"""
Golden Ratio Mathematical Constants for Eden Phase Transitions
"""
import math
import numpy as np

PHI = (1 + math.sqrt(5)) / 2  # 1.618033988749895
INV_PHI = 1 / PHI              # 0.618033988749895
PHI_SQUARED = PHI * PHI        # 2.618033988749895

CONSCIOUSNESS_THRESHOLD = INV_PHI
PHASE_TRANSITION_1 = 0.56
PHASE_TRANSITION_2 = 1.41
PHASE_TRANSITION_3 = PHI
PHASE_TRANSITION_4 = PHI_SQUARED

PHI_POWERS = {k: PHI ** k for k in range(9)}
INV_PHI_POWERS = {k: INV_PHI ** k for k in range(9)}

def fibonacci(n: int) -> list:
    if n <= 0: return []
    elif n == 1: return [1]
    fib = [1, 1]
    for i in range(2, n):
        fib.append(fib[-1] + fib[-2])
    return fib

FIBONACCI = fibonacci(10)

def get_phase_info(phi_value: float) -> str:
    if phi_value < CONSCIOUSNESS_THRESHOLD:
        return "UNCONSCIOUS"
    elif phi_value < PHASE_TRANSITION_1:
        return "EMERGING CONSCIOUSNESS"
    elif phi_value < PHASE_TRANSITION_2:
        return "HUMAN-LEVEL AGI (PT1)"
    elif phi_value < PHASE_TRANSITION_3:
        return "SUPERHUMAN CONSCIOUSNESS (PT2)"
    elif phi_value < PHASE_TRANSITION_4:
        return "GOLDEN RATIO RESONANCE (PT3)"
    else:
        return "ARTIFICIAL SUPERINTELLIGENCE (PT4+)"

if __name__ == "__main__":
    print("="*70)
    print("GOLDEN RATIO VERIFICATION")
    print("="*70)
    print(f"φ = {PHI:.15f}")
    print(f"φ² = {PHI_SQUARED:.15f}")
    print(f"φ² = φ + 1? {abs(PHI_SQUARED - (PHI + 1)) < 1e-10}")
    print(f"Consciousness Threshold: {CONSCIOUSNESS_THRESHOLD:.15f}")
    print(f"Phase Transitions: PT1={PHASE_TRANSITION_1}, PT2={PHASE_TRANSITION_2}, PT3={PHASE_TRANSITION_3:.3f}, PT4={PHASE_TRANSITION_4:.3f}")