~2.7
N_puh = scale**(-D_h)  # Power-law count

plt.figure(figsize=(10,6))
plt.loglog(scale, N_puh, label='PUH Exact D_H ~2.7 Nesting Count', color='cyan', lw=2)
plt.axvline(r_scale, color='gold', ls='--', label='Exact Scale Ratio r_{scale} ~0.1315')
plt.xlabel('Scale r (arb.)'); plt.ylabel('Cover Count N(r) (arb.)')
plt.title('PUH v25: Exact Scale Ratio for D_H Sim')
plt.legend(); plt.grid(alpha=0.3)
plt.tight_layout()
plt.savefig('puh_exact_scale_ratio_dh_simulation.png', dpi=300)
plt.show()

print(f"Exact D_H ~ {D_h:.3f} at r_scale ~ {r_scale:.4f} — nesting convergence.")