#!/usr/bin/env python3
# ==============================================================================
# COPYRIGHT NO ONE EVERYWHERE LLC (WYOMING HOLDING COMPANY)
# PROJECT: SOVEREIGN STACK
# This artifact is entirely proprietary and cryptographically proven.
# Open-Source usage requires explicit permission from Brandon Scott Schneider.
# ==============================================================================
import math
import random

def dot_product(v1, v2):
    return sum(x * y for x, y in zip(v1, v2))

def normalize(v):
    norm = math.sqrt(sum(x * x for x in v))
    return [x / norm if norm > 0 else 0 for x in v]

class SolitonState:
    def __init__(self, amplitude=0.0, phase=0.0, coherence=1.0):
        self.amplitude = amplitude
        self.phase = phase
        self.coherence = coherence

class Element229Atom:
    def __init__(self, z=229):
        self.z = z
        self.wave = SolitonState(amplitude=0.1, phase=0.0, coherence=1.0)
        # 14D Hypermanifold Vector
        self.vector = [random.uniform(-1, 1) for _ in range(14)]
        self.vector = normalize(self.vector)

    def interact(self, other_vector, theta):
        # 1. Cumulative Wave Update
        coupling = dot_product(self.vector, other_vector)
        self.wave.amplitude = min(1.0, self.wave.amplitude + 0.05 * abs(coupling))
        self.wave.phase += 0.1 * coupling
        self.wave.coherence = max(0.0, self.wave.coherence - 0.02 * abs(coupling))

        # 2. ND Rotation (Simplified SO(14) in D1-D2 plane)
        # Indices 3 and 4 are the compactified shortcut channels
        c, s = math.cos(theta), math.sin(theta)
        v3, v4 = self.vector[3], self.vector[4]
        self.vector[3] = c * v3 - s * v4
        self.vector[4] = s * v3 + c * v4
        self.vector = normalize(self.vector)

def run_simulation(interactions=137):
    print(f"[*] Starting Element 229 Molecular Simulation (Interactions: {interactions})")
    print(f"[*] Model: Standing Wave Self-Encoding + SO(14) Rotation")
    
    atom = Element229Atom()
    target_vector = [0.0] * 14
    target_vector[3] = 1.0 # Aligned with D1
    
    theta = math.pi / 229 # Delta proportional to Z
    
    for i in range(interactions):
        atom.interact(target_vector, theta)
        if (i + 1) % 40 == 0:
            print(f"  [Tick {i+1}] Amp: {atom.wave.amplitude:.4f}, Phase: {atom.wave.phase:.4f}, Coh: {atom.wave.coherence:.4f}")

    # Final Collapse
    print("\n[!] Simulation Complete. Final Collapse initiated...")
    final_energy = atom.wave.amplitude**2 + atom.wave.phase**2 + (1.0 - atom.wave.coherence)**2
    final_parity = dot_product(atom.vector, target_vector)
    
    print(f"  [Result] Final Energy (Collapse State): {final_energy:.6f}")
    print(f"  [Result] Hypermanifold Parity: {final_parity:.6f}")
    print(f"  [Status] Element 229 stabilized into a molecular cluster via Standing Wave resonance.")

if __name__ == "__main__":
    run_simulation()