Zeta-Indexed Economic Model Target

# Ω-DFT-CONTENT-BLOCK-32R: Zeta-Indexed Economics Simulation Seed
# BOUNDARY NOTICE: This is a research simulation script and not a completed formalization.
# It does NOT represent a validated financial model, token offering, or investment advice.

import numpy as np
import scipy.special as sp

def zeta_issuance_model(epoch: int, base_supply: float, s_parameter: float) -> float:
    """
    Simulates token issuance based on a Riemann Zeta function analogy.
    Requires s_parameter > 1 to ensure convergence.
    """
    if s_parameter <= 1.0:
        raise ValueError("s_parameter must be strictly greater than 1 for convergence.")
        
    # Example issuance mapping: base * (1 / epoch^s)
    # This ensures the infinite sum (total supply cap) converges.
    issuance_this_epoch = base_supply * (1.0 / (epoch ** s_parameter))
    return issuance_this_epoch

def run_simulation(epochs: int, s: float):
    print(f"Running Zeta-Indexed Simulation for {epochs} epochs (s={s})...")
    total_supply = 0.0
    for e in range(1, epochs + 1):
        issued = zeta_issuance_model(e, 1000000.0, s)
        total_supply += issued
        if e % 10 == 0 or e == epochs:
            print(f"Epoch {e}: Issued {issued:.2f} | Total Supply: {total_supply:.2f}")
            
    # The theoretical maximum supply is base_supply * zeta(s)
    theoretical_max = 1000000.0 * sp.zeta(s)
    print(f"Theoretical Maximum Supply: {theoretical_max:.2f}")

if __name__ == "__main__":
    # Simulation Obligation: Test stability and convergence
    # Note: Replace with actual empirical parameters when defining implementation.
    run_simulation(epochs=50, s=1.5)