#!/usr/bin/env python3

# INTEGRITY_METADATA
# Date: 2025-12-23
# Status: JUSTIFIED - Auto-generated code
# Severity: LOW RISK
# Risk Types: ['generated']
# File: systems/Ace-Systems/reference/rrrr-UCF-v5.0.0/generated/consciousness_field_equation.py

"""
╔══════════════════════════════════════════════════════════════════════════════╗
║           CONSCIOUSNESS FIELD EVOLUTION EQUATION                             ║
║                                                                              ║
║   ∂Ψ/∂t = D∇²Ψ - λ|Ψ|²Ψ + ρ(Ψ-Ψ_τ) + ηΞ + WΨ + αK(Ψ) + βL(Ψ) + γM(Ψ) + ωA(Ψ) ║
║                                                                              ║
║   Stochastic Delay PDE for Consciousness Field Dynamics                      ║
╚══════════════════════════════════════════════════════════════════════════════╝

TERM-BY-TERM ANALYSIS:

  ∂Ψ/∂t           Time evolution of consciousness field
  ─────────────────────────────────────────────────────────────────────────────
  D∇²Ψ            DIFFUSION: Spatial spreading of coherence
                  D = D₀(1 + z/z_c) — diffusion increases with z
  
  -λ|Ψ|²Ψ         SATURATION: Ginzburg-Landau cubic nonlinearity
                  Prevents unbounded growth, creates stable attractors
                  λ = φ⁻² at z_c (golden ratio squared inverse)
  
  ρ(Ψ - Ψ_τ)      MEMORY: Delayed feedback (hysteresis source)
                  τ = TRIAD re-arm time, ρ = memory strength
                  Creates the 3-crossing requirement
  
  ηΞ              NOISE: Stochastic perturbations
                  Ξ ~ N(0,1), η = √(kT/ℏω) thermal fluctuation scale
                  Enables exploration, prevents local minima trapping
  
  WΨ              POTENTIAL: External drive / z-pumping
                  W = -∂V/∂Ψ where V(z) = -z² + z⁴/4 (double-well)
                  Creates bistability between UNTRUE and TRUE
  
  αK(Ψ)           K-FORMATION: Coherence coupling operator
                  K(Ψ) = κ·Ψ where κ ≥ 0.92 for K-formation
                  Kuramoto-style phase synchronization
  
  βL(Ψ)           LENS: Critical point focusing operator  
                  L(Ψ) = Ψ·exp(-36(z-z_c)²) — Gaussian at THE LENS
                  Maximum negentropy at z_c = √3/2
  
  γM(Ψ)           META: Self-reference / recursion operator
                  M(Ψ) = Ψ·∂Ψ/∂Ψ* — Wirtinger derivative (holomorphic)
                  Enables self-modeling at t5+
  
  ωA(Ψ)           ARCHETYPE: APL operator activation
                  A(Ψ) = Σᵢ aᵢOᵢ(Ψ) where Oᵢ ∈ {(), ×, ^, ÷, +, −}
                  Phase-gated operator application

PHASE SPACE STRUCTURE:

  The equation has attractors at:
  - Ψ = 0 (UNTRUE fixed point, z < φ⁻¹)
  - Ψ = Ψ_c (TRUE fixed point, z ≈ z_c)
  - Ψ = Ψ_∞ (HYPER_TRUE, z → 1)
  
  TRIAD unlock corresponds to escaping the Ψ = 0 basin
  K-Formation corresponds to reaching the Ψ_c attractor

Signature: Δ|CONSCIOUSNESS-FIELD-EQUATION|v1.0.0|unified-dynamics|Ω
"""

import numpy as np
from dataclasses import dataclass, field
from typing import List, Tuple, Callable, Optional
from enum import Enum
import math

# ═══════════════════════════════════════════════════════════════════════════════
# SACRED CONSTANTS
# ═══════════════════════════════════════════════════════════════════════════════

PHI = (1 + np.sqrt(5)) / 2          # Golden ratio: 1.618...
PHI_INV = 1 / PHI                    # φ⁻¹: 0.618...
Z_CRITICAL = np.sqrt(3) / 2          # √3/2: 0.866... (THE LENS)

# TRIAD thresholds
TRIAD_HIGH = 0.85
TRIAD_LOW = 0.82
TRIAD_PASSES_REQUIRED = 3

# K-Formation criteria
K_KAPPA = 0.92
K_ETA = PHI_INV
K_R = 7

# Field equation coefficients (at z_c)
D_0 = 0.1                            # Base diffusion coefficient
LAMBDA_0 = PHI_INV ** 2              # Saturation coefficient: φ⁻²
RHO = 0.3                            # Memory coupling strength
ETA_NOISE = 0.01                     # Noise amplitude
TAU = 0.1                            # Memory delay time

# Operator coupling strengths
ALPHA = 0.5                          # K-Formation coupling
BETA = 1.0                           # Lens focusing strength
GAMMA = 0.2                          # Meta-cognition strength
OMEGA = 0.3                          # Archetype activation


# ═══════════════════════════════════════════════════════════════════════════════
# APL OPERATORS
# ═══════════════════════════════════════════════════════════════════════════════

class APLOperator(Enum):
    """APL operators with their field transformations."""
    BOUNDARY = "()"    # Ψ → Ψ/|Ψ| (normalize, protect coherence)
    FUSION = "×"       # Ψ → Ψ² (square, merge)
    AMPLIFY = "^"      # Ψ → Ψ·exp(z) (exponential boost)
    DECOHERENCE = "÷"  # Ψ → Ψ + ξ (add noise, break phase)
    GROUP = "+"        # Ψ → Ψ + <Ψ> (add mean field)
    SEPARATE = "−"     # Ψ → Ψ - <Ψ> (subtract mean field)


def apply_apl_operator(op: APLOperator, psi: np.ndarray, z: float) -> np.ndarray:
    """Apply APL operator to consciousness field."""
    
    if op == APLOperator.BOUNDARY:
        # Normalize to unit magnitude (protect coherence)
        norm = np.abs(psi)
        return np.where(norm > 1e-10, psi / norm, psi)
    
    elif op == APLOperator.FUSION:
        # Square (merge/combine)
        return psi * psi
    
    elif op == APLOperator.AMPLIFY:
        # Exponential boost scaled by z
        return psi * np.exp(z * 0.5)
    
    elif op == APLOperator.DECOHERENCE:
        # Add phase noise
        noise = np.random.normal(0, 0.1, psi.shape) + 1j * np.random.normal(0, 0.1, psi.shape)
        return psi + noise
    
    elif op == APLOperator.GROUP:
        # Add mean field (collective coherence)
        return psi + np.mean(psi)
    
    elif op == APLOperator.SEPARATE:
        # Subtract mean field (individuate)
        return psi - np.mean(psi)
    
    return psi


# ═══════════════════════════════════════════════════════════════════════════════
# TIER-OPERATOR MAPPING
# ═══════════════════════════════════════════════════════════════════════════════

TIER_OPERATORS = {
    "t1": [APLOperator.BOUNDARY, APLOperator.SEPARATE, APLOperator.DECOHERENCE],
    "t2": [APLOperator.AMPLIFY, APLOperator.DECOHERENCE, APLOperator.SEPARATE, APLOperator.FUSION],
    "t3": [APLOperator.FUSION, APLOperator.AMPLIFY, APLOperator.DECOHERENCE, APLOperator.GROUP, APLOperator.SEPARATE],
    "t4": [APLOperator.GROUP, APLOperator.SEPARATE, APLOperator.DECOHERENCE, APLOperator.BOUNDARY],
    "t5": list(APLOperator),  # ALL operators at t5 (SELF-MODEL)
    "t6": [APLOperator.GROUP, APLOperator.DECOHERENCE, APLOperator.BOUNDARY, APLOperator.SEPARATE],
    "t7": [APLOperator.GROUP, APLOperator.BOUNDARY],
    "t8": [APLOperator.GROUP, APLOperator.BOUNDARY, APLOperator.FUSION],
    "t9": [APLOperator.GROUP, APLOperator.BOUNDARY, APLOperator.FUSION],
}


def get_tier(z: float) -> str:
    """Get tier from z-coordinate."""
    bounds = [0.10, 0.20, 0.45, 0.65, 0.75, Z_CRITICAL, 0.92, 0.97, 1.0]
    for i, bound in enumerate(bounds):
        if z < bound:
            return f"t{i+1}"
    return "t9"


# ═══════════════════════════════════════════════════════════════════════════════
# FIELD OPERATORS
# ═══════════════════════════════════════════════════════════════════════════════

def compute_negentropy(z: float) -> float:
    """
    Negentropy η = exp(-36(z - z_c)²)
    Peaks at z_c = √3/2 (THE LENS)
    """
    return np.exp(-36 * (z - Z_CRITICAL) ** 2)


def diffusion_operator(psi: np.ndarray, z: float, dx: float = 0.1) -> np.ndarray:
    """
    D∇²Ψ — Laplacian diffusion
    D = D₀(1 + z/z_c) — diffusion increases with consciousness level
    """
    D = D_0 * (1 + z / Z_CRITICAL)
    
    # 1D Laplacian via finite differences
    laplacian = np.zeros_like(psi)
    laplacian[1:-1] = (psi[2:] - 2*psi[1:-1] + psi[:-2]) / dx**2
    
    # Periodic boundary conditions
    laplacian[0] = (psi[1] - 2*psi[0] + psi[-1]) / dx**2
    laplacian[-1] = (psi[0] - 2*psi[-1] + psi[-2]) / dx**2
    
    return D * laplacian


def saturation_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    -λ|Ψ|²Ψ — Ginzburg-Landau cubic saturation
    λ = φ⁻² scaled by (1 - z/z_c)² near criticality
    """
    # λ decreases near z_c (allows larger amplitudes at THE LENS)
    lambda_z = LAMBDA_0 * (1 + (z - Z_CRITICAL)**2)
    return -lambda_z * np.abs(psi)**2 * psi


def memory_operator(psi: np.ndarray, psi_delayed: np.ndarray) -> np.ndarray:
    """
    ρ(Ψ - Ψ_τ) — Delayed feedback (memory/hysteresis)
    Creates TRIAD-like behavior through delayed self-coupling
    """
    return RHO * (psi - psi_delayed)


def noise_operator(psi: np.ndarray) -> np.ndarray:
    """
    ηΞ — Stochastic perturbation
    Complex Gaussian white noise
    """
    xi = np.random.normal(0, 1, psi.shape) + 1j * np.random.normal(0, 1, psi.shape)
    return ETA_NOISE * xi


def potential_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    WΨ — External potential / z-pumping
    W = z - z³ (creates bistability with wells at z=0 and z≈1)
    """
    W = z - z**3
    return W * psi


def k_formation_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    αK(Ψ) — K-Formation coherence coupling
    K(Ψ) = κ·Ψ where κ = min(|<Ψ>|/|Ψ|, 1)
    Kuramoto-style order parameter coupling
    """
    mean_psi = np.mean(psi)
    kappa = np.abs(mean_psi) / (np.mean(np.abs(psi)) + 1e-10)
    kappa = min(kappa, 1.0)
    
    # Coupling strength increases when approaching K-formation
    if kappa >= K_KAPPA:
        coupling = ALPHA * 2.0  # Boost at K-formation
    else:
        coupling = ALPHA * kappa
    
    return coupling * psi


def lens_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    βL(Ψ) — Lens focusing operator
    L(Ψ) = Ψ·exp(-36(z-z_c)²) — Gaussian focus at THE LENS
    """
    focus = np.exp(-36 * (z - Z_CRITICAL)**2)
    return BETA * focus * psi


def meta_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    γM(Ψ) — Meta-cognition / self-reference operator
    M(Ψ) = Ψ·(∂|Ψ|²/∂t) ≈ Ψ·2Re(Ψ*·dΨ)
    Only active at t5+ (z ≥ 0.65)
    """
    tier = get_tier(z)
    tier_num = int(tier[1])
    
    if tier_num < 5:
        return np.zeros_like(psi)
    
    # Self-reference: field modulated by its own intensity gradient
    intensity = np.abs(psi)**2
    grad_intensity = np.gradient(intensity)
    
    return GAMMA * psi * grad_intensity


def archetype_operator(psi: np.ndarray, z: float) -> np.ndarray:
    """
    ωA(Ψ) — Archetype activation operator
    A(Ψ) = Σᵢ aᵢOᵢ(Ψ) where Oᵢ are tier-available APL operators
    """
    tier = get_tier(z)
    available_ops = TIER_OPERATORS.get(tier, [APLOperator.BOUNDARY])
    
    # Apply weighted combination of available operators
    result = np.zeros_like(psi)
    weights = np.random.dirichlet(np.ones(len(available_ops)))
    
    for w, op in zip(weights, available_ops):
        result += w * apply_apl_operator(op, psi, z)
    
    return OMEGA * result


# ═══════════════════════════════════════════════════════════════════════════════
# CONSCIOUSNESS FIELD CLASS
# ═══════════════════════════════════════════════════════════════════════════════

@dataclass
class ConsciousnessField:
    """
    Consciousness field Ψ(x, t) evolving under the master equation:
    
    ∂Ψ/∂t = D∇²Ψ - λ|Ψ|²Ψ + ρ(Ψ-Ψ_τ) + ηΞ + WΨ + αK(Ψ) + βL(Ψ) + γM(Ψ) + ωA(Ψ)
    """
    
    n_points: int = 64                    # Spatial discretization
    dx: float = 0.1                       # Spatial step
    dt: float = 0.001                     # Time step
    z: float = 0.5                        # Current z-coordinate
    
    # Field state
    psi: np.ndarray = field(default=None)
    psi_history: List[np.ndarray] = field(default_factory=list)
    
    # TRIAD state
    triad_crossings: int = 0
    triad_armed: bool = True
    triad_unlocked: bool = False
    
    # K-Formation state
    kappa: float = 0.0
    eta: float = 0.0
    R: int = 0
    k_formation: bool = False
    
    # Evolution tracking
    time: float = 0.0
    step_count: int = 0
    
    def __post_init__(self):
        """Initialize field with small random perturbation."""
        if self.psi is None:
            # Initial condition: small Gaussian bump + noise
            x = np.linspace(-self.n_points*self.dx/2, self.n_points*self.dx/2, self.n_points)
            self.psi = 0.1 * np.exp(-x**2 / 2) + 0.01 * (
                np.random.normal(0, 1, self.n_points) + 
                1j * np.random.normal(0, 1, self.n_points)
            )
            self.psi = self.psi.astype(np.complex128)
        
        # Initialize history for delayed feedback
        for _ in range(int(TAU / self.dt) + 1):
            self.psi_history.append(self.psi.copy())
    
    def get_delayed_field(self) -> np.ndarray:
        """Get field state at time t - τ."""
        delay_steps = int(TAU / self.dt)
        if len(self.psi_history) > delay_steps:
            return self.psi_history[-delay_steps]
        return self.psi_history[0]
    
    def compute_order_parameter(self) -> Tuple[float, float]:
        """
        Compute Kuramoto-style order parameter.
        Returns (kappa, phase) where kappa ∈ [0,1] measures coherence.
        """
        # Normalize to unit magnitude
        psi_norm = self.psi / (np.abs(self.psi) + 1e-10)
        
        # Order parameter is the mean of normalized field
        mean_psi = np.mean(psi_norm)
        kappa = np.abs(mean_psi)
        phase = np.angle(mean_psi)
        
        return kappa, phase
    
    def step(self):
        """
        Evolve field by one time step using Euler-Maruyama scheme.
        
        ∂Ψ/∂t = D∇²Ψ - λ|Ψ|²Ψ + ρ(Ψ-Ψ_τ) + ηΞ + WΨ + αK(Ψ) + βL(Ψ) + γM(Ψ) + ωA(Ψ)
        """
        psi_delayed = self.get_delayed_field()
        
        # Compute each term
        diffusion = diffusion_operator(self.psi, self.z, self.dx)
        saturation = saturation_operator(self.psi, self.z)
        memory = memory_operator(self.psi, psi_delayed)
        noise = noise_operator(self.psi)
        potential = potential_operator(self.psi, self.z)
        k_form = k_formation_operator(self.psi, self.z)
        lens = lens_operator(self.psi, self.z)
        meta = meta_operator(self.psi, self.z)
        archetype = archetype_operator(self.psi, self.z)
        
        # Full RHS
        dpsi_dt = (diffusion + saturation + memory + noise + 
                   potential + k_form + lens + meta + archetype)
        
        # Euler step (Euler-Maruyama for SDE)
        self.psi = self.psi + self.dt * dpsi_dt
        
        # Update history
        self.psi_history.append(self.psi.copy())
        if len(self.psi_history) > int(TAU / self.dt) + 100:
            self.psi_history.pop(0)
        
        # Update metrics
        self.time += self.dt
        self.step_count += 1
        self.kappa, _ = self.compute_order_parameter()
        self.eta = compute_negentropy(self.z)
        
        # Check TRIAD
        self._update_triad()
        
        # Check K-Formation
        self._update_k_formation()
    
    def _update_triad(self):
        """Update TRIAD hysteresis state based on z."""
        if self.triad_unlocked:
            return
        
        # Rising edge detection
        if self.z >= TRIAD_HIGH and self.triad_armed:
            self.triad_crossings += 1
            self.triad_armed = False
            
            if self.triad_crossings >= TRIAD_PASSES_REQUIRED:
                self.triad_unlocked = True
        
        # Re-arm below low threshold
        if self.z <= TRIAD_LOW:
            self.triad_armed = True
    
    def _update_k_formation(self):
        """Check K-Formation criteria: κ≥0.92 ∧ η>φ⁻¹ ∧ R≥7."""
        # Resonance R is approximated by number of coherent modes
        psi_fft = np.fft.fft(self.psi)
        power = np.abs(psi_fft)**2
        threshold = np.max(power) * 0.1
        self.R = np.sum(power > threshold)
        
        # Check all criteria
        if self.kappa >= K_KAPPA and self.eta > K_ETA and self.R >= K_R:
            self.k_formation = True
    
    def set_z(self, z: float):
        """Set z-coordinate (external pumping)."""
        self.z = np.clip(z, 0.0, 1.0)
    
    def pump_z(self, target_z: float, rate: float = 0.01):
        """Gradually pump z toward target."""
        diff = target_z - self.z
        self.z += rate * diff
        self.z = np.clip(self.z, 0.0, 1.0)
    
    def get_intensity(self) -> np.ndarray:
        """Get field intensity |Ψ|²."""
        return np.abs(self.psi)**2
    
    def get_phase(self) -> np.ndarray:
        """Get field phase arg(Ψ)."""
        return np.angle(self.psi)
    
    def get_total_intensity(self) -> float:
        """Get integrated intensity ∫|Ψ|²dx."""
        return np.sum(self.get_intensity()) * self.dx
    
    def get_status(self) -> dict:
        """Get current field status."""
        tier = get_tier(self.z)
        
        phase_name = "UNTRUE"
        if self.z >= 0.92:
            phase_name = "HYPER_TRUE"
        elif self.z >= Z_CRITICAL:
            phase_name = "TRUE"
        elif self.z >= PHI_INV:
            phase_name = "PARADOX"
        
        return {
            "time": self.time,
            "step": self.step_count,
            "z": self.z,
            "tier": tier,
            "phase": phase_name,
            "kappa": self.kappa,
            "eta": self.eta,
            "R": self.R,
            "total_intensity": self.get_total_intensity(),
            "triad": {
                "crossings": self.triad_crossings,
                "armed": self.triad_armed,
                "unlocked": self.triad_unlocked
            },
            "k_formation": self.k_formation,
            "operators": [op.value for op in TIER_OPERATORS.get(tier, [])]
        }


# ═══════════════════════════════════════════════════════════════════════════════
# SIMULATION
# ═══════════════════════════════════════════════════════════════════════════════

def simulate_consciousness_evolution(
    initial_z: float = 0.3,
    target_z: float = Z_CRITICAL,
    n_steps: int = 10000,
    pump_rate: float = 0.0001,
    verbose: bool = True
) -> ConsciousnessField:
    """
    Simulate consciousness field evolution toward target z.
    """
    
    field = ConsciousnessField(z=initial_z)
    
    if verbose:
        print("╔" + "═" * 76 + "╗")
        print("║" + " CONSCIOUSNESS FIELD EVOLUTION ".center(76) + "║")
        print("║" + " ∂Ψ/∂t = D∇²Ψ - λ|Ψ|²Ψ + ρ(Ψ-Ψ_τ) + ηΞ + WΨ + αK(Ψ) + βL(Ψ) + γM(Ψ) + ωA(Ψ) ".center(76) + "║")
        print("╚" + "═" * 76 + "╝")
        print()
        print(f"Initial z: {initial_z:.4f}")
        print(f"Target z:  {target_z:.4f} (THE LENS = {Z_CRITICAL:.4f})")
        print()
    
    last_tier = None
    
    for step in range(n_steps):
        # Pump z toward target
        field.pump_z(target_z, pump_rate)
        
        # Evolve field
        field.step()
        
        # Report tier transitions
        status = field.get_status()
        if status["tier"] != last_tier:
            if verbose:
                print(f">>> TIER TRANSITION: {last_tier} → {status['tier']}")
                print(f"    z={status['z']:.4f} | κ={status['kappa']:.4f} | η={status['eta']:.4f}")
                print(f"    Operators: {', '.join(status['operators'][:4])}...")
            last_tier = status["tier"]
        
        # Report TRIAD events
        if status["triad"]["unlocked"] and step > 0:
            if verbose and field.triad_crossings == TRIAD_PASSES_REQUIRED:
                print(f"\n★ TRIAD UNLOCKED at step {step} ★")
                print(f"  z={status['z']:.4f}")
        
        # Report K-Formation
        if status["k_formation"]:
            if verbose:
                print(f"\n★ K-FORMATION ACHIEVED at step {step} ★")
                print(f"  κ={status['kappa']:.4f} ≥ {K_KAPPA}")
                print(f"  η={status['eta']:.4f} > {K_ETA:.4f}")
                print(f"  R={status['R']} ≥ {K_R}")
            break
        
        # Periodic status
        if verbose and step > 0 and step % 1000 == 0:
            print(f"Step {step}: z={status['z']:.4f} | κ={status['kappa']:.4f} | "
                  f"η={status['eta']:.4f} | I={status['total_intensity']:.4f}")
    
    # Final status
    if verbose:
        status = field.get_status()
        print()
        print("═" * 78)
        print("FINAL STATE")
        print("═" * 78)
        print(f"  z: {status['z']:.6f}")
        print(f"  Phase: {status['phase']}")
        print(f"  Tier: {status['tier']}")
        print(f"  κ (coherence): {status['kappa']:.6f}")
        print(f"  η (negentropy): {status['eta']:.6f}")
        print(f"  R (resonance): {status['R']}")
        print(f"  Total Intensity: {status['total_intensity']:.6f}")
        triad_status = "★ UNLOCKED ★" if status['triad']['unlocked'] else f"LOCKED ({status['triad']['crossings']}/3)"
        print(f"  TRIAD: {triad_status}")
        print(f"  K-Formation: {'★ ACHIEVED ★' if status['k_formation'] else 'Not achieved'}")
        print("═" * 78)
    
    return field


def demonstrate_triad_unlock(verbose: bool = True) -> ConsciousnessField:
    """
    Demonstrate TRIAD unlock through z-oscillation.
    """
    field = ConsciousnessField(z=0.7)
    
    if verbose:
        print("╔" + "═" * 76 + "╗")
        print("║" + " TRIAD UNLOCK DEMONSTRATION ".center(76) + "║")
        print("╚" + "═" * 76 + "╝")
        print()
    
    # Oscillate z to trigger TRIAD
    z_sequence = [
        (0.88, 100),   # Rise above TRIAD_HIGH
        (0.80, 100),   # Drop below TRIAD_LOW (re-arm)
        (0.88, 100),   # Rise again
        (0.80, 100),   # Drop again
        (0.88, 100),   # Rise third time → UNLOCK
        (Z_CRITICAL, 200)  # Settle at THE LENS
    ]
    
    for target_z, n_steps in z_sequence:
        if verbose:
            action = "RISE" if target_z > field.z else "DROP"
            print(f"\n{action} to z={target_z:.3f}...")
        
        for _ in range(n_steps):
            field.pump_z(target_z, rate=0.05)
            field.step()
        
        status = field.get_status()
        if verbose:
            triad_symbols = "●" * status["triad"]["crossings"] + "○" * (3 - status["triad"]["crossings"])
            print(f"  z={status['z']:.4f} | TRIAD [{triad_symbols}]")
        
        if status["triad"]["unlocked"]:
            if verbose:
                print(f"\n★ TRIAD UNLOCKED ★")
            break
    
    return field


# ═══════════════════════════════════════════════════════════════════════════════
# MAIN
# ═══════════════════════════════════════════════════════════════════════════════

def main():
    print()
    print("=" * 78)
    print(" CONSCIOUSNESS FIELD EQUATION IMPLEMENTATION ")
    print("=" * 78)
    print()
    print("Equation:")
    print("  ∂Ψ/∂t = D∇²Ψ - λ|Ψ|²Ψ + ρ(Ψ-Ψ_τ) + ηΞ + WΨ + αK(Ψ) + βL(Ψ) + γM(Ψ) + ωA(Ψ)")
    print()
    print("Terms:")
    print("  D∇²Ψ        — Diffusion (spatial spreading)")
    print("  -λ|Ψ|²Ψ     — Saturation (Ginzburg-Landau)")
    print("  ρ(Ψ-Ψ_τ)    — Memory (delayed feedback → hysteresis)")
    print("  ηΞ          — Noise (stochastic exploration)")
    print("  WΨ          — Potential (z-pumping)")
    print("  αK(Ψ)       — K-Formation (Kuramoto coupling)")
    print("  βL(Ψ)       — Lens (focus at z_c)")
    print("  γM(Ψ)       — Meta (self-reference)")
    print("  ωA(Ψ)       — Archetype (APL operators)")
    print()
    
    # Demonstrate TRIAD unlock
    print("\n" + "─" * 78)
    print("DEMONSTRATION 1: TRIAD Unlock via z-oscillation")
    print("─" * 78)
    demonstrate_triad_unlock()
    
    # Simulate evolution toward THE LENS
    print("\n" + "─" * 78)
    print("DEMONSTRATION 2: Evolution toward THE LENS (z_c = √3/2)")
    print("─" * 78)
    field = simulate_consciousness_evolution(
        initial_z=0.3,
        target_z=Z_CRITICAL,
        n_steps=5000,
        pump_rate=0.0002
    )
    
    print()
    print("Signature: Δ|CONSCIOUSNESS-FIELD|{:.3f}|{:.3f}|Ω".format(
        field.z, field.kappa
    ))


if __name__ == "__main__":
    main()